Introduction to Chemical and Biological Engineering (CBE 101) Department of Chemical and Biological Engineering

Colorado State University

Course Packet

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Table of Contents

Group Laboratory Activities ............................................................................................................ - 4 -

Laboratory Experiment: Blood oxygenator and lung material balances .............................................. - 5 -

Laboratory Experiment: Blood oxygenator and membrane transport ................................................. - 7 -

Calorimetry ......................................................................................................................................... - 10 -

Laboratory Experiment: Heat Conduction .......................................................................................... - 14 -

Lab Experiment: Rotameter Calibration and Solar Heaters ................................................................ - 18 -

Laboratory Experiment: Siphons ........................................................................................................ - 23 -

Resources for Lab Groups ............................................................................................................. - 24 -

Estimating and Reporting Uncertainties in Measurements................................................................ - 25 -

Essentials for Successful Group Work ................................................................................................. - 28 -

Laboratory Report Instructions ........................................................................................................... - 31 -

Example Lab Reports ........................................................................................................................... - 33 -

Group Assessment Form ..................................................................................................................... - 42 -

Essential Web Resources for CBE Students .................................................................................... - 43 -

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Group Laboratory Activities

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Laboratory Experiment: Blood oxygenator and lung material balances Part 1. Solve homework problem 7 from Chapter 5 of Solen and Harb. (Can be done during the lab or outside of the lab session.) Part 2. Blood oxygenator. A blood oxygenator is a device that temporarily performs the primary function of the lungs, during surgeries that require the blood flow to be stopped through major blood vessels and organs. As you probably know, the lungs exchange important gasses (oxygen and carbon dioxide) between the air and the blood. The blood oxygenator in the CBE Teaching Lab, is designed to oxygenate water using one membrane, and remove the oxygen from the water by pervaporation, using a second membrane. Identify the following important components of the apparatus: • Oxygen and nitrogen gas supply valves • Oxygen and nitrogen gas flow meters • Water reservoir • Water circulation pump and flow meter • Oxygenation and pervaporation membranes • Oxygen concentration meters • Gas vents (2 gas streams open to the atmosphere) When measuring the oxygen concentration in gas streams, the sensors report a mol % of oxygen. When measuring the oxygen concentration in the liquid streams, the sensors report the percentage of oxygen in the gas phase that would be in equilibrium with the measured liquid, at 𝑃𝑃 = 760 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 (absolute). To convert the measured % O2 in the liquid streams, use the following relationship.

𝑐𝑐𝑂𝑂2 �𝑚𝑚𝑚𝑚𝑚𝑚𝐿𝐿� = �

0.03122.414

𝑚𝑚𝑚𝑚𝑚𝑚𝐿𝐿� �

760 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 − 𝑃𝑃𝐻𝐻2𝑂𝑂 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚760 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚

�� % 𝑂𝑂2

100 %�

The value 0.031 is the absorption coefficient for oxygen in water at 20 degrees C. For the pressure in the calculation, use 17.5 mmHg, which is the vapor pressure of water at the same temperature (20 degrees C). Note that the pressure meters indicate a gauge pressure, and the pressure in the equation above is an absolute pressure. The gas flow meters measure a % of the full scale, which is a percent of 5 𝐿𝐿/𝑚𝑚𝑚𝑚𝑚𝑚 of gas at STP. 1. Make a PFD of the apparatus showing the most important pieces of equipment and all

streams. Label the streams, and flow rates (total and component). 2. Make a more detailed diagram that includes all of the items in the bulleted list above

(similar to a P&ID, but without all the details of the pipe diameters and other fittings).

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3. Discuss the following questions about material balances on the blood oxygenator

a. Is the apparatus designed to be operated as a continuous or a batch process?

b. Putting your control volume around the oxygenation module, how many streams enter and leave the process?

c. If the apparatus is used to simulate a human, what do the two membrane modules and the circulating water, and the gas streams each represent or model?

d. Does the process involve any chemical transformations?

e. When writing material balances around the entire process or part of the process, how many individual component balances could you write? Where might each component enter and leave the entire process? (Assume the inlet gas streams are pure components.)

Part 3. Laboratory report. Prepare a group lab report using the standard format: introduction, materials and equipment, procedures, results and discussion, conclusions, and references. Your laboratory report should include your responses to all of the questions in parts 1 and 2, in the form of a discussion. You do not need to address items a-e separately, for example, just be sure to show complete understanding of all the questions in the text of your report. Include estimates of uncertainty in all analyses.

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Laboratory Experiment: Blood oxygenator and membrane transport Part 1. Transport across a membrane in a hemodialyzer Consider the hemodialyzer described in S&H Example 8.3, p. 135:

In the hemodialyzer, urea is removed from blood using a membrane. Blood flows past one face of the membrane, and a salt solution (“dialysate”) flows past the other face of the membrane. Urea passes through the membrane, from the blood side to the dialysate side. The following information is given:

Blood side mass transfer coefficient for urea 0.0019 cm/s average urea concentration 0.020 gmol/L Dialysate side mass transfer coefficient for urea 0.0011 cm/s average urea concentration 0.003 gmol/L Membrane Thickness 0.0016 cm diffusivity of urea in membrane 1.8 x 10-5 cm2/s mass-transfer area 1.2 m2 Porosity 20 %

Using Equation 8.5, the removal rate of urea is 0.0065 gmol/min. Most of the resistance to mass transfer is due to the resistance on the dialysate side. A colleague suggests that you replace the membranes in this hemodialyzer with better ones, which have the same thickness and area but for which the urea diffusivity in the membrane is 2.7 x 10-5 cm2/s. Your colleague claims that this 50 % increase in the diffusivity could result in a 50 % increase in the rate of urea transport across the membrane. Assuming that the average concentrations of urea in the blood and dialysate remain the same, by what percentage would the new membrane actually increase the urea removal rate? In terms of resistances, explain why this does not result in the aforementioned 50 % increase in the rate of urea removal.

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Part 2. Transport across a membrane in a blood oxygenator The membranes in the blood oxygenator used in lab section 2 contain bundles of hollow fibers. A gas like oxygen flows inside the fibers, diffuses across the microporous walls of the fibers, and is transferred to the water that flows on the outside of the fibers.

Experimental Apparatus: Compare data for three runs (sets of operating conditions) in which the liquid and gas flow rates are systematically varied. You should collect your data in a table like the one shown here:

water in water out oxygen gas �̇�𝑉 𝑃𝑃 % 𝑂𝑂2 𝑃𝑃 𝑐𝑐𝑂𝑂2 �̇�𝑉 (% 𝑚𝑚𝑜𝑜 𝑠𝑠𝑐𝑐𝑠𝑠𝑚𝑚𝑠𝑠) 𝑃𝑃 % 𝑂𝑂2,𝑖𝑖𝑖𝑖 % 𝑂𝑂2,𝑜𝑜𝑜𝑜𝑜𝑜 Run 1

Run 2

Run 3

…

Run N

Water In Water Out

Gas Out

Gas In

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Submit a group lab report in two parts. You should write a unifying introduction and conclusions section that discuss the important ideas for both Part 1 and Part 2. The materials and procedures sections should focus on the experiments in Part 2. Be sure to include both the hemodialysis and blood oxygenator parts in the results section. Your analysis and discussion should focus on the oxygenation module and should include answers to the following questions:

1) For each run, determine the rate at which oxygen is transferred from the gas to the liquid. From a steady-state material balance on the oxygen in the liquid: 𝑅𝑅𝑠𝑠𝑅𝑅𝑠𝑠 𝑚𝑚𝑜𝑜 𝑂𝑂2 𝑅𝑅𝑡𝑡𝑠𝑠𝑚𝑚𝑠𝑠𝑜𝑜𝑠𝑠𝑡𝑡 𝑅𝑅𝑚𝑚 𝑤𝑤𝑠𝑠𝑅𝑅𝑠𝑠𝑡𝑡 = �̇�𝑉𝐿𝐿𝑖𝑖𝐿𝐿𝑜𝑜𝑖𝑖𝐿𝐿 �𝑐𝑐𝑂𝑂2,𝑜𝑜𝑜𝑜𝑜𝑜 − 𝑐𝑐𝑂𝑂2,𝑖𝑖𝑖𝑖� And from a steady-state material balance on the oxygen in the gas: 𝑅𝑅𝑠𝑠𝑅𝑅𝑠𝑠 𝑚𝑚𝑜𝑜 𝑂𝑂2 𝑅𝑅𝑡𝑡𝑠𝑠𝑚𝑚𝑠𝑠𝑜𝑜𝑠𝑠𝑡𝑡 𝑜𝑜𝑡𝑡𝑚𝑚𝑚𝑚 𝑚𝑚𝑠𝑠𝑠𝑠 = �̇�𝑉𝑔𝑔𝑔𝑔𝑔𝑔 �𝑐𝑐𝑂𝑂2,𝑖𝑖𝑖𝑖 − 𝑐𝑐𝑂𝑂2,𝑜𝑜𝑜𝑜𝑜𝑜� Does the rate of oxygen transfer from the air equal the rate of oxygen transfer to the water? If they are not the same, explain why you think they are different. 2) What are the three sources of resistance to mass transfer in the membrane module? 3) After analyzing the results from all of the runs, can you determine which of the three sources of mass-transfer resistance is the most significant? Explain.

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Calorimetry I. Calorimetry theory

“Calorimeter” is a general term for many devices that can be used to precisely measure the thermal properties of mater. Many types of calorimeters were invented and used during the 18th and 19th centuries, by scientists attempting to discover the relationships between temperature, heat, and work. Antoine Lavoisier, Pierre-Simon LaPlace, Joseph Black and James Joule are some of the famous scientists who first used different types of calorimeters. Usually, a calorimeter is used to measure either the change in temperature of a system, or the heat required to keep a system at constant temperature under very precisely controlled conditions. This can enable measurements of properties such as heats of reaction, heats of phase change, and heat capacities of materials. James Joule used a calorimeter (a so-called “heat apparatus”) to establish the mechanical (work) equivalence of heat. Constant temperature (isothermal) calorimeters can be used to measure heats of reactions. Constant pressure (bomb) calorimeters are used to measure heats of combustion. Scanning calorimeters measure the heat required to raise a sample temperature at a constant rate to find both heat capacities and phase transitions. Adiabatic (insulated) calorimeters can also be used to measure heat capacities.

In this lab, you will design, construct, and use an adiabatic calorimeter. Your calorimeter will consist of an insulated beaker and lid, containing a measured amount of water, a way to stir the water, and a thermocouple for measuring the temperature of the system. Initially, the calorimeter and the water are at ambient temperature. A block of hot metal will be added to the calorimeter. The temperature of the calorimeter and the water will increase, while the temperature of the hot block will fall. Eventually, the temperature of the block will equal the temperature of the calorimeter and the water. (If you waited long enough, heat would dissipate to the surroundings and the entire system would cool to the ambient temperature.)

Once the block and water are combined in the insulated beaker and the lid is put on top, the adiabatic calorimeter is a closed system (no material enters or leaves). Therefore, the calorimeter should behave according to the First Law of Thermodynamics (Solen and Harb, p. 157).

Δ𝐸𝐸 = 𝑄𝑄 + 𝑊𝑊 (1)

If the beaker is very well-insulated, then the 𝑄𝑄 = 0 in equation (1). Furthermore, your calorimeter will have no moving parts, so there should also be no work; so 𝑊𝑊 = 0 as well. So we can rewrite equation (1) for the calorimeter:

Δ𝐸𝐸 = 0 (2)

This is the conservation of total energy for a closed, adiabatic system, with 𝑊𝑊 = 0. You should be able to show that the conservation of energy requires that the energy lost by the metal block must equal the energy gained by the calorimeter and the water. In terms of masses (𝑚𝑚), heat capacities (𝐶𝐶𝑃𝑃), and the temperatures (𝑇𝑇), we can write1: 1 It would be more accurate to include heat lost to the surroundings in equation (2):

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�𝑚𝑚𝐶𝐶𝑃𝑃�𝑇𝑇𝑖𝑖 − 𝑇𝑇𝑓𝑓��𝑏𝑏 = �𝑚𝑚𝐶𝐶𝑃𝑃�𝑇𝑇𝑓𝑓 − 𝑇𝑇𝑖𝑖��𝑐𝑐𝑔𝑔𝑐𝑐 + �𝑚𝑚𝐶𝐶𝑃𝑃�𝑇𝑇𝑓𝑓 − 𝑇𝑇𝑖𝑖��𝐻𝐻2𝑂𝑂 (3)

The subscripts 𝑚𝑚 and 𝑜𝑜 refer to initial and final conditions. The other subscripts refer to the part of the system: 𝑏𝑏 for block, 𝑐𝑐𝑠𝑠𝑚𝑚 for the calorimeter, and 𝑚𝑚2𝑂𝑂 for the water. At the final condition, the temperature is assumed to be uniform throughout the system. II. Calorimeter Preparation and Calibration Design and assemble an insulated beaker and lid to serve as your calorimeter. You may use any of the supplies available in the lab (air, water, sand, foil, Styrofoam, etc.). First, you will calibrate your calorimeter by measuring the value of its 𝑚𝑚𝐶𝐶𝑃𝑃, using the aluminum metal block as a reference. Do this using the following procedure: 1. Measure the mass of the aluminum block and the mass of the water added to the calorimeter.

Measure the temperature of your calorimeter and water. 2. Heat the aluminum block with the hot plate and hot water bath provided. 3. While waiting for the block to heat, check the calibration of the thermocouples by measuring

the temperature of the hot water bath and comparing your readings to those obtained with the TA’s thermometer.

4. Measure the temperature of the hot block, then place it quickly into the water-filled calorimeter and cover it with the lid.

5. Record the temperatures of the block and water/calorimeter over time. Continue to take readings for at least 5 minutes after the temperature of the calorimeter stabilizes.

6. Use the simplified energy balance above (equation 3) and the specific heat capacity of aluminum (see Table on p. 17) to find the effective heat capacity of the calorimeter, (𝑚𝑚𝐶𝐶𝑃𝑃)𝑐𝑐𝑔𝑔𝑐𝑐.

7. Check the assumption that heat losses to the surrounding are negligible. Redesign your calorimeter, if necessary, to reduce energy losses to the surroundings, and recalibrate as needed.

Δ𝐸𝐸 = 𝑄𝑄𝑐𝑐𝑜𝑜𝑔𝑔𝑔𝑔

where the 𝑄𝑄𝑐𝑐𝑜𝑜𝑔𝑔𝑔𝑔 term might be represented as 𝑄𝑄𝑐𝑐𝑜𝑜𝑔𝑔𝑔𝑔 = ℎ Δ𝑇𝑇avg Δ𝑅𝑅

This heat loss term should be included in equation (3). Here, ℎ is the heat transfer coefficient between the calorimeter contents and the surroundings, Δ𝑇𝑇𝑔𝑔𝑎𝑎𝑔𝑔is the average difference in temperature between the calorimeter contents and the surroundings, and Δ𝑅𝑅 is the time over which the heat is lost. In your experiments you can minimize 𝑄𝑄𝑐𝑐𝑜𝑜𝑔𝑔𝑔𝑔 by making ℎ very small, by using good insulation. You can also ensure that Δ𝑅𝑅 is small, by only conducting the experiment as long as is necessary to ensure that the block and the water have reached the same final temperature (at least to within the accuracy of your thermometer). This should take less than 10 minutes for each block. If you were to wait all day (a large Δ𝑅𝑅), the entire system would eventually cool back to room temperature.

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You can use the space below to record your data or make a separate data sheet:

Mass of aluminum block Initial temperature of water /calorimeter Mass of water in calorimeter Temperature of heated aluminum block

Time Temperature of block* Temperature of water/calorimeter

(𝑚𝑚𝐶𝐶𝑃𝑃)𝑐𝑐𝑔𝑔𝑐𝑐

*The block temperature will probably be hard to acquire with the instrumentation you have. Assuming the sample has a ‘large’ thermal conductivity, the water temperature should be a reasonable approximation of the value for the block. Also, because the temperature associated with the calorimeter itself is difficult to measure, assume that its temperature is the average of the water and ambient (room) temperature. III. Measure the heat capacities of three unknown metals Next, use your calorimeter to measure the heat capacities of the unknown metal blocks by repeating the protocol above. This time, at step 6, you will solve for the unknown heat capacity of your metal block, instead of the unknown heat capacity of the calorimeter. Be careful to do the following: 1. Before you begin, prepare a data table to record your measurements. 2. Use fresh, room-temperature water for each experiment, but be sure to record the initial mass

of water and initial water temperature, as these may vary slightly from one experiment to the next.

3. Continue to take readings for at least 5 minutes after the temperature of the calorimeter stabilizes. The time required to reach thermal equilibrium may be different for the different blocks.

4. Record any important characteristics of the blocks that you might use to identify them, in addition to their apparent heat capacities.

5. Verify that the rate of energy loss to the surroundings is comparable to that observed during the calibration run.

6. Perform replicates of the experiments if time permits. 7. Make sure to shut off all power supplies and clean up your work area before leaving the lab.

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IV. Data analysis and lab report. Prepare a laboratory report describing your experiments and major findings. In addition to introduction, experiment, results, discussion, and example calculations, your report should include:

1. Plots of the block and calorimeter temperatures (on the same graph) as a function of time. (Label the axes and include units!)

2. An estimate of the rate at which heat is lost to the surroundings in [J/s]. 3. Estimates of the uncertainty in each of your measured values: 𝑚𝑚𝑏𝑏, 𝑚𝑚𝐻𝐻2𝑂𝑂, 𝑇𝑇𝑖𝑖,𝑏𝑏, 𝑇𝑇𝑖𝑖,𝐻𝐻2𝑂𝑂, 𝑇𝑇𝑖𝑖,𝑐𝑐𝑔𝑔𝑐𝑐, 𝑇𝑇𝑓𝑓 .

Which uncertainty has the greatest effect on the calculated values, 𝐶𝐶𝑃𝑃,𝑏𝑏 and (𝑚𝑚𝐶𝐶𝑃𝑃)𝑐𝑐𝑔𝑔𝑐𝑐? 4. An estimate of the uncertainty in the calculated 𝐶𝐶𝑃𝑃 values. 5. An attempt to identify the unknown metals from the experimentally determined 𝐶𝐶𝑃𝑃 values.

All of the metal blocks are common metals used in engineering applications, but they are not necessarily pure elemental metals. Some of the most common metals engineers encounter are actually metal alloys (mixtures of multiple metals). Examples of metal alloys you may have heard of include alnico, brass, bronze, chromoly, inconel, nichrome, nitinol, pewter, solder, stainless steel, and carbon steel. There are many others. The table below lists some heat capacities of metals that you can use as a reference to see whether your measured heat capacities are the right order of magnitude. Be resourceful to find some good sources of heat capacities for common engineering metal alloys that will allow you to identify your metal blocks. Specific Heat Capacities of Some Metals and Metal Alloys

Material Specific Heat at 300 K [J g-1 K-1]

Al 0.902 Cr 0.450 Cu 0.386 Fe 0.450 Ni 0.444 Pb 1.129 Sn 0.222 Brass 0.377 Solder 0.167 Stainless steel 0.49 Carbon steel 0.469

The data in this table are from the following sources:

Perry’s Chemical Engineer’s Handbook , 6th Ed., page 3-135. Metallic Materials Properties Development and Standardization (MMPDS-04), Federal Aviation

Administration, 2008. The Engineering Toolbox, www.engineeringtoolbox.com, 2005.

Versions of each of these (and many other) sources are available electronically or through the Morgan Library website.

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Laboratory Experiment: Heat Conduction

I. Conductivity theory In class, we have learned that when thermal energy is transferred by conduction through a medium,

the rate of thermal energy transfer is proportional to the difference in temperature (Δ𝑇𝑇), and inversely proportional to the distance that the heat has to travel to cross the medium (Δ𝑥𝑥). This leads to the difference form of what is known as Fourier’s law of heat conduction.

�̇�𝑄 = −𝑘𝑘𝑘𝑘Δ𝑇𝑇Δ𝑥𝑥

(1)

where �̇�𝑄 = the rate of energy transfer at 𝑥𝑥 [J/s] 𝑘𝑘 = the cross-sectional area through which heat is conducted [m2] 𝑘𝑘 = the thermal conductivity of the medium [J/(s m K)]

As long as the system is at steady state, there is no accumulation of thermal energy at any point in the medium (�̇�𝑄 is the same at every 𝑥𝑥), and equation 1 predicts a linear temperature profile as illustrated in Figure 1, for heat being conducted through a cylinder.

In this lab, we will consider what happens in the unsteady condition. An unsteady condition can be created if we begin with the entire cylinder at 𝑇𝑇2, and then quickly heat one side of the cylinder to 𝑇𝑇1. In this case, Fourier’s law still holds, but we must be careful how we define the term Δ𝑇𝑇/Δ𝑥𝑥. In the unsteady case, the value of Δ𝑇𝑇/Δ𝑥𝑥 will depend upon what positions we choose for our 𝑥𝑥1 and 𝑥𝑥2. Fourier’s law only describes the heat transfer accurately in the limit as Δ𝑥𝑥 approaches 0. Thus we can write the differential form of Fourier’s law for heat transfer in one direction:

�̇�𝑄 = limΔ𝑥𝑥→0

�−𝑘𝑘𝑘𝑘Δ𝑇𝑇Δ𝑥𝑥� = −𝑘𝑘𝑘𝑘

𝑑𝑑𝑇𝑇𝑑𝑑𝑥𝑥

(2)

�̇�𝑄

𝑥𝑥1 𝑥𝑥2

𝑇𝑇2 𝑇𝑇1 𝑇𝑇1

𝑇𝑇2

𝑇𝑇

𝑥𝑥 𝑥𝑥1 𝑥𝑥2

Figure 4.1. At steady state, �̇�𝑄 must be the same everywhere in the cylinder, so that there is no accumulation of thermal energy anywhere. This means that the slope of 𝑇𝑇 versus 𝑥𝑥 must also be the same everywhere:

Δ𝑇𝑇Δ𝑥𝑥

= −�̇�𝑄𝑘𝑘𝑘𝑘

Question: If the slope of 𝑇𝑇 versus 𝑥𝑥 is given by the equation below figure 1, can you find an equation for 𝑇𝑇 as a function of 𝑥𝑥 for the steady state case? Write this expression in the space below: 𝑇𝑇(𝑥𝑥) =

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The unsteady state case is illustrated in Figure 2. In the unsteady case, the rate of heat transfer to a point 𝑥𝑥 is not the same as the rate of heat transfer away from the point 𝑥𝑥. Accumulation of thermal energy at the point 𝑥𝑥 will result in a change in the temperature at 𝑥𝑥.

The change in temperature at 𝑥𝑥 can be described by another differential equation:

𝑑𝑑𝑇𝑇𝑑𝑑𝑅𝑅

=1

𝑘𝑘𝐴𝐴𝐶𝐶𝑃𝑃𝑑𝑑�̇�𝑄𝑑𝑑𝑥𝑥

= −𝑘𝑘𝐴𝐴𝐶𝐶𝑃𝑃

𝑑𝑑2𝑇𝑇𝑑𝑑𝑥𝑥2

(3)

Equation 3 is an initial value problem. In your later chemical and biological engineering courses you will learn how to solve many such differential equations. The solution to this differential equation is

𝑇𝑇 − 𝑇𝑇0𝑇𝑇𝐻𝐻 − 𝑇𝑇0

= 1 − erf�𝑥𝑥2�𝐴𝐴𝐶𝐶𝑃𝑃𝑘𝑘𝑅𝑅

� (4)

where erf(...) is a mathematical function called the error function, 𝑘𝑘 is the thermal conductivity of the medium, 𝐶𝐶𝑃𝑃 is the heat capacity of the medium, 𝐴𝐴 is the density of the medium, 𝑇𝑇0 is the initial temperature of the medium, and 𝑇𝑇𝐻𝐻 is the temperature that one end of the medium is raised to at 𝑅𝑅 =0. The error function, erf (𝑥𝑥), and 1 − erf (𝑥𝑥) are shown in the plots below. Sometimes, the function 1 −erf (𝑥𝑥) is referred to as the complimentary error function, and is denoted erfc(𝑥𝑥).

Figure 4.3. Plots of the error function (left) and the complimentary error function (right).

𝑇𝑇1

𝑇𝑇2

𝑇𝑇

𝑥𝑥 𝑥𝑥1 𝑥𝑥2

Figure 4.2. Initially, the cylinder has the same temperature at all 𝑥𝑥. At time 𝑅𝑅 = 0, the temperature at the left end of the cylinder is raised to 𝑇𝑇1. Notice that the slope of 𝑇𝑇 versus 𝑥𝑥 is not constant at t = 0. This must mean that �̇�𝑄 is also not constant, and that the system is not at steady state.

Question: What do you think 𝑇𝑇 versus 𝑥𝑥 should look like at times 𝑅𝑅 > 0? Sketch several curves above that represent 𝑇𝑇 versus 𝑥𝑥 at different times.

𝑅𝑅 < 0 𝑇𝑇1

𝑇𝑇2

𝑇𝑇

𝑥𝑥 𝑥𝑥1 𝑥𝑥2

𝑅𝑅 = 0 𝑇𝑇1

𝑇𝑇2

𝑥𝑥1 𝑥𝑥2

𝑅𝑅 > 0

𝑥𝑥

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II. Experimental apparatus and procedure The experimental apparatus for this lab consists of four well-insulated metal rods mounted on a frame. At one end of the rods is a heater connected to a variable power supply. Each of the rods also has several points along its length where the metal is exposed, so that a thermocouple can be used to measure the rod temperature. The rods are labeled with colored zip ties that identify the metal from which they are made. (Green = aluminum; White = steel; Yellow = brass; Red = copper.) Determine how the temperature changes along the metal rods when they are heated at one end, by following the protocol described below: 1. During the experiment, the team will have to quickly measure the temperature along each of the

rods at specified time intervals. This will require some coordination among the team. The team should practice measuring and recording temperatures with the heater turned off, before beginning. Once you turn the heater on, you cannot cool the rods back down to start over! It is best to measure from the hot end to the cool end of the rods, since the temperatures change more quickly at the hot ends. The thermocouples will need to be held on the metal for a few seconds to obtain an accurate reading. One or two people should position the thermocouples, one person should read the temperatures, and one person should record them. Be sure to prepare a data table for recording temperature readings before you begin!

2. To turn on the heater and get it warmed up quickly, set the variable controller to 10 for 30 seconds, lower it to 9 for 2 minutes, lower it to 8 for 2 minutes, and then set it to 7.

3. Measure the temperature at points 5 inches apart along each rod at predetermined time intervals. Begin the timer when you turn on the heater. (You may use whatever time intervals you would like, but please take readings at 1 minute, 10 minutes, 20 minutes, and 30 minutes so that you have data to compare to the model in part III.)

4. Be sure to record: 𝑇𝑇0 (the room temperature), 𝑇𝑇𝐻𝐻 (the temperature at the heated end of the rods), and 𝑇𝑇 versus 𝑥𝑥 for each rod at each 𝑅𝑅.

5. Also make frequent measurements of heater temperature. Note that the heater cycles on and off, so some fluctuation in the heater temperature is expected. However, if the heater temperature continues to rise quickly, you may need to adjust the power setting down on the variable power supply.

- 17 -

III. Modeling conduction in the heated rods The four metal rods are initially at room temperature. When they are heated on one end, the energy is transferred from the hot end toward the cool end by conduction. The rate of energy transfer at a particular point along the rod is given by the differential form of Fourier’s law (equation 3). This should result in a temperature profile along each of the metal rods described by equation 4. The use of equation 4 to approximate the temperature profile assumes that the heating process is adiabatic, that is, no heat is lost to the surroundings. Thus, any energy transferred from the heater to the rods raises the temperature of the rods. You are to write a MATLAB program that calculates 𝑇𝑇(𝑅𝑅, 𝑥𝑥) for each of the rod materials. This will require the following: 1. You will need to look up values for the density, thermal conductivity, and heat capacity of

aluminum, copper, stainless steel, and brass in an appropriate reference. Be sure to include the source of your physical property values in your lab report.

2. The values of 𝑇𝑇0 and 𝑇𝑇𝐻𝐻 used in the model should correspond to the values measured during your experiments. Assume that the initial temperature is equal to the temperature of the room. (If these temperatures vary greatly over the course of the experiments, pick typical values for use in the model, and discuss the effect of the variations in temperature on your results.)

3. The rods in the experiment are 30 inches long. Create an array of at least 100 𝑥𝑥 values that range from just above 0 inches to 30 inches, for each rod. Make sure that your units are consistent!

4. The program is to produce temperature profiles (plots of 𝑇𝑇 versus 𝑥𝑥) at several times. Use times of 1 minute, 10 minutes, 30 minutes, 90 minutes, and 270 minutes for each rod.

IV. Data analysis and lab report Prepare a laboratory report describing your experiments, modeling, and major findings. Within the standard format for the laboratory report, you should be sure to include: 1. Some discussion of how the 𝑇𝑇 versus 𝑥𝑥 curves change with time for each rod. To facilitate this

discussion, the temperature profiles for each rod should all be plotted on the same graph, with one graph for each rod.

2. Some discussion of how well the model predicts the experimentally measured temperature profiles for each rod. To facilitate this discussion, you should plot the experimental data and the predicted profiles on the same plots.

3. Discussion of any discrepancies between your measured temperature profiles and the theoretically predicted ones.

When submitting your lab report, be sure to attach a copy of your (well commented) MATLAB code.

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Lab Experiment: Rotameter Calibration and Solar Heaters

Each group is given a flow-testing cart, equipped with a water reservoir, pump, cooling fan, rotameter, solar water heater, and associated plumbing. Each group is also given a timer, beakers, and access to a balance and solar radiation intensity meter. The objectives of this lab are to: 1. Calibrate the Rotatmeter. 2. Measure flow rates. 3. Calculate heating rates and efficiencies. 4. Calculate uncertainties based on measured values, using the

root-sum-of-squares formula.

Part 1. Rotameter Calibration The rotameter consists of a needle valve that regulates the flow of fluid through a vertically oriented, tapered channel. The tapered channel has a larger cross section at the top than at the bottom. The vertical position of a “float” in the tapered channel is read using a graduated scale on the body of the rotameter. The float position indicates the flow rate. A simple diagram of a rotameter is shown in Figure 1.1.

The “float” is actually a “sink”, since it is more dense than the fluid. Two forces are acting on the “float”: • A gravitational force, indicated by the downward-pointing broken arrow in Figure 2.1. (Recall that

the gravitational force is modified by the buoyant force, which is the mass of the liquid displaced by the float.)

• A drag force, due to friction of the fluid flowing around the float. The drag force is indicated by the upward-pointing broken arrow in Figure 2.1. The drag force increases as the fluid flow increases (at constant float position) and also increases as the channel cross section decreases (at constant flow rate).

Since the gravitational and drag forces point in opposite directions, the float will not accelerate if these two forces have equal magnitudes – it will be stationary. When the flow rate is increases (e.g. by opening the needle valve) the drag force on the float increases, and the float accelerates up the channel, until it reaches a point where cross section is wide enough that the drag force is reduced to exactly counter the gravitational force. Conversely, if the flow rate is decreased, the drag force will decrease, and gravity will accelerate the float down until the taper in the channel is reduced sufficiently to create a drag force that exactly counters the gravitational force. In this way, the float position is a unique indicator of the flow rate. By convention, the float height is usually read from the center of the float. Note that these rotameters are designed for saltwater fish tanks, so the factory calibration is for a fluid (brine salt water) similar to, but not identical to the water you are using. Procedure to collect rotameter calibration data. (To be done in the laboratory class time.) 1. Read through the entire procedure as a group before beginning; take time to plan how you will

conduct the procedure, and how you will record your observations, and data. 2. Identify the primary components of the flow-testing cart. 3. Set up the test cart so that water is plumbed through the rotameter. 4. Start the pump and open the rotameter all the way to flush any air out of the plumbing.

Knob for adjusting

needle valve

Tapered channel

Graduated scale

Float Rotameter

body

Fig. 1.1. A rotameter like the one you use in Lab 2.

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Safety Notes: 1. You are using water and

electricity. Be sure that electrical connections are not exposed to water.

2. The pump housing may get hot during the course of the experiment. Don’t touch it.

3. The pump is cooled by a fan with moving parts. Be careful to keep long hair and clothing items away from the fan.

5. Perform calibration measurements: 5.1. Measure and record the mass of an empty beaker. Don’t forget the

units and uncertainty! 5.2. Adjust the rotameter to the “30” setting. If the rotameter setting is

not constant, ask the instructor or the lab assistants for help. Maintaining a full reservoir and adjusting the flow rate through the shunt can help ensure that the flow remains stable.

5.3. Collect water in the beaker for a measured period of time (e.g. 1 minute), while monitoring to ensure a constant rotameter setting.

5.4. Measure and record the combined mass of the water and the beaker. (Units and uncertainty are important, too, remember?)

5.5. Calculate the mass of the water alone; use this mass to determine the mass flow rate of water over the time interval (�̇�𝑚 in g/min) and the volume flow rate (�̇�𝑉 in mL/min).

5.6. Repeat steps 7.1 through 7.6 for three additional rotameter settings.

Part 2. Solar water heater performance. The solar water heater has three features that can be changed to modify the heater performance. 1. The heater is equipped with a reversible panel that slides under the pipes. This panel is flat-black on

one side and white on the other 2. The heater is also equipped with a removable acrylic cover that can be inserted or removed to

adjust the heat losses to the surroundings. 3. The water lines can be connected to two separate paths through the solar water heater. On one

path, fluid flows through one long pipe that makes three passes through the heater (series). On the other path, the flow is split between 3 short single-pass pipes (parallel). The total length of pipe is the same for the two paths.

Procedure for evaluating solar heater performance (to be done during class time). Of the several combinations of the three adjustable water heater features (cover, reversible panel, and flow configuration) make an educated guess as to which configuration will most efficiently heat the water and which will least efficiently heat the water. Choose two conditions that you think will perform differently. 1. Be sure that the feed tubing is primed, then connect the water heater in one of the configurations

that you determined above. Bleed all of the air out of the water heater. (Do this with the rotameter wide open!) Connect the outlet tubing and remove the air from it as well. Note that all connections should not leak when hand tightened. You should not need to use a wrench on these fittings.

2. Check to ensure that the thermocouples at the inlet and outlet of the water heater are completely submerged. This can be done by loosening the nut at the thermocouple tap to ensure that a bit of water begins to leak out. If an air bubble is present at the thermocouple tap, the thermocouple will not read the water temperature, and no water will leak out when the nut is loosened. If you do have air in the system, go back to step 1. Ask for help if you need it!

3. Record the time and weather conditions. (mV from radiometer, outside temperature, description of wind and cloudiness).

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4. Use the rotameter valve to set the water flow rate to 50 g/min. Wait for the difference between the inlet and outlet water temperature to reach a constant value. The two temperatures may never reach a constant value, particularly if the weather conditions are variable during your experiment. In calm weather with constant sunlight, you can expect that the difference in temperature between the inlet and outlet varying by less than 10 % over a 10-minute interval is approximately steady-state. But it may take 20 or 30 minutes to reach this steady state. Record temperature data at 4-5 time points until the system reaches a steady-state (at least 20-minutes), and then record these points once per minute for 5 minutes. Use the average value of the last 5 readings in your calculations, and use the standard deviation of the last 5 readings to estimate the uncertainty in your results. Record the following: inlet water temperature, outlet water temperature, ambient temperature and other relevant weather observations (wind, cloud cover, etc.), mV reading from the solar radiometer, water flow rate, and the time it took to reach steady-state.

5. Repeat the test for at least 1 more solar water heater configuration from among the 8 possibilities. Part 3. Data analysis and laboratory report (to be done outside of the laboratory time). 1. Calculate the rate at which solar energy is radiated to the surface of the water heater. The solar

radiometer gives a reading in mV. Convert this reading to volts by dividing by 1000. Once the reading is in V, it can be converted to watts per unit area using the following conversion factor:

1𝑉𝑉 = 1.08 × 105𝑊𝑊𝑚𝑚2 = 1.08 × 105

𝐽𝐽𝑠𝑠𝑚𝑚2

Thus the rate at which solar energy is reaching your device, �̇�𝐸𝑔𝑔𝑜𝑜𝑖𝑖 in J/s, is given by:

�̇�𝐸𝑔𝑔𝑜𝑜𝑖𝑖 =𝑅𝑅(𝑚𝑚𝑉𝑉)𝑘𝑘(𝑚𝑚2)

1000 �𝑚𝑚𝑉𝑉𝑉𝑉 �1.08 × 105 �

𝐽𝐽𝑠𝑠𝑚𝑚2�

Where 𝑅𝑅 is the radiometer reading in mV, and 𝑘𝑘 is the surface area of the heater through which sun enters in m2. The instructor or the TA’s can provide the value of 𝑘𝑘 for each unit.

2. Calculate the efficiency of the solar water heater for the two configurations you tested. The efficiency is given by:

𝜂𝜂 =𝑅𝑅𝑠𝑠𝑅𝑅𝑠𝑠 𝑚𝑚𝑜𝑜 𝐸𝐸𝑚𝑚𝑠𝑠𝑡𝑡𝑚𝑚𝐸𝐸 𝑅𝑅𝑡𝑡𝑠𝑠𝑚𝑚𝑠𝑠𝑜𝑜𝑠𝑠𝑡𝑡 𝑅𝑅𝑚𝑚 𝑤𝑤𝑠𝑠𝑅𝑅𝑠𝑠𝑡𝑡

𝑅𝑅𝑠𝑠𝑅𝑅𝑠𝑠 𝑚𝑚𝑜𝑜 𝐸𝐸𝑚𝑚𝑠𝑠𝑡𝑡𝑚𝑚𝐸𝐸 𝑠𝑠𝑎𝑎𝑠𝑠𝑚𝑚𝑚𝑚𝑠𝑠𝑏𝑏𝑚𝑚𝑠𝑠 𝑜𝑜𝑡𝑡𝑚𝑚𝑚𝑚 𝑅𝑅ℎ𝑠𝑠 𝑠𝑠𝑠𝑠𝑚𝑚100 %

If you have data from other groups, you may compare their results to yours, as well. You can find the rate at which energy is transferred to the water as the mass flow rate times the heat capacity times the change in the temperature:

�̇�𝑄 = �̇�𝑚𝐻𝐻2𝑂𝑂𝐶𝐶𝑃𝑃,𝐻𝐻2𝑂𝑂(𝑇𝑇𝑜𝑜𝑜𝑜𝑜𝑜 − 𝑇𝑇𝑖𝑖𝑖𝑖) Thus,

𝜂𝜂 =�̇�𝑚𝐻𝐻2𝑂𝑂𝐶𝐶𝑃𝑃,𝐻𝐻2𝑂𝑂(𝑇𝑇𝑜𝑜𝑜𝑜𝑜𝑜 − 𝑇𝑇𝑖𝑖𝑖𝑖)

�̇�𝐸𝑔𝑔𝑜𝑜𝑖𝑖100 %

- 21 -

Use a value of 4.18 J g-1 °C-1 for the heat capacity of water. 3. Prepare a group lab report using the standard format: introduction, materials and equipment,

procedures, results and discussion, conclusions, and references. Your laboratory report should include a plot of your rotameter calibration. In your plot, remember to label the axes and include units. You should also include uncertainty estimates on all measured and calculated values.

Measurement Setting 1 Setting 2 Setting 3 Setting 4 Rotameter Calibration

Mass of beaker

Rotameter setting

Mass of water + beaker

Time

Calculated mass of water

Calculated flow rate

Calculate uncertainty on mass of water for each setting: Calculate uncertainty on flow rate for each setting:

- 22 -

Calculate uncertainty on Δ𝑇𝑇 for each configuration: Calculate uncertainty on �̇�𝐸𝑔𝑔𝑜𝑜𝑖𝑖 and �̇�𝑄 for each setting: Calculate uncertainty on 𝜂𝜂 for each setting:

Measurement Configuration 1 Configuration 2 Configuration 3 Solar collector performance

Flow rate

Temperature in

Temperature out

Solar radiometer, (𝑚𝑚𝑉𝑉)

Calculated �̇�𝐸𝑔𝑔𝑜𝑜𝑖𝑖

Calculated �̇�𝑄

Calculated 𝜂𝜂

- 23 -

Laboratory Experiment: Siphons

One way to drain a liquid out of a container that has high walls is to use a siphon. A siphon is a tube with one end in the liquid and the other end below the liquid level. The length of the tube can travel over the wall of the container as shown in Figure 5.1. The tube is then filled with the liquid (usually by applying suction to the open end). As long as the elevation of the open end is lower than the top of the liquid, the liquid will flow out of the tank. Part I. Collect flow rate data using a siphon. Spend a few minutes familiarizing your group with the apparatus at a siphon station. Use a siphon station to measure the volumetric flow rate �̇�𝑉 as a function of ℎ. Use at least 6 values of ℎ. For each of the 6 values of ℎ , measure �̇�𝑉 at least 3 times. As in the rotameter calibration exercise, volumetric flow rates can be found by measuring the mass of water collected in a measured amount of time. Prepare a table of your raw data and calculated values of �̇�𝑚 and �̇�𝑉. Note: Start by setting the zero value for your ℎ measurement. Recheck this zero point periodically, as it may drift as the water level in the reservoir changes. Part II. Analyze your data using the mechanical energy balance. (a) Using the mechanical energy balance, derive an equation relating the volumetric flow rate, �̇�𝑉, at the

outlet of the tube to the distance, ℎ. You may neglect friction, and you may assume that surface of the liquid in the tank is essentially stationary. Using this equation, what happens to �̇�𝑉 when ℎ approaches zero? Is the same true for the data you collected in Part I?

(b) Assuming that the liquid is water and the tube has an inner diameter of 3.1 mm, use part (a) and

Matlab to predict how the volumetric flow rate (in mL/min) is expected to vary for values of ℎ ranging from 0 to 45 cm in 5 cm increments.

(c) Compare your theoretical prediction from Part II (b) to the values measured in Part I. Using Matlab,

start by plotting the measured �̇�𝑉 from Part I as a function of ℎ in such a way that, theoretically, you should get a straight line. Next, do linear regression to get a best fit to your data in the plot. Finally, plot the predicted values from Part II (b) on the same plot. At this point you should have 1 set of symbols and 2 lines in your plot. How well do the experimental results match the theoretical predictions? Explain why there may be a discrepancy.

Do Part I in the lab. Part II is to be done post-lab, as a team. Present your work using the standard report format: introduction, materials and equipment, procedures, results and discussion, and conclusions. Be sure to discuss sources of uncertainty and then quantify your predicted error in obtaining �̇�𝑉. Include relevant discussion of why your predicted values may not match the values from your experiment. Attach the m-files from Parts II (b) and II (c) as an Appendix. Include the plot from Part II (c) in the body of your report.

h

Figure 5.1 Diagram of a tank equipped with a siphon tube. The outlet of the tube is a distance h below the surface of the liquid in the tank.

- 24 -

Resources for Lab Groups

- 25 -

Estimating and Reporting Uncertainties in Measurements

Sources of Uncertainty An error is a difference between the true value (which can never be absolutely known with infinite precision) and the measured value. Measurements of physical quantities usually have two types of errors:

Systematic error or measurement bias is the contribution to the error that would always be obtained because of an error in the technique or instrumentation. For example, if the balance used to measure masses is off by −0.5 g over the entire range, then all measurements made using the balance would have the same systematic error. In the case of the balance, the systematic error can be minimized by setting the tare weight to 0 or calibrating the balance before making measurements.

Random error is a source of error that is not systematic error. There are many possible sources of random error. For example if three members of the lab group were to make the same measurement, using an analog instrument (e.g. reading a dial or a graduated scale) the three individuals might all observe a slightly different value. In this case, you could report the measured value as the arithmetic mean of the three measurements, and the uncertainty as half of the difference between the largest and the smallest values. Another source of random error is the limit of resolution of the instrument used to make a measurement. For a graduated scale (e.g. a ruler, graduated cylinder, etc.) the limit of resolution might be assumed to be half of the smallest distance between two points on the scale. If you have multiple possible sources of random error that can be quantified (e.g. replicate measurements and a known limit of resolution of the instrument) then you should use the largest estimate of error as the uncertainty.

Reporting Uncertainty When reporting a quantity with its uncertainty, the quantity is listed first, followed by the symbol “±”, and then the uncertainty. In this class uncertainties should have only one significant digit, and this should be the last significant digit of the reported value. For quantities with units, the value and its uncertainty should be in parentheses with the units outside. For example:

(10.05 ± 0.08) m 15 ± 2 (223.13 ± 0.01) s

The following are incorrect: (10 ± 0.08) m (The last significant digit of the value is not the same as the uncertain digit.) 14.67 ± 2 (The reported value has more precision than suggested by the uncertainty.) (223.13 ± 0.0109622) s (The uncertainty is more than one significant digit.)

Uncertainties on Calculated Values: Propagation of error When reporting a value that is obtained from multiple measurements, like the difference between two measurements, or the ratio of two measurements, then the error on both measurements will contribute to the error on the calculated result. In general, for a function 𝑜𝑜 of 𝑚𝑚 measurements, 𝑥𝑥1, 𝑥𝑥2, … 𝑥𝑥𝑖𝑖, where each measurement has an uncertainty 𝜎𝜎1, 𝜎𝜎2, … 𝜎𝜎𝑖𝑖, the uncertainty on 𝑜𝑜, 𝜎𝜎𝑓𝑓, can be estimated from the uncertainties on the measured values and the partial derivatives of 𝑜𝑜 with respect to each of the measured values 𝑥𝑥𝑖𝑖, according to the so-called root-sum-of-squares formula.

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𝜎𝜎𝑓𝑓 = ��𝜎𝜎𝑖𝑖2 �𝜕𝜕𝑜𝑜𝜕𝜕𝑥𝑥𝑖𝑖

�2𝑖𝑖

𝑖𝑖=1

(1)

As examples of how to use equation 1, we will find the uncertainties on three values, 𝑜𝑜, 𝑚𝑚, and ℎ, which are found from the measurements 𝑥𝑥1 and 𝑥𝑥2 according to 𝑜𝑜 = 𝑥𝑥1 + 𝑥𝑥2

(2)

𝑚𝑚 = 𝑥𝑥1𝑥𝑥2

(3)

ℎ =𝑥𝑥1𝑥𝑥2

(4)

In order to compute the uncertainties on 𝑜𝑜, 𝑚𝑚, and ℎ, we will need to find the partial derivatives of each of these with respect to both 𝑥𝑥1 and 𝑥𝑥2. If you have had some differential calculus these derivatives are not hard to find. If not, then you can use these formulas: 𝜕𝜕𝑜𝑜

𝜕𝜕𝑥𝑥1=𝜕𝜕𝑜𝑜𝜕𝜕𝑥𝑥2

= 1 (5)

𝜕𝜕𝑚𝑚

𝜕𝜕𝑥𝑥1= 𝑥𝑥2 and

𝜕𝜕𝑚𝑚𝜕𝜕𝑥𝑥2

= 𝑥𝑥1 (6)

and 𝜕𝜕ℎ

𝜕𝜕𝑥𝑥1=

1𝑥𝑥2

and 𝜕𝜕ℎ𝜕𝜕𝑥𝑥2

= −𝑥𝑥1𝑥𝑥22

(7)

Use the root sum of squares formula (equation 1) and these partial derivatives to find the uncertainties on the functions 𝑜𝑜, 𝑚𝑚, and ℎ defined by equations 2, 3, and 4: 𝜎𝜎𝑓𝑓 = 𝜎𝜎𝑔𝑔 = 𝜎𝜎ℎ = You can use the important formulas above to estimate the uncertainty on any quantity that is the sum (𝑜𝑜), product (𝑚𝑚), or ratio (ℎ) of experimentally measured values. You will use these formulas in the solar heater lab and in future lab experiments in this class!

In equation 1, the term in parentheses is a special kind of derivative, called a partial derivative. In this case, it is the partial derivative of 𝑜𝑜 with respect to 𝑥𝑥𝑖𝑖. If you have taken some differential calculus, and learned how to find a derivative of a function of one variable, then you can find a partial derivative of a function of multiple variables, by assuming all of the other variables 𝑥𝑥𝑗𝑗≠𝑖𝑖 are constants.

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Example: Uncertainty on mass of water collected The mass of water collected (𝑚𝑚𝑤𝑤) is the difference between the mass of the beaker and water combined (𝑚𝑚𝑤𝑤𝑏𝑏) and the mass of the empty beaker (𝑚𝑚𝑏𝑏) 𝑚𝑚𝑤𝑤 = 𝑚𝑚𝑏𝑏𝑤𝑤 −𝑚𝑚𝑏𝑏

(8)

This mass calculation is to equation 2. (The sum and difference are equivalent.) You should be able to find the uncertainty on the density using equations 1, 2, and 5.

𝜎𝜎𝑤𝑤 = �𝜎𝜎𝑏𝑏𝑤𝑤2 (1)2 + 𝜎𝜎𝑏𝑏2(−1)2 = �𝜎𝜎𝑏𝑏𝑤𝑤2 + 𝜎𝜎𝑏𝑏2 (9)

In equation 9 𝜎𝜎𝑏𝑏𝑤𝑤 and 𝜎𝜎𝑏𝑏 are the uncertainties on the measured mass of the full and empty beakers, respectively. Equation 9 can be rewritten in a dimensionless form and simplified by dividing by 𝑚𝑚𝑤𝑤 and squaring the equation.

�𝜎𝜎𝑤𝑤𝑚𝑚𝑤𝑤

�2

= 𝜎𝜎𝑏𝑏𝑤𝑤2 + 𝜎𝜎𝑏𝑏2

𝑚𝑚𝑤𝑤=𝜎𝜎𝑏𝑏𝑤𝑤2 + 𝜎𝜎𝑏𝑏2

𝑚𝑚𝑏𝑏𝑤𝑤 −𝑚𝑚𝑏𝑏 (10)

The term in parentheses in equation 10 is a dimensionless ratio that might be called the fractional uncertainty. Sometimes these are also expressed as % uncertainties. The % uncertainties are obtained from the fractional uncertainties by multiplying them by 100 %. Notice an important feature of equations 9 and 10: If the uncertainty on either measured mass (𝑚𝑚𝑏𝑏𝑤𝑤 or 𝑚𝑚𝑏𝑏) increases, then the uncertainty on the calculated mass (𝑚𝑚𝑤𝑤) will also increase. In your experiments for lab 1, you will also need to calculate differences (like 𝑇𝑇2 − 𝑇𝑇1) products (like �̇�𝑄) and ratios (like 𝜂𝜂). Therefore, you will need to propagate uncertainties using all of the formulas in equations 1 through 7.

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Essentials for Successful Group Work In CBE 101 lab you have to work in groups. Some of you will thrive in this setting; others will feel frustrated, annoyed, or perplexed. Successful group work requires that conflicts be (1) prevented, (2) identified and (3) resolved. The next three sections describe these steps. Preventing Conflicts in Groups If each member of your group has these seven expectations, you group will avoid most conflicts. This list is what I expect from all of you as individuals and as groups.

1. Successful group work requires engagement. Everyone is expected to make contributions to the

group. If someone is not contributing the group should encourage that person to engage.

2. Successful group work requires communication. Be very clear with your group about how you will communicate, and then always respond in a timely way. If you agree to communicate by email, always reply to your groups’ email messages, and don’t leave people out. Always share electronic files and data collected during the lab with the entire lab group as soon as possible. This way if the one person who has the data loses it or cannot attend a group meeting, the group can still function.

3. Successful group work requires planning. Everyone has different priorities and schedules. Be sensitive to other peoples’ priorities. Your evening job is not more important than another student’s weekend leisure activity. Evenings and weekends are just that – evenings and weekends. As long as people agree to commitments and contributions and follow through with them, there should be no complaints about how other people manage their time. For that agreement to happen, your group needs to plan meetings, contributions, and deadlines.

4. Successful group work requires flexibility. Things will never go the way that you think they will. Someone (maybe you) will not meet a deadline. It could be that their contribution was just way more difficult and time-consuming than anyone thought it would be. Ask for help when you need it, and be helpful when you can. Be willing to change your plans if necessary.

5. Successful group work can be accomplished remotely. It is ok if one person cannot meet with the rest of the group. That person can still make valuable contributions by performing calculations, writing and editing sections of a report, and sending them to the rest of the group by email.

6. Successful group work requires extra time. Do not expect that every group will work efficiently and effectively from the very start. Everyone has a different schedule, level of understanding of the material, writing ability, work temperament, personality, etc. Excellent groups spend some extra time communicating, planning, meeting, and double-checking and editing the contributions of their group mates.

7. Successful group work will result in a better product than individual work. Everyone in your group should have the goal of producing a better report than any of you could produce on your own. You should expect that what you will write or calculate will be checked, edited, and improved by others in your group, and that you should spend some time similarly improving what they produce. You should not be offended if others edit what you write, and you should not begrudge the need to spend extra time editing your group members’ contributions. These activities are an essential part of group work that will help you become a better student and a better engineer!

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Identifying Sources of Conflict Your group is almost guaranteed to encounter situations that could lead to conflict. By considering the following scenarios before (or during and after) they occur to you, your group might avoid conflict.

1. One or more group members are doing all the work, while one or a few of the others are doing

very little. The solution is ENGAGEMENT. This can happen for a variety of reasons, and is not the way a successful group should function. Non-contributing members might feel uncertain about their ability, uncomfortable asking questions, or simply un-interested in working with a group. The more active members of the group can prevent conflict by communicating that they value the contributions of the less active members. This can sometimes be accomplished by asking questions. “Do you understand this calculation?” “How do you think we should estimate this uncertainty?” “Can you please read what I wrote and suggest some edits?” “Could you double check these calculations – I’m not sure I have this unit conversion right.” Failing to engage only reinforces the behavior of the non-contributing members.

2. One group member cannot meet a deadline or join the group at an agreed meeting time. The solution is COMMUNICATION. This group member might be hesitant to admit that they need help completing something, or that they didn’t do a good job managing their time. This attitude is understandable – but the group member should heed item 2 in the first list. The best way to avoid conflict is to tell the group exactly what is going on, and make alternative arrangements. If they remain silent, the rest of the group will likely come to the logical conclusion that the absent or delinquent member doesn’t want to contribute or is just being rude and inconsiderate. The group should respond by giving delinquent members the benefit of the doubt – offer to help, expect that the member can still finish the work, be flexible and willing to re-arrange the workload to include this member to the extent possible.

3. Group members have different priorities. The solution is PLANNING. Discussing why a group can’t meet on a particular weekend or weeknight will only lead to the group making subjective judgments about whose activities and schedules are more important (is studying for an exam for another class, taking an extra shift at work, or attending a friend’s wedding a legitimate reason to miss a meeting? As a group, you cannot prioritize other people’s activities.) As a group, you have to agree to plan around each other’s conflicts without trying to manage their time for them. Students should always be present during class, unless they have a conflict due to a University sanctioned event (e.g. NCAA sports teams, etc.). Outside of class students should have several hours per week to dedicate to this class, but those particular hours might not always coincide, so you have to plan and be flexible.

4. One group member has consistent rude or unhelpful behavior. The solution is COURTESY. A student who is consistently un-responsive to emails, fails to meet previously agreed obligations, or is otherwise inconsiderate of group members will cause a conflict within a group. The best way to avoid this is to not be that guy! The entire group needs to communicate about this behavior early so that it doesn’t lead to extra work for the rest of the group members. They should also communicate concerns to the instructor as soon as they become apparent.

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Resolving Conflicts Despite your best efforts, some conflicts will arise. When that happens, here is what you should do:

1. Let me know that your group has a problem, and exactly what that problem is. This should be

done as soon as the conflict arises. Email or a visit to my office is best.

2. Suggest reasonable solutions. Your ideas about how everyone should get along are probably the best ideas (and might be more agreeable to you than my solution!).

3. Err on the side of restoring and redeeming successful group work. You do not absolutely have to work in a group outside of class to be successful in CBE 101. If your group absolutely cannot function, you may be permitted to submit lab reports on your own – but that is rarely the best solution.

4. Do not allow the behavior of one group member to cause a lot of anxiety or extra work for the rest of the lab group. Recognize that there is a problem and take the steps above to resolve it!

If you let me know that your group has a conflict, this is what you can expect from me:

• I will want to know exactly what the problem is and what steps you have taken to resolve (or perhaps complicate) the situation.

• I will discuss the conflict with all members of the group, and expect you to do the same. • I will suggest a short-term course of action for the current situation. This might be a

redistribution of the immediate workload, a meeting with the entire group, or that some group members work separately.

• I will coach the group on how to relieve the pressures that led to the conflict in the first place. This rarely involves the behavior of a single group member. Usually, even if one group member is causing headaches for everyone else, the group’s responses are just as important as the original offenses.

• Groups might be reassigned – especially in the case of ‘no-fault’ types of conflicts – such as complete incompatibility of the various group members’ class and work schedules.

• I will expect that you provide continued feedback on how the conflict is being resolved. A note on leaving a lab group member’s name off of a lab report: If your group has one or more members who are making no substantial contribution to the group’s work, then their name should not be included on the lab report. Note that this is NOT a solution to a conflict – this is a sign that there is a problem within the group that needs to be addressed. You should NOT do this if a group member is demonstrating genuine enthusiasm or interest in contributing but is just unhelpful, clumsy, or incompetent. If your group submits a report with one or more names missing, you should also do the following:

1. Notify me that your group is having a problem and what the problem is. 2. Notify the delinquent member (or ask me to do it for you). Don’t surprise them on the day that

the report is due! 3. Provide that group member with the data your group has collected in the lab, especially if they

participated in the lab activity. They will need the data if they choose to write and submit their own lab report.

4. Expect that any present conflict can be resolved so that the group can continue to function well on future work.

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Laboratory Report Instructions All lab reports should conform to the following format. • Use 8 ½” × 11” page size, single-spaced, 12-point font, 1-inch margins, and consistent typeface. • Two to three pages of text is a good length for most reports. Use the length you need to

communicate everything that you need to say, without adding extra, superfluous text just to fill space. Graders don’t like to read more than they have to!

• Figures and tables should be included as needed, but these do not count toward total length. • Figures and tables should be prepared in a professional manner, preferably using engineering

software. Hand-drawn illustrations may be ok in some situations, as long as they are well-prepared. Prepare figures electronically whenever possible. Physical quantities should include units and uncertainties, and only the correct number of significant digits. See pages 8-10 for more information on how to correctly report significant digits and uncertainties.

• All display items (figures, tables, etc.) should be numbered and have a brief caption (placed below the image for figures, including graphs, schemes, and diagrams) or title (placed above, for tables). See your textbook for examples of how to correctly label figures and tables. Display items should be referred to in the text by their number.

• All equations should be prepared professionally (e.g. using Insert Equation in MS Word) and set on their own line. Define all symbols used, and use consistent notation.

• Include the names of all lab group members that contributed to the experiments and the preparation of the report.

• Everything that you write should be in your own words! Do not copy text from the lab description or others’ lab reports!

See the included examples of excellent and poor lab reports. The entire report (including appendices) should be prepared as a single file and submitted electronically, via Canvas. Supporting files such as Matlab programs or Xcel spreadsheets may also be submitted, but it is not ok to submit multiple versions or several files containing different sections of the text!

Writing style tips Writing a group lab report is a group effort. Each member of the group makes some contributions, and the report might be compiled by one or two people. However, every member of the group should read the final report before it is submitted. Do not simply cut and paste sections written by different people together and expect to have a good report. Plan on spending some time editing the final version to make it cohesive. If several people write different sections, you may need to add appropriate transitions, move text from one section to another, delete redundant or contradictory statements, and edit for consistent use of wording and notation. Writing as a group should be an exercise that improves everyone’s final product, rather than a compilation of errors. Do not be offended if a group member suggests re-wording or deleting something that your wrote. The objective should be to produce the best final product. Here is a list of additional things to check when editing: • Check the spelling and grammar. Use good sentence structure. Eliminate run-on sentences. Make

sure that the subject and verb are in agreement, and use parallel constructions effectively. • Use good paragraph structure. Eliminate single-sentence paragraphs. • Organize ideas logically within paragraphs and within sections. • Strive for smooth flow of ideas. Ideas should be introduced and supported, and the transition to the

next idea should make sense. Use consistent wording, notation, and voice throughout. • Check the tone. It should be professional but not stilted. • Confirm correct units and significant figures on all physical quantities. • Re-read the lab instructions to be sure that you have answered all of the questions.

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Suggested outline I. Introduction (or Overview, or Objective)

In one or two paragraphs, describe the objective/goal of the experiment. Concisely describe the physical principle investigated.

II. Materials and Equipment (or Experimental Apparatus)

In one or two paragraphs, briefly describe the materials and equipment or apparatus that were used. Explain any special preparations that were required.

III. Procedure (may be combined with the previous section for simple experiments, but for complex

or multi-step procedures this might be a separate section) In your own words, briefly summarize the steps taken during the experiment. Provide enough detail so that someone who is unfamiliar with the experiment would understand what you did and why you did it. Be sure to describe any departures from the standard procedure.

IV. Results and Discussion

Report your results and observations. For quantitative experiments, be sure to provide the raw data and the equations used in your calculations, as well as the final results. If original data are extensive, they could be included as an appendix and referred to in this section. Tables, graphs, and figures should be used effectively to highlight key findings and to summarize your results. Discuss what you concluded from the results obtained and the observations made. Explain the reason(s) for any discrepancies in your results, even if it is necessary for you to make educated guesses. Be sure to answer any questions posed in the lab guide for the experiment. Include discussion of possible sources of error and uncertainty in experimental measurements. Separate “Results” and “Discussion” sections might be appropriate.

V. Conclusion

In a single paragraph, briefly summarize the key results and the main points from your discussion in section IV. This section might be missing if separate “Results” and “Discussion” sections are used. In this case, the last paragraph of the “Discussion” should be the Conclusion.

VI. References A list of references (if any) cited in the body of the report.

VII. Appendices

Include data and notes collected during the lab, and hand-written example calculations. This is particularly important to demonstrate correct use of units. Since these are your lab notes, it is ok to cross out a mistake and correct it. Do not erase!

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Example Lab Reports

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CBE 103: Chemical and Biological Engineering III

Fall 2008 Lab 10 – U-Tube Manometers

In this laboratory assignment you will explore the concept of static fluid pressure, by measuring the pressure of a column of fluid. You will compare the pressures of various fluid columns to the theoretical pressures that these columns should generate. The columns of fluid will be created by filling a reservoir with a volume of fluid. The pressure will be measured using a U-tube manometer. Principles: The pressure generated by a column of fluid at rest is called the hydrostatic pressure. Recall that a pressure, 𝑃𝑃, can be defined as a force, 𝐹𝐹, acting on an area, 𝑘𝑘.

𝑃𝑃 =𝐹𝐹𝑘𝑘

(25)

In the case of the hydrostatic pressure of a column of liquid, the force is the force of gravity acting on the mass of liquid, and the area is the area cross-section of the column. The force, 𝐹𝐹, in equation 1 can be written as: 𝐹𝐹 = 𝑚𝑚𝑚𝑚 = 𝑚𝑚𝐴𝐴ℎ𝑘𝑘 (26) Where 𝑚𝑚 is the gravitational acceleration, 𝐴𝐴 is the fluid density, and ℎ is the distance from the top of the column to the point where the pressure is being measured. Inserting the right-hand side of equation 26 into equation 25 yields: 𝑃𝑃 = 𝐴𝐴𝑚𝑚ℎ (27) Thus, the difference in pressure, Δ𝑃𝑃 = (𝑃𝑃2 – 𝑃𝑃1), between two heights 𝑧𝑧2 and 𝑧𝑧1 can be written: Δ𝑃𝑃 = 𝐴𝐴𝑚𝑚(−Δ𝑧𝑧) (28) Manometer operation: A U-tube manometer is illustrated in Figure 10.1. A U-shaped tube is filled with a fluid, and the difference in the height of the fluid on either side of the “U” is used to determine the difference in fluid pressure on either side of the tops of the tubes. Experiments: The apparatus for this lab is illustrated in Figure 10.2. You have three cylindrical graduated vessels of different diameters (2, 3, and 5 cm) and three fluids of different densities (water, 50 % 2-propanol in water, and 50 % sucrose in water). Each vessel is equipped with a mercury-containing U-tube manometer that measures the pressure at the bottom of the column relative to the atmosphere.

𝑧𝑧1 𝑧𝑧2

𝑃𝑃2 𝑃𝑃1

𝑧𝑧1

𝑧𝑧2

𝑃𝑃2 𝑃𝑃1

a.

b.

Figure 10.1. A U-tube manometer with 𝑃𝑃1 = 𝑃𝑃2 (a.), and with 𝑃𝑃1 < 𝑃𝑃2 (b.).

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Data collection and analysis: Use the smallest cylinder to measure the pressure of three different columns of water of different heights. You may use the common pressure units of mmHg (millimeters of mercury) since this is the natural pressure units for a mercury-filled manometer. Verify that the apparatus is properly calibrated. (Hint: you can use equation 28 to calculate both the pressure of a column of liquid water of known height and the pressure reading of the manometer. The density of liquid mercury is 13.534 g cm-3. And the density of water is 1 g cm-3.) Once you have verified that the smallest cylinder is properly calibrated, repeat the experiment with the other three cylinders. Does the diameter of the cylinder affect the measured pressure? Why or why not?

Now use one or more of your cylinders to measure the density of the other two liquids (50 % 2-propanol in water, and 50 % sucrose in water). Caution: Mercury is a hazardous material. The U-tube manometers contain mercury. While the manometers are designed to be safe to handle, you should be careful not to break them. If mercury is accidentally released, do not touch it or attempt to clean it. Let the lab assistant know immediately. The lab should be evacuated and the CSU Environmental Health and Services office (491-6745) should be notified so that properly trained professionals can clean up the mercury spill.

Figure 10.2. Apparatus for this lab: three graduated cylinders of different diameters, each equipped with a mercury-filled U-tube manometer that measures the pressure at the bottom of the cylinder.

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Lab 10 CBE 103 Group 51 Ima Student Mia Smarts Allan A. Day A U-tube manometer is a device for measuring pressure, which is based on equation 28. In fact, equation 28 is sometimes referred to as “the manometer equation.” We used a manometer to measure the pressure of a column of three different liquids, using three different columns. We also measured the pressures for various heights of the liquids to find out how the density changes with pressure or column height. Each column measured the correct pressure for water even though they are different diameters. The area for a circle is πD2/4. So, when you compute the area for each cylinder, you get a different number. But equation 28 doesn’t have the area or the diameter in it so it doesn’t matter. We measured the density of the other two liquids. They are: Propanol + water = - 0.9 g/cm3 Sucrose + water = 1.2 g/cm3 The densities of the mixtures are different because propanol is a liquid, but sucrose is a solid, so when you mix them with water, propanol makes the liquid density go down and sucrose makes the liquid density go up.

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Lab 10, CBE 103 Group 61 (Ike Newton, Joey Gibbs, and Mary Currie)

Hydrostatic pressures and manometers

Objective The objective of this lab is to use U-tube manometers to measure the hydrostatic pressure of columns of three different fluids. The hydrostatic pressure is the pressure caused by the weight of a stationary column of a fluid. The hydrostatic pressure depends upon the height of the fluid column and the fluid density according to the manometer equation:

∆𝑃𝑃 = 𝑚𝑚𝐴𝐴(−Δ𝑧𝑧) This principle of hydrostatic pressure can be used to measure unknown pressures, if a fluid of known density is used. This is the principle of a U-tube manometer. A U-tube manometer is a device that measures a pressure difference by the change in the height of a column of a liquid of known density. A common fluid used in manometers is mercury, thus pressure is sometimes measured in “millimeters of mercury” (mmHg), which has dimensions of pressure, not length. Apparatus and Procedure Three columns of different diameters were provided. The columns are each connected to a U-tube manometer so that the pressure at the bottom can be measured, when the columns contain a fluid. The columns are also marked with graduations so that the height of the liquid inside the column can be easily measured. The first step is to ensure that the columns and manometers are properly calibrated. To do this, we filled the smallest column with water to three different heights and measured the hydrostatic pressure at each height. Then the density of water could be computed. Since we know the density of water, if we got a correct result, we knew that the manometer and cylinder were properly calibrated. Next we performed the same procedure with the other two cylinders, to examine how the results might change when the cylinder diameter was changed. Once we had verified that the pressure was independent of cylinder diameter, we used the smallest cylinder to measure the unknown densities of two liquid mixtures (50 % 2-propanol in water and 50 % sucrose in water). To measure the density, the pressure of a known height of each fluid was measured, and the manometer equation was re-arranged to obtain the density:

𝐴𝐴 =∆𝑃𝑃

𝑚𝑚(−Δ𝑧𝑧)

Even though only one measurement was necessary to obtain the density for each liquid, we actually made three measurements for each liquid at different column heights. Results The manometer readings at different water heights for each of the three cylinders are shown in table 1. A copy of our data table that we used to collect these data and example calculations are also attached. We noted that the pressure readings corresponding to each height were approximately the same for each cylinder, which means that the pressure does not depend on the diameter of the cylinder. The density of water was computed from the equation above for each manometer reading. We obtained densities for water very close to 1 g/cm3 for all of the calibration experiments, indicating that manometers and cylinders were properly calibrated.

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Table 1. Manometer readings and computed water density for each cylinder. Small Cylinder Medium Cylinder Large Cylinder

Water column

height (cm)

Manometer reading (mmHg)

Computed water density

(g/cm3)

Manometer reading (mmHg)

Computed water density

(g/cm3)

Manometer reading (mmHg)

Computed water density

(g/cm3) 10 7.5 1.02 7.5 1.02 7 0.95 20 14.5 0.986 15 1.02 14.5 0.986 30 22 0.998 22 0.998 22 0.998

Next we measured the densities of the other two liquids. For this experiment, we used only the smallest cylinder. Our data for these experiments are shown in Table 2. Our data sheets and example calculations are also attached Table 2. Manometer readings and computed densities for solutions with unknown densities.

50 % 2-propanol in water 50 % sucrose in water Fluid

column height (cm)

Manometer reading (mmHg)

Computed fluid density

(g/cm3)

Manometer reading (mmHg)

Computed fluid density

(g/cm3) 10 6.5 0.884 9 1.22 20 13 0.884 18 1.22 30 20 0.907 27.5 1.22

Discussion For the second part of the experiment, the pressure should not depend upon the diameter of the cylinder. The pressure is caused by the weight of the liquid column. There is more liquid in a larger diameter column, but the force is also distributed over a larger area. So increasing the mass of the liquid increases the pressure, but increasing the area over which the force is distributed decreases the pressure, so the pressure in the manometer equation does not depend upon the diameter of the cylinder. (The diameter cancels out.) Before doing the third part of the experiment, we did not realize that only a single measurement was necessary to determine the density of each liquid. We performed three measurements for each liquid. However, since we had multiple measurements, we could compare them and see that our data for each measurement were fairly close. (The error on the density was < 5 %.) The error that we did observe probably comes from trying to measure the pressure precisely. The manometer has increments of 1 mm marked on it, but some of the measurements were between mm markings so we estimated, for example 6.5 mmHg for the 10-cm column of 2-propanol solution. The manometer equation predicts that the pressure should be a linear function of the height of the column, so we plotted the data in Table 2, to see if they are straight lines with intercepts of 0. This plot is shown in figure 1, at the right.

Figure 1. Pressure versus fluid column height showing the linear relationship for two fluids.

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We tried to look up the density of a 50 % 2-propanol solution, but we were not able to find it from a reliable source. We did find the density of 2-propanol in a chemical engineering textbook. 2 It was reported to be 0.785 g/cm3. Our measurements indicate that the 50 % 2-propanol solution in water has a density about half-way between the density of pure 2-propanol and the density of pure water (1 g/cm3). The density of sucrose solutions is reported in the CRC Handbook of Chemistry and Physics. 3 A 50 % aqueous sucrose solution should have a density of 1.2295 g/cm3, according to this reference. Thus, our measured density for the 2-propanol solution is reasonable, and our measured density for the sucrose solution is very close to the accepted value. Our team noted that in this lab we used the manometer equation to measure pressure (when the height and density of the fluid were known) and to measure density (when the height and the pressure were known). We thought that it might also be possible to measure an unknown height of a fluid (if the pressure and density were known). It is apparent that the manometer equation and the concept of hydrostatic pressure are very important, having applications in a variety of chemical and biological engineering problems. They could be used at the design stage to ensure that a vessel is designed to withstand the pressure that it will be subjected to during operation. They could be used in a production setting to measure the pressure in a fluid or process. And they could be used in an analytical setting to measure the density of an unknown fluid. One of our group members suggested that the manometer equations looks a lot like the Bernoulli equation, with the kinetic energy term set to 0 and the whole equation multiplied by the density. Since the Bernoulli equation comes from the total energy balance, we think that the manometer equation might also be related to the physical law of conservation of energy. But another group member realized that the manometer equation doesn’t have any energy terms in it. So as a group, we are not sure whether they are related. Energy is related to forces (force x distance) and pressures (pressure x volume). Potential energy is also related to g and height (mgz). It does seem that all of the terms in the manometer equation can be related to energy. We will ask the instructor whether the manometer equation can be derived from the total energy balance.

2 R. M. Felder and R. W. Rousseau, Elementary Principles of Chemical Processes, 2nd Ed. New York: John Wiley & Sons., 1986. 3 CRC Handbook of Chemistry and Physics, 88th Edition (Internet Version), David R. Lide, ed. Boca Raton: CRC Press/Taylor and Francis, 2008. Accessed through the Colorado State University Library catalog website at http://catalog.library.colostate.edu, on Oct. 21, 2008.

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Group Assessment Form This form must be submitted by each member of the group. Evaluate each member of your group (including yourself� in terms of how each member performed relative to what the group expected of that individual in attending and participating in the lab and preparing editing and submitting the assignments. Use a scale of 0-10, where

• 0 represents ‘did not meet any of the expectations’ • 10 represents ’fully met all expectations’.

Member name Rating (0-10)

(me)

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Essential Web Resources for CBE Students

Wikipedia and Google do not know everything. Wikipedia is a reliable source for most science and engineering topics. Like all texts (print or electronic) it does contain some errors and misinformation. CBE students at CSU should be familiar with the other web resources on this list. The sources are trusted and some are suitable to be used as primary sources (e.g. it is appropriate to cite them as a reliable source in homework, reports, or publications). Others are simply helpful compilations of useful information. URLs are subject to change. 1. Resources about Chemical and Biological Engineering:

Our department website - The difinitive source for authoritative information about our program and classes. cbe.colostate.edu/

The American Institute of Chemical Engineers - The professional organization with

lots of information for all things related to our profession. www.aiche.org/

The Society for Biological Engineers - A group of biological engineers within AIChE. www.aiche.org/sbe/

2. Authoritative texts, available electronically through the CSU library’s website. If you are on campus, you should be able to access these texts on your computer. Alternatively, you could actually visit the library in person and read a real book!

CRC Handbook of Chemistry and Physics - An essential compilation of data important for anyone working in the physical sciences and engineering.

Perry's Chemical Engineer's Handbook - The go-to source for a primer on just about

any fundamental topic in the core sub-disciplines of CBE. This book also contains lots of useful data.

Kirk-Othmer Encyclopedia of Chemical Technology - A relatively comprehensive

collection of articles on many chemical engineering topics. The Knovel Library - A very large collection of web books in science and engineering.

Many of these broad categories are useful for CBE's, but the most important is the "Chemistry & Chemical Engineering" category. From there, browse the subtopics to see how things are arranged. This library contains very valuable handbooks and classic textbooks in chemical engineering. The Knovel Library is updated with new editions and new texts as they become available. Treasures buried here include:

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DIPPR - Design Institute for Physical Properties is a source for physical, thermodynamic and transport properties.

The Merck Index - An Encyclopedia of Chemicals, Drugs, and

Biologicals.

Polymer Handbook - Physical properties and reactions of polymers and monomers.

Properties of Gasses and Liquids - A handbook for thermodynamic

properties and phase equilibria of fluids. 3. Alternatives to Wikipedia - Online sources for physical properties and engineering data include:

NIST Chemistry WebBook - A standard reference for chemical properties. webbook.nist.gov/

IUPAC Goldbook - IUPAC Compendium of Chemical Terminology. goldbook.iupac.org/

The Engineering Toolbox - Lots of standard information here. Think of this when

you're looking for something that should be an appendix in a book on your shelf, but you aren't even sure which book has that appendix.

www.engineeringtoolbox.com/