labreport4 322 uploaded
Post on 04-Jun-2018
217 Views
Preview:
TRANSCRIPT
8/13/2019 LabReport4 322 Uploaded
http://slidepdf.com/reader/full/labreport4-322-uploaded 1/12
MAE 322
Thermal and Fluids Lab
Instructor
Dr. Gall
Flow Measurement using the Bernoulli Principle
Submitted by
April 3, 2013
1. Introduction
8/13/2019 LabReport4 322 Uploaded
http://slidepdf.com/reader/full/labreport4-322-uploaded 2/12
2. Experimental Apparatus and Procedure
2.1 Apparatus
2.2 Procedure
Pitot-Static Tube and Turbine Meter
1. First, the local air temperature and barometric pressure are recorded.
2. The manometer is set to zero with no flow in the duct.
3. The pitot-static tube is aligned with the axis of the duct.
4. The blower to drive the air flow in the duct is turned on.
5. Next, the deflection in the manometer is recorded.
6. The time for the flow meter to complete 10 revolutions is recorded.
7. The pitot tube is then moved in quarter inch increments towards the far wall of the duct.
8. Steps 5-7 are repeated until the tube is at the desired position.
Venturi Meter and Rotameter
1. First, the water pump is turned on and the desired flow rate is set on the rotameter.
2. The valve on the outlet of the venture meter is set, so the water levels in the manometer
are within the graduated scale.
3. The values for each tube are recorded.
4. The flow rate is increased by the 1 gallon per minute.
5. Steps 3 and 4 are repeated for the desired values until the flow rate can no longer be
increased.
2.3 Data Reduction
8/13/2019 LabReport4 322 Uploaded
http://slidepdf.com/reader/full/labreport4-322-uploaded 3/12
First, the atmospheric pressure will be converted from millimeters of mercury to pounds per
square foot. Next the density will be calculated will be calculated using the determined
atmospheric pressure and the room temperature. The ideal gas law is used
and is given by the following equation.
After determining the pressure and density, the change in pressure will be determined using the
density, gravity, and the height. The equation is given by
The velocity of the pipe will be determined using a simplified version of the Bernoulli equation.
Next, numerical integration will be used to determine the mass flow rate. Since the
measurements were taken in quarter inch increments, the velocity will be taken for quarter inch
spacing. The results will be tabulated in a table. The equation for mass flow and the integral over
the radius are given by the following equations
The integral will be taken from 0 to the total radius, but since the integration will be calculated
numerically, a summation will be used. The equation is given by
The average velocity will be calculated using the total mass flow rate, area, and density. The
equation is given by
8/13/2019 LabReport4 322 Uploaded
http://slidepdf.com/reader/full/labreport4-322-uploaded 4/12
Next, the flow rate will be determined for the pitot tube and the flowmeter. The flow rate can be
calculated using a simple formula using the velocity and the cross sectional area of the pipe.
First, the velocity of the fan will be determined by taking the change in distance of the change in
time, and the determined velocity of the fan will be used to determine the velocity of the pipe.
Then, the flow rates can be determined using the following equation
Next, the calculations will be determined for the venturi meter. First, the it will be
assumed that the actual flow rate and the flow rate for the rotometer are equal. The equation for
the actual flow rate is given by the following formula
where A2 is the throat area and A1 is the inlet area. The equation can be rearranged to determined
the value for C. The equation is given by
The change in pressure will be calculated by using the difference between the highest and lowest
reading values on the venturi meter. The equation is given by
Then the height of H2O will be converted to a change in pressure given in pounds per foot
squared. Lastly, the Reynolds number will be calculated using the following formula.
8/13/2019 LabReport4 322 Uploaded
http://slidepdf.com/reader/full/labreport4-322-uploaded 5/12
3. Theory
The theory of this lab is simple overall. Measurements were taken using various devices.
This lab focused on the application of the Bernoulli equation. In the first part of the experiment,
the velocity was determined using a simplified portion of Bernoulli’s equation. The portion used
is given by
Also, the bernouli principle was used to measure the flow rate of the fluid using the venturi
meter. The flow in a venturi meter is calculated in a very similar way to the flow calculated in
the orifice meter. For the pitot-static tube, the flow velocity is accurately measured as long as the
flow behaves normally. Basically, the Bernoulli principle is applied in nearly all fluid flow
applications. The principle states that for incrompressible flow, the summation of the dynamic
pressure, static pressure, and pressure head are equal to a constant.
4. Discussion and Results
The first part of the lab was done in the Pitot Tube where it was moved a quarter of an inch
down from the top after each recording. These results are found in Table 1: Pitot Tube Data. This data
was then used to determine the velocity of the air being blown through the pipe. The closer the pitot
tube got to the center of the pipe the higher the velocity got. In Figure 4.1, a plot of the radial position
versus the velocity can be seen. It can be seen that when the pitot tube passes the center of the pipe the
velocity will begin to decrease.
8/13/2019 LabReport4 322 Uploaded
http://slidepdf.com/reader/full/labreport4-322-uploaded 6/12
Table 1: Pitot Tube Data
r Δh Tamb Pamb ρamb ΔP V
in in R lb/ft2 sl/ft3 lb/ft2 ft/s
2.375 0.125 534 2039 0.002225147 0.650708333 24.18403928
2.125 0.375 534 2039 0.002225147 1.952125 41.88798476
1.875 0.625 534 2039 0.002225147 3.253541667 54.07715579
1.625 0.875 534 2039 0.002225147 4.554958333 63.98495362
1.375 1.125 534 2039 0.002225147 5.856375 72.55211783
1.125 1.375 534 2039 0.002225147 7.157791667 80.2093842
0.875 1.625 534 2039 0.002225147 8.459208333 87.19679366
0.625 1.875 534 2039 0.002225147 9.760625 93.66438136
0.375 2.125 534 2039 0.002225147 11.06204167 99.71334839
0.125 2.375 534 2039 0.002225147 12.36345833 105.4157833
8/13/2019 LabReport4 322 Uploaded
http://slidepdf.com/reader/full/labreport4-322-uploaded 7/12
Figure 4.1: Plot of the radial position versus the velocity of the air in the pipe creating a velocity
profile.
From this same data the velocity profile can be used for numerical integration. This integration
can be used to find the mass flow rate of the air in the pipe. In Table 2: Numerical Integration of Velocity
Profile, these values can be seen. As the radial position gets closer to the center the mass flow rate
decreased.
-2.500
-2.000
-1.500
-1.000
-0.500
0.000
0.500
1.000
1.500
2.000
2.500
0 20 40 60 80 100 120
R a d i a l P o s i t i o n
Velocity (ft/s)
8/13/2019 LabReport4 322 Uploaded
http://slidepdf.com/reader/full/labreport4-322-uploaded 8/12
Table 2: Numerical Integration of Velocity Profile
Location r r from CL dr ΔP V ṁ
in in in in H20 ft/s sl/s
1 0.125 2.375 0.25 0.09 20.50967 0.00118173
2 0.375 2.125 0.25 0.13 24.64955 0.00127076
3 0.625 1.875 0.25 0.15 26.47786 0.00120443
4 0.875 1.625 0.25 0.16 27.34622 0.00107807
5 1.125 1.375 0.25 0.17 28.18784 0.00094029
6 1.375 1.125 0.25 0.175 28.59936 0.00078056
7 1.625 0.875 0.25 0.18 29.00505 0.00061571
8 1.875 0.625 0.25 0.18 29.00505 0.00043979
9 2.125 0.375 0.25 0.18 29.00505 0.00026388
10 2.375 0.125 0.25 0.175 28.59936 8.6729E-05
Table 3 shows a comparison of the mass flow rate, velocity and the volumetric flow rate of the
pitot tube and fan flowmeter. These values were all greater at the pitot tube than at the fan flowmeter.
This could be because the pitot tube was closer to the air source than the fan flowmeter which was at
the end of the tube.
Table 3
ṁ Vavg Q
sl/s ft/s CFM
Pitot Tube 0.007862 25.9253 211.5505
Fan Flowmeter 0.000212 0.693 5.67
8/13/2019 LabReport4 322 Uploaded
http://slidepdf.com/reader/full/labreport4-322-uploaded 9/12
In the second part of the lab pressure differences were looked at through a venture meter using
different flow rates. There were a total of eleven different tubes that were filled with different H2O
heights which were due to the pressure at that point in the pipe. These values and they’re pressure in
lb/ft2 can be seen in Table 4. These pressure results were then graphed on Figure 4.2 and it can be seen
that as the flow rate decreases the less the pressure differential there is between the largest pressure
and smallest pressure poin
Figure 4.2: Plot of the pressure differential versus the position of the tube for each flow rate.
0
5
10
15
20
25
30
35
40
45
50
0 2 4 6 8 10 12
Δ P
x
5.7 GPM
4.7 GPM
3.7 GPM
2.7 GPM
1.7 GPM
Δh ΔP Δh ΔP Δh ΔP Δh ΔP Δh ΔP Δh ΔP Δh ΔP Δh ΔP Δh ΔP Δh ΔP Δh Δ
GPM in H2O lb/ft2
in H2O lb/ft2
in H2O lb/ft2
in H2O lb/ft2
in H2O lb/ft2
in H2O lb/ft2
in H2O lb/ft2
in H2O lb/ft2
in H2O lb/ft2
in H2O lb/ft2
in H2O lb/5.7 213 43.65382 207 42.42413 151 30.94707 69 14.14138 88 18.03538 132 27.05307 155 31.76686 172 35.25097 184 37.71034 192 39.34992 196 40.1
4.7 231 47.34287 227 46.52308 186 38.12024 128 26.23328 139 28.4877 174 35.66087 190 38.94003 203 41.60434 209 42.83403 211 43.24392 220 45.0
3.7 209 42.83403 205 42.01424 180 36.89055 144 29.51244 150 30.74213 175 35.86581 184 37.71034 192 39.34992 196 40.16971 200 40.9895 202 41.
2.7 197 40.37466 194 39.75982 179 36.6856 159 32.58665 161 32.99655 174 35.66087 179 36.6856 184 37.71034 185 37.91529 188 38.53013 189 38.7
1.7 201 41.19445 200 40.9895 189 38.73508 176 36.07076 178 36.48066 184 37.71034 186 38.12024 189 38.73508 190 38.94003 191 39.14497 193 39.5
Table 4
Tube F Tube G Tube H Tube J Tube K Tube LFlow Rate
Tube A Tube B Tube C Tube D Tube E
8/13/2019 LabReport4 322 Uploaded
http://slidepdf.com/reader/full/labreport4-322-uploaded 10/12
Table 5 shows the comparison of the discharge coefficient and the Reynolds Number for each
flow rate. This comparison was then plotted on Figure 4.3.
Table 5
FlowrateC
ΔP Re
GPM lb/ft2
5.7 0.947698 29.48 17387.88
4.7 0.927592 21.09 14394.88
3.7 0.913297 13.31 11259.36
2.7 0.877025 7.78 8266.368
1.7 0.671029 5.12 5130.849
Figure 4.3: Plot of discharge coefficient versus the Reynolds Number.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 5000 10000 15000 20000
C
Re
8/13/2019 LabReport4 322 Uploaded
http://slidepdf.com/reader/full/labreport4-322-uploaded 11/12
5. Conclusions and Recommendations
In conclusion this lab gave greater detail on different ways of measuring pressure in pipes of
different fluids. The pitot-static tube is useful in determining the pressure at different internal radiuses
of a pipe, which then can be used to determine velocity profile in the pipe. This can be helpful in
knowing the type of flow that is being produced in the pipe. In the venturi meter the measured pressure
drop of the fluid flowing in the pipe is very helpful when the pipe may only be able to hold a certain
pressure drop. By changing the flow rate of the fluid entering the pipe can change how the pressure
drop is affected.
References
MAE 322 “Impact of a Jet.” Experiment #1 handout.
8/13/2019 LabReport4 322 Uploaded
http://slidepdf.com/reader/full/labreport4-322-uploaded 12/12
Appendices
top related