orfice free jet flow (1).docx

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CIVIL & ENVIRONMENTAL ENGINEERING DEPARTMENT

PRAIRIE VIEW A&M UNIVERSITY

CVEG 3063 HYDRAULICS LABORATORY

FALL 2014

LABORATORY REPORT ON

ORIFICE AND FREE JET FLOW

CONDUCTED ON

NOVEMBER 6, 2014

SUBMITTED BY

SHEKHYNAH YMIAH CURTIS

ON

NOVEMBER 13, 2014

TO

DR. IFTEKHAR AHMED, PHD, PE, CPESC

HYDRAULICS LABORATORY INSTRUCTOR


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CIVIL & ENVIRONMENTAL ENGINEERING DEPARTMENT

HYDRAULICS LABORATORY

LABORATORY GRADING SHEET

FALL 2014

Title of Experiment: ORIFICE AND FREE JET FLOW

Name: Shekhynah Ymiah Curtis

Date Lab Was Performed: November 6th Report Due Date: November 13th

Ability to Conduct Experiments MAX Score Comments

Ability to demonstrate general lab safety (by your conduct and

observations).

3

Ability to follow and properly state the procedure used for the

experiment, while maintaining all safety precautions. 9

Ability to demonstrate knowledge of how equipment function, their

limitations, and the uncertainty associated with reading theinstruments.

6

Ability to collect and record data using appropriate units of

measurement and identify the dependent and independent

variables in the experiment. 15

Total for Ability to Conduct Experiments 33

Percentage for this Performance Criteria

Ability to Analyze and Interpret experimental Data

Provides appropriate abstracts for the experimental report 5

Ability to analyze the data using appropriate software to generatethe required parameters using consistent units and significant

figures.

22

Use of statistical analysis as needed including uncertainty analysis 5

Ability to present the data (raw /derived) in tabular and graphical

form to meet the objectives and to aid in interpretation. 14

Ability to discuss the raw and derived data/graphs and assess the

validity of the results in relation to the underlying theory. 14

Ability to draw appropriate and reasonable conclusions in relations

to each of the experimental objectives.

7

Total for Ability to Analyze and Interpret experimental Data

67

Percentage for this Performance Criteria

TOTAL FOR THIS LAB


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Letter of Transmittal

November 13, 2014

Dr. Iftekhar Ahmed, PhD, PE, CPESCCivil & Environmental Engineering Department

Prairie View A&M University

Dear Dr. Ahmed,

The attached technical laboratory report contains the detailed results of the Orifice and Free Jet

Flow laboratory work done on November 6, 2014. The report contains the objectives of the

experiment, the concept of .., and its implications to the observations made. Alsoincluded are raw measurements taken in the lab, details describing calculations made, and a

discussion of the interpretation of the results.

Please contact me by phone at 713.443.3623 or by email [email protected] youhave any question or regarding this report.

Sincerely,

Shekhynah Ymiah Curtis
mailto:[email protected]:[email protected]:[email protected]:[email protected]


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Abstract

The objective of the lab whose analysis is described here was to determine the correctional factor

Cvapplied to convert the ideal velocity of an projectile free jet to a more accurate velocity. Todetermine these values we used a Orifice and Free Jet Apparatus in conjunction with a hydraulic

bench and analyze results according to projectile motion physics concepts. The results discovered

may help up us to understand orifice free jet flow and raise questions as far as the implications of

friction and also from a technical stand point may help us to draw conclusions about the usefulness

of the common engineering estimations and equations.

Dimensions in this report are presented in both SI units.


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Table of Contents

PageAbstract.. iv

List of Figures.....vi

List of Tables.vii

1. Ability to Conduct Experiments..11.1 Introduction..11.2 Theory11.3 Material and Apparatus .31.4 Experimental Safety.. 3

1.5 Experimental Procedure.... 31.6 Experimental Data................................... 4

2. Ability to Analyze Experimental Data .....52.1 Computational Analysis .....52.2 Presentation of Tables of Derived Results .....5

3. Ability to Interpret Experimental Data .... 63.1 Interpretation of Results ...63.2 Conclusions .......63.3 Recommendations ........7

References.....8

Appendix:Equations Used ...... 9


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List of Figures

Page

Figure 1: Orifice and Jet Apparatus Diagram.........1


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List of Tables

Page

Table 1: Raw Data ....... 4

Table 2: Calculated Data for 0.06mm Orifice.......... 5

Table 3: Calculated Data for 0.03mm Orifice . 6


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Chapter One: Ability to Conduct Experiments

1.1 Introduction

This experiment is based on concepts of projectile motion (see Equations 5 and 6 below),Bernoullis Energy equation (see Equation 1), and the idea that a factor, in this case velocity thatdescribes some part of a process, in this case free jet projectile motion calculated according to

simplified equations is bound to be inaccurate to some degree because of factors that the equation

may not take into consideration. In evens such as these we try to identify a correctional factor that

will describe how a calculated velocity differs from the actual velocity. This lab will describe the

analytical process to discover that correctional factor.

1.2 Theory

The following illustration shows the basic setup of the Orifice and Free Jet setup.

Figure 1: Orifice and Jet Apparatus Diagram

To begin the analysis of the free jet flow in terms of velocity, we can begin with Bernoullis energyequation.

Eqn. 1

where, P = pressure (Pa)

Z = height displacement from the origin (m)

V = velocity of flow (m/s)

= specific weight. (N/m3)g = gravitational acceleration (m/s2)

We know that the pressure at (1) is atmospheric and therefore negligible because the tank is open

to the atmosphere. We can see that the height displacement term, Z1, corresponds with h on the


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diagram. We know that we negate the velocity at (1) because the tank is significantly larger in

volume than the free jet flow. We know that the pressure at (2) of the free jet is again atmospheric

and negligible. And lastly, we know that the height displacement at (2) with the orifice being the

origin is zero. Considering these things, we can reduce Bernoullis equation to the following,

Eqn. 2

where, h= displacement from origin to (2), referred to as headin this report, (m)

In terms of velocity at (2) this relationship is,

Eqn. 3If we know that the V2that we calculate using the above equation is more accurately the theoretical

or ideal velocity rather than the actual velocity, then there may be a relationship between the ideal

and the actual velocities such that,

Eqn. 4where, Cv represents a correctional factor.

Because the free jet can be analyzed as a projectile, we can form the following relationships in

terms of vertical and horizontal displacement of the Free Jet Flow.

Eqn. 5Where, x = horizontal displacement of the jet, (m) as a function of

t = time (s)

Also,

Eqn. 6Where, yo= initial displacement

Vo= initial velocity

Because there is no initial displacement, nor initial velocity, this equation can be rewritten as,

Eqn. 7Or as a function of time as,

Eqn. 8

Now if we plug in Equation 4 and Equation 8 into Equation 5 we get a relationship in terms of

horizontal displacement that reduces to,

Eqn. 9


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1.3 Materials & Apparatus

-

F1-10 Hydraulics Bench, designed to measure flow rate in terms of velocity, volume, and

time.

- F1-17 Orifice and Jet Apparatus

1.4 Materials & Apparatus

The hydraulic bench should be set up so that the flow rate is steady, and the head does not

fluctuate. Also the projectile free jet should move at a consistent trajectory. With the Orifice and Jet

Apparatus attached, adjust the needles so that the tip of each only barely touches the water flow.

Once the needles are set, attach white paper on the clip board above the needles in order to trace

and then measure the horizontal distance on vertical distances from the origin at the orifice to a

point along the trajectory of the flow. The X and Y coordinates found will enable the experimenter

to find the correctional velocity factor, CVaccording the relationship described by Equation 9.

1.5 Experimental Safety

Because water may have the tendency to spray or splash, experimenters should wear goggles while

working with the fluids. Also experimenters should wear gloves or be prepared to wash if they

come into contact with any of the fluids.

1.6 Experimental Data

The head, h, for both orifice diameters was measured and maintained at 0.389m.

Table 1: Raw DataOrifice Diameter (mm) Horizontal distance, x (m) Vertical distance, y (cm)

0.04 0

0.09 0.01

0.14 0.01

0.19 0.025

6 0.24 0.04

0.29 0.06

0.34 0.08

0.39 0.105

0.04 0

0.09 0.006

0.14 0.0145

0.19 0.027

3 0.24 0.041

0.29 0.0635

0.34 0.0845

0.39 0.113


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When measuring the jet trajectory of the flow for both orifices, the needles remained setup the

same way as far as horizontal distance. In other words, the horizontal distances are determined by

experimental setup and not the free jet trajectory. The vertical displacement, however, increases as

horizontal distance increases. In other words, the further from the origin horizontally, and to the

right, the further down vertical displacement of the trajectory is. Note that positive x-direction is

measured to the right and the positive y-direction is measured down.


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Chapter Two: Ability to Analyze Experimental Data

2.1 Computational Analysis

By Equation 9 we can see that is also true that where Cvis a function of x and y, alsonoting that the vertical distance, y, is a function of the horizontal distance, x. By plotting a graph of x

versus yhwe can derive a slope where, . Using the slope and two data points that fallexactly on the best fit line we can determine Cvfor each orifice. We can also determine the percent

by which Videalchanges when multiplied by the correctional factor, Cv.

In order to create these graphs we need to calculate, , and . It alsohelps to calculate manually however these calculations dont take into considerationdata points that deviate from the best fit line.

2.2 Presentation of Tables of Derived Results

The following table shows calculation needed to determine Cv.

Table 2: Calculated Data for 0.06mm Orifice

0 - -

0.062 1.99 0.722

0.062 3.100 1.122

0.099 2.66 0.963

6 0.125 2.760 2.658 0.962

0.153 2.622 0.950

0.176 2.662 0.964

0.202 2.666 0.965

Average Manually Calculated Cv: 0.949


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Here we see that the experimental measurements were relatively consistent in that only threedeviate from the best fit line. According to the graphs the slope is 0.5434, which make Cv= 0.920.

The ideal velocity of the free jet from the orifice should be adjusted by 92% to more accurately

reflect the actual velocity. Whats interesting here is how much the Cvby the slope differs from themanually calculated Cv.

Table 3: Calculated Data for 0.03mm Orifice

0 - -

0.049 2.573 0.931455

0.075 2.575 0.932050.102 2.560 0.926973

3 0.126 2.760 2.625 0.950199

0.157 2.549 0.922585

0.181 2.590 0.937661

0.210 2.570 0.930081

Average Manually Calculated Cv: 0.933

y = 0.5434x - 0.0069

R = 0.9778

0

0.05

0.1

0.15

0.2

0.25

0 0.1 0.2 0.3 0.4 0.5

(yh)^0.

5

Horizontal distance, X (m)

0.06 mm Orifice Diameter


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Here we see that the experimental measurements were relatively consistent in that only twodeviate from the best fit line. According to the graph the slope is 0.572, which make Cv= 0.874.

y = 0.572x - 0.0104

R = 0.9921

0

0.05

0.1

0.15

0.2

0.25

0 0.1 0.2 0.3 0.4 0.5

(yh)^0.

5

Horizontal distance, X (m)

0.03 mm Orifice Diameter


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Chapter Three: Ability to Interpret Experimental Data

3.1 Interpretation of Results

For the 0.06mm orifice, the ideal velocity of the free jet from the orifice should be adjusted by 92%to more accurately reflect the actual velocity. For the 0.03mm orifice the ideal velocity of the free jet

from the orifice should be adjusted by 87% to more accurately reflect the actual velocity. Ninety-

two percent of the actual velocity is relatively close. Eighty-seven percent is less accurate but still

close. It would seem that the for some reason calculations with the 0.03 orifice offers less accurate

results than the 0.06mm orifice. It could be a possibility that with a narrower orifice there are other

slight factors that come into play that these calculation do not account for. For example I would

guess that with a smaller orifice, friction would be more of a factor. Even though the control volume

of the free jet ideally stays the same as it exits the orifice, I am sure that on a more detailed scale

that control volume diameter widens which would allow velocity to slow down more and therefore

allow friction to intrude more on the flow of the free jet.

Also, we note that in both cases the correctional factor decreasedthe ideal velocity rather than

increased it. Again, this echoes the fact that there must be some factor that slows velocity that isntaccounted for using Bernoullis equation or projectile motion equations.

3.3 Conclusions

In conclusion this experiment and analysis demonstrates how calculation such as those presented

here, (see Theory and Computational Analysis) provide Water Resource Engineers with closely

accurate values that model real-life situations. The correctional factors for the two orifices only

adjust the ideal velocity by a relatively small percentage.

3.3 Recommendations

I would like to know how to compensate for a slower velocity due to friction. A question that

remains is why the correctional factor is greater for the smaller orifice and why it deviates more

from a manually calculated correctional factor when the correctional factor for the wider orifice

more exactly matches manual calculations.


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ReferencesDaugherty, Robert L., Joseph B. Franzini, and E. John. Finnemore. Fluid Mechanics With Engineering

Applications. New York: McGraw-Hill, 1985. Print.

Appendix: Equations Used

Eqn. 9


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orfice free jet flow (1).docx

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