Conservation of Energy Long Form Final

8/10/2019 Conservation of Energy Long Form Final

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Conservation of Energy

Fluid Mechanics ME 332

Tyler Finses

Tuesday 11:20 AM

Ethan

11/4/2014


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Abstract

The main principles of this report are to reinforce the concepts of control volume analysis and

the conservation of energy using the energy equation. A characteristic load curve will be examined in

detail in addition to a system load curve that will determine the operation point. Pressure drop across

valves and tubes will be examined in detail to look at the losses associate with these flows. Three

separate experiment will be done to prove key concepts of the conservation of energy.

Each of the experiments was approached with an experimental mind set but also a predictive,

mathematical mindset that will challenge the experimental results. This will help to verify the results.

Prior to the first experiment the operating point will be predicted using the parallel combined system

model. This will be compared with the measured operation point found in the first experiment using the

pressurized flow system. The predicted operation point and the measuring point calculated out to be

within 5% of each other giving a high confidence in the accuracy of the experiment.

In the second experiment the FLL unit will be in conjunction with several DMM units to measure

the pressure drop across 3 given valves. Those valves are the gate valve, globe valve, and butterfly valve.

Each valve has a unique internal geometry that causes losses. The valve that causes the lowest pressure

differential is the gate valve due the non-intrusive nature of the gate mechanism. Following the gate

valve was the butterfly and globe valve in that order.

In the last experiment the loss values were calculated for a plumbing structure made up of

individual components that all added to the K value. The effects of gravity were also examined and

found to be negligible for plumbing structures with a delta z that is not extremely large. This is due to

the density of air being extremely light in comparison to most fluids.


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Table of Contents

Abstract ......................................................................................................................................................... 2

Nomenclature ............................................................................................................................................... 4

Introduction .................................................................................................................................................. 5

Description of Experiment 1 ................................................................................................................... 11



Experimental Setup ..................................................................................................................................... 17

Procedure Experiment 1 ......................................................................................................................... 17



Results and Discussion ................................................................................................................................ 20

Results Experiment 1 .............................................................................................................................. 20



Conclusions ................................................................................................................................................. 30

Appendix ..................................................................................................................................................... 31

References .................................................................................................................................................. 32


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Nomenclature- Internal discharge coefficient- Discharge coefficient of the jet

- Discharge coefficient of the stack

g- Gravity

h- Height

hl- Head loss

- Mass fluxp- Fluid pressure

patm- Atmospheric pressure

prec- Recorded pressure

ps- Static pressure

pt- Stagnation pressure

A - Area

K- Loss coefficient

L- Jet span

Q- Flow rate

- Average velocity- Fluid velocity vectorV- Velocity

W- Jet width

- Shaft work- Change in pressure-Kinetic energy correction factor- Density- Degree of valve opening- Dimensional coefficient for the jet- Dimensional coefficient for the stack


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Introduction

There are a total of 3 separate experiments that are to be conducted in this experiment. These

three experiments will prove the conservation of energy theme of this lab using the pressurized flow

system, and two different experiments that use the FLL system. This lab will reinforce concepts of

control volume and energy equation formulation related mostly to the characteristic curve, system load

curve, and operating point. Last several pressure drop characteristics of 3 different valves will be

analyzed to determine several values.

The formulation of conservation of energy has already been done out in the classroom portion

of ME 332 but the basics will be reviewed for the clarity of this report. This experiments assumes

incompressible flows, zero heat added, the flow is at steady state, and the gravitational effects do not

play a part. For a fixed control volume the energy equation is given below in equation 1.

( )

Equation 1:

In equation 1 is the work done by a machine with and describing the fluid velocityvector and speed to the second power. The variables p and representing the fluid pressure anddensity respectively. The source of the negative sign is based on a sign convention from

thermodynamics that says the sign of machine work is defined as positive for output out of a control

volume. In this case the sign is negative because energy is inputted into the system. The last term in the

equation describes losses that are irreversible processes. In this case we are talking about processes

that convert mechanical energy to thermal energy typically through friction. These losses in flow


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situations are called loss coefficient K and the head loss . Mathematically they can be defined byequation 2 below. In this equation and are the mass flux and characteristic average flow in thetube where the loss occurs. K is a dimensionless quantity and has units of length.

Equation 2:

Equations 1 and 2 are the base for what will be expanded on in terms of the control volume

analysis. It is often assumed that the pressure is uniform across the inlets and outlets of a control

volume when doing calculations with equation 1. This cannot be assumed for the kinetic energy flux

which must be integrated in terms of which is the kinetic energy correction factor. This allowsaverage quantities to be used when calculating the kinetic energy flux. This is detailed in equation 3.

( )

Equation 3:

Alpha, the kinetic energy correction factor, is equal to unity under a uniform velocity profile and

is greater than unity for velocity profiles that are not uniform. In the case of turbulent flows alpha is

between 1.04 and 1.11. Equations 1,2 , and 3 can be combined into the following equation.

Equation 4:

Each of the subscripts 1 and 2 represent the inlet and outlet respectively. This makes V the

velocity at the inlet and the outlet and all the other variables stay consistent with their previous


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definitions. The equation could also be applied to systems with multiple inlets and outlets using a

summation of the inlets and outlet.

In a system the pump provides a power input to the system. The power in does not often get

translated into flow rate. The true flow rate is determined by the power input and the load that is seen

throughout different parts of the flow.

The characteristic cure will now be introduced and dissected. If a fan or pump is examined with

equal inlet areas and outlet areas it is expected that V1 = V2and that 12. Then if all the losses are

collected under pump efficiency the actual power delivered to the flow is the result of the equation

below.

Equation 5:

The simple relation of simplifies the above equation into the following.

Equation 6:

As it would seem, the pump will increase the pressure in the flow which is a direct result of the

power being delivered to the flow. In the example of the FLL system the FLL draws air from the test

section and delivers it to the ambient in the lab. This makes it pretty clear that . In the caseof the PFS it is totally opposite.

The characteristic curve is the relationship between pressure rise and flow rate in a pump.

Additionally it is a function of the device type and internal design. The characteristic curve is typically


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provided by the manufacturer. The characteristic curve of the fan that is in the PFS system has been

determined in previous experiments and is displayed below. The PFS uses a centrifugal fan that is driven

at a constant rpm resulting in the particular characteristic curve.

Figure 1: The Characteristic curve.

The change in p, pressure differential, across a flow system describes a system load curve. The

relationship associated with this is represented by . This can be examined in the case of thePFS as a flow passes over the sharp edge of the jet. Previously it has been proven that [ ]and Q gives the volume flow rate.

Equation 7:

-1.00E+00

0.00E+00

1.00E+00

2.00E+00

3.00E+00

4.00E+00

5.00E+00

0 200 400 600 800 1000 1200 1400 1600PressureRisePpl-Patm(InchesWater)

Flow Rate Q (CFM)

Characteristic Curve vs. System Load Curve


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Equation 8:

The additions in this equation as far as variable are limited to cdwhich is the slit jet discharge

coefficient. In this case the value is given to be 0.61. The slip jet follows a simple square law behavior

provided in the previous equation is a dimensioned coefficient. By applyingequation 5 along with the idea that we can obtain a slightly more useful equation.

Equation 9:

A1 and A2represetn the inlet and outlet areas and A is the area where losses occur. and K areindependent of the Reynolds number and velocity and therefore are not functions of flow rate.

There is one special case for equation 10 that uses constant area, so that the velocity in is equal

to the velocity out. An example of this flow system would be flow through a 90 degree elbow, or a

valve. In these flows there is a pressure drop across system that is a result of the system loss coefficient.

That is described by the equation below.

Equation 10:

The operating point is the joint solution of two curves. Those curves are for a flow passage that

is connected to a plenum that has a system load curve ( and a characteristic curve that isdescribed by . The operation conditions of this flow are determined from the graphical


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intersection of the two curves. This is often referred to as the system operating point. A simple

operating point graph is shown below.

Figure 2: The system operating point.

Figure 2 represents a system that has what is called a single prime or single load combination

that uses the square-law system loading curve. In other words this would work for a PFS with only one

inlet and one outlet, but it will not work with the PFS set up in the lab unless the stack is closed. In the

case of this experiment the stack opening will be at a fixed opening of 3.5 inches. In this case the system

is in a parallel configuration. The combined system loading curve for the parallel set up is described by

following equation.

[ ]Equation 11:


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The flow rates through the slit jet and the stack are Qjand Qs respectively

.

Figure 3: The flow rates through the slit jet and stack.

Description of Experiment 1

In the first experiment the pressurized flow system, or PFS for short, will be used to measure the

operating point of the PFS. Prior to measuring the operation point, the operating point will be predicted

using a series of equations.

The stack open diameter that was given was 3.5 inches. Therefore, the entire experiment will

revolve around that opening diameter. Using equation 12 the system load curve for the slit-jet can be

obtained.

Equation 12:

In equation 12represents the area of the jet. This is the width and length of the jet span. Represents the slit jet discharge coefficient that is given to be 0.61. The equation can then be computed

to get the value. Simalrily equation 13 can be used to obtain the system load curve for the stack.


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Equation 13:

In order to obtain the combined system loading curve equation 14 will be used. The combined

loading curve will be very important to determine the operating point.

Equation 14


The setup for experiment 2 is shown in figure below. It consists of 3 different valves each

connected to the same plenum pressure by the same diameter and length pipe. The losses of 3

different valves will be examined in the experiment. To generate the flow for the experiment the FLL

will be used with the door open.

Figure 4: The basic set up for experiment 2.


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In equation 16 A describes the cross-sectional area of the connecting pipe. K is the valve loss

coefficient which depends on the type of valve. Between different valves the internal geometry changes

which is really what makes the K value vary. A valve is used to control the flow rate of a fluid based on

the amount the valve is opened. When the valve is being opened the K value decreases. The system

load curve for the valve also moves to the right. When the valve is being closed the K value decreases as

one would expect and the system load curve moves to the left.

Using a validyne pressure transducer and should be measured. Each valveneeds to go from fully open to fully close in 8 steps. This means that in the case of the gate valve each

step will be 1turns. In the case of the globe valve each step will be of a turn. Last the butterfly valvestep will be as marked on the top of the valve.


In the third experiment the flow rate behavior and pressure drop in a piping system is in a

system made up of several different pipe components connected together in series. The variety of

components available to use are shown below in the figure.


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Figure 6: Shows the individual components available.e:

The FLL will be used slightly different in this experiment that it is usually used. This time the

door to the FLL will be left open as shown in the figure below. This is because it is desired that the

ambient pressure in the room is desired to be the atmospheric pressure. The piping system takes the air

at the inlet outside of the FLL and flows it through the valves. This causes a pressure differential in the

tube that causes the flow. A Pitot tube is located at the centerline of the exit that will be used to

determine the velocity.

Equation 18:

The variable represents the total pressure that is given from the Pitot tube. The flow ratethrough the tube can be easily determined by using Q=VA. Q is the flow rate, V is the velocity and A is

the area of the system. A simple diagram of the entire system is shown below.

Figure 7: Basic set up.


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The pressure drop across the pipe system will be determined to determine the K and values which are

known as the system losses. The pressure drop across components composed of components

connected in series can be analyzed as the sum of pressure drops across each individual component.

This is shown mathematically in the equation below.

Equation 19

is the pressure drop across the individual component. Therefore the pressure drop across

each component can also be shown as the following equation.

Equation20:

This leaves the two system loss coefficient equations to be the result of the following equation.

Equation 21:


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Experimental Setup

Procedure Experiment 1

In the first experiment the pressurized flow system, or PFS for short, will be used to measure the

operating point of the PFS. Prior to measuring the operation point, the operating point will be predicted

using a series of equations described in the introduction. The stack open diameter that was given was

3.5 inches. Therefore, the entire experiment will revolve around that opening diameter. Using equation

1 the system load curve for the slit-jet can be obtained.

The system load curve for the slit jet can be obtained using equation 13. Using a similar

equation but different values for the stack opening, the system load equation for the stack opening can

be obtained. The parallel combined system loading curve can be determined using equation 14.

In order to measure the operation point of the PFS the PFS inlet flow rate and pressure

differential [ppl-patm] must be determined using the process previously outlined in the Conservation of

Mass principles from the conservation of mass lab. The digital multimeter (DMM) will be used to get

this value. For convenience this equation is displayed below.

Equation 22:

The PFS inlet pressure differential will help get to the flow rate which is show above. The

measurement for the PFS plenum pressure that is measured is [ ]which ismeasured in volts straight out of the DMM, but can be converting into inches of water. Then the flow

rate and change in pressure can be calculated and compared to the calculated value we predicted

earlier. This is shown in the results section.


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The set up for experiment 2 had 3 tubes connected to three different valves. A butterfly, globe

and gate valve were the three that were connected to the end of the tubes. These tubes were

connected to the flow exit portion of the test section on the FLL. This was designed in such a way that

the unrestricted flow should be even across all three tubes.

In this experiment we will be looking to obtain the loss coefficient for each of the valves, Kgate,

Kglobe, Kbutterfly, as a function of the valve opening angle. 8 increments of valve opening will be obtained in

this experiment. For each valve the increment will be different. This means that in the case of the gate

valve each step will be 1turns. In the case of the globe valve each step will be of a turn. Last the

butterfly valve step will be as marked on the top of the valve.

This experiment, unlike most others, will be done with the door to the FLL room open. This will

enable the pressure in the room to be atmospheric pressure. The FLL can be turned on and all of the

valves should be adjusted to be fully open. One valve should be chosen to perform the first data

collection. LabView is the program that is used to collect the data from the pressure taps. There are a

few preliminary set ups that need to be done in the LabView program before recording data. The first is

that the channel 0 and channel 1 must be set to Y=A0*E and Y=A1*E respectively. The A0 value is

exactly what the DMM reads out for and should be inputted for both channel 0 and channel1.

With the FLL on, door open, and all the valves open the pressure tap for the valve that will be

studied first should be connected. One person should be controlling the computer and inputting the

step number as another person changes the opening of the valve based on the earlier specified amount.


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This should be done two more times for the other two valves that are left. LabView outputs a plot that

can be seen in the results section.

Considering each of the valve openings individually the pressure drop

and

the pressure differential [ ]. With these values the average velocity for each of thevalves can be computed using the following equation.

[ ]

Equation 23:

Additionally the loss coefficient K can be computed using the following equation. This should be

done for all three valves.

Equation 24:


Experiment 3 will again use the FLL system. The setup for this experiment will have the inlet

flow of the FLL connected to 1 tube that extends into the test section area. Using individual

components a self-made plumbing system will be made by connecting several different pieces together

to form a full system. This will be done for 4 different configurations. An important note is that one of

the configurations must be out of the elevation plane of the tube. In other words an angle piece must

be used to give the plumbing system z axis height.


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This experiment will be performed with the door to the FLL room open in order to have

atmospheric pressure throughout the room. This will make calculations easier. The diameter of the

pipe that is connected to the FLL inlet should be recorded as well as the overall length. For each

configuration the pressure drop across the system, , must be determined in order tocalculate the velocity, V, and flow rate, Q, through the system. Finally the piping systems overall losses

can be calculated. The following equations can be used to calculate these values. The values will be

read off of two DMM units that are connected to respective pressure taps. It is important to record the

mpvalue of the DMM in order to convert the pressure in volts from the transducer to inches of water

which will be more useful for calculations later on.

Equation 25:

Equation 26:

A sketch of each configuration should be shown and the trend based on configurations should

be inferred from the results. The gravitational influence will also be calculated in the results section.

Results and Discussion

Results Experiment 1

The results of experiment 1 revolve around a stack opening diameter of 3.5 inches. The

predicted values of the operating point will be presented first followed by the measured values.


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System load Curve Slit-Jet

Jet Width W (in) Jet Span L (in) Jet Area AJ (ft^2) Discharge Coefficient [Cd]j j

0.75 43.5 0.22656 0.61 26.177

System load Curve Stack

Stack Diameter D (in) Stack Shape Stack Area As(ft^2) Discharge Coefficient [Cd]s s

0.75 Cylindrical 0.06681 0.61 26.177

Table 1: The results for experiment 1.

The combined system loading curve can then be found using equation 14 That value turns out

to be parallel= 15.5767 1/ft4. The system load curve which is described by the following equation can be

plotted against the characteristic curve also shown below. The predicted operating point pressure which

was found by setting the system load curve equal to the characteristic load curve was found to be 4.70536

inches of water. The predicted flow rate was easily found using the flow relation Q=VA to be 16.83cubic

feet per second.

Equation 27:


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Figure 8: Shows the characteristic curve superimposed on the combined load curve.

The experimental measurement of the operating point used the same procedure outlined in the

conservation of mass lab.

Patm-Pi (in H20) Inlet Discharge Coefficient Cd

Measured Volume Flow Rate Q

(CFS)

Plenum

Pressure (In

H20

1.4717 0.955376 7.616 2.0914

Table 2: Shows the results form experiment 1.

Using a standard percent difference calculation the percent difference between the measured

pressure differential and the predicted pressure differential can be obtained. Additionally the same can

be done for the predicted flow and the measured flow. The predicted flow and measured flow had a

large difference in the values. While energy was still conserved it would appear that there were either

significant losses or that there was an error in measurement.

-1.00E+00

0.00E+00

1.00E+00

2.00E+00

3.00E+00

4.00E+00

5.00E+00

0 200 400 600 800 1000 1200 1400 1600PressureRisePpl-Patm(InchesW

ater)

Flow Rate Q (CFM)

Characteristic Curve vs. System Load Curve

Characteristic Curve

System Load


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Pressure Percent Difference Flow percent Difference

4.6% 129%

Table 3: The percent differential.

Last in the results for experiment one the characteristic curve graph that was seen earlier was

used to show the system load curve for the gate valve. This is assuming the gate valve is superimposed

into the PFS with only one flow exit. The Gate valves system load curve was taken at all 8 increments

and plotted below.

Figure 9: The Gate Valve Load Curve and Individual Openings

0.00

1.00

2.00

3.00

4.00

5.00

0 500 1000 1500

PressureRisePpl-Pa

tm(inchesof

Water)

Flow Rate Q (CFM)

Gate Valve Load Curve At Individual Openings

Characteristic Curve

Gate 0

Gate 1/8

Gate 1/4

Gate 3/8

Gate 1/2

Gate 5/8

Gate 3/4


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Figure 10: The flow rate out as a function of gate valve opening.

Results Experiment 2

In experiment two the diameter of the pipe was measured to be 2 inches and the area of the

pipe was calculated to be 0.021817 square feet. Then for each of the valve openings the two pressure

readings were recorded and the velocity, flow rate, and K value at each point could be calculated. The

results are show below.

y = -0.97x + 0.9978y = -0.3088x + 0.9978

R = 0.9964

0.0000

0.2000

0.4000

0.6000

0.8000

1.0000

1.2000

0 1/2 1 1 1/2 2 2 1/2 3

FlowrateCFM

Area ft^2/ Valve opening in steps

Flow Rate as a Function of Gate Opening in Terms of Area and

Steps

Gate Opening in Steps

Gate Opening in Area

Linear (Gate Opening in Steps)

Linear (Gate Opening in Area)


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Gate Valve Opening

Gate Opening 0 1/8 1/4 3/8 1/2 5/8 3/4 7/8

[pi-prec] (in.H2O) 0.12 0.247 0.402 0.565 0.697 0.818 0.907 0.965

[pi-prec] (psf) 0.624 1.2844 2.0904 2.938 3.6244 4.2536 4.7164 5.018

[ppl-pi] (in. H2O) 0.698 0.585 0.453 0.314 0.208 0.115 0.051 0.014

[ppl-pi] (psf) 3.6296 3.042 2.3556 1.6328 1.0816 0.598 0.2652 0.0728

V (ft/s) 44.21 40.48 35.62 29.66 24.14 17.95 11.95 6.26

Q (ft^3/s) 0.9646 0.8831 0.7771 0.6470 0.5266 0.3915 0.2607 0.1366

K gate 0.2741 0.6732 1.4149 2.8689 5.3427 11.3409 28.3551 109.8989

Table 4: The results for the gate valve.

Globe Valve Opening

Globe Opening 0 1/8 3/8 5/8 7/8

[pi-prec] (in.H2O) 0.711 0.729 0.746 0.76 0.782 0.837 0.868 0.891

[pi-prec] (psf) 3.6972 3.7908 3.8792 3.952 4.0664 4.3524 4.5136 4.6332

[ppl-pi] (in. H2O) 0.131 0.119 0.108 0.096 0.08 0.041 0.022 0.01

[ppl-pi] (psf) 0.6812 0.6188 0.5616 0.4992 0.416 0.2132 0.1144 0.052

V (ft/s) 19.15449 18.25612 17.39189 16.39723 14.96856 10.71586 7.849578 5.292184

Q (ft^3/s) 0.417886 0.398287 0.379432 0.357732 0.326563 0.233784 0.171251 0.115458

K gate 8.653509 9.7673 11.01309 12.62224 15.58514 32.54884 62.90584 142.0599

Table 5: The results for the globe valve.


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Butterfly Valve Opening

ButterFly Opening 0 1/8 1/4 3/8 1/2 5/8 3/4 7/8

[pi-prec] (in.H2O) 0.929 0.926 0.914 0.911 0.979 1.092 1.17 1.206

[pi-prec] (psf) 4.8308 4.8152 4.7528 4.7372 5.0908 5.6784 6.084 6.2712

[ppl-pi] (in. H2O) 0.204 0.205 0.212 0.213 0.16 0.078 0.03 0.011

[ppl-pi] (psf) 1.0608 1.066 1.1024 1.1076 0.832 0.4056 0.156 0.0572

V (ft/s) 23.90287 23.96138 24.36705 24.42445 21.16874 14.78027 9.166332 5.55049

Q (ft^3/s) 0.52148 0.522756 0.531606 0.532859 0.46183 0.322455 0.199978 0.121093

K gate 7.260717 7.201966 6.873917 6.819189 9.75566 22.32143 62.18112 174.8029

Table 6: The results for the butterfly valve.

From the tables above one can rank the order of the lowest pressure drop while the valves are

fully open. From lowest pressure drop to highest pressure drop the order is the gate valve, butterfly

valve, and the globe valve. This is consistent with the internal geometry of the valve as the gate valve

when fully open is far clear of the fluid flow. Whereas the globe valve still has a significant amount of

surface area that causes a higher pressure differential over the other valves. Additionally as the value

increases the K values also increases. This is somewhat apparent upon thinking about the mechanics of

the system along with a good understanding of the definition of the K value. As the valve closes there is

more geometry that impedes the flow of fluid which causes the K value to go up by its definition. If one

does not understand the definition of the K value it can be proven mathematically as well.

In the experiment the fully closed position was not measured but one could use pattern

recognition and understanding of the concept to determine what it would be with the valve fully closed.

With the valve fully closed no fluid will flow through the valve therefore rendering the K value to be


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infinite. This can also be proven mathematically using the following equation: As the velocityapproaches zero in the equation above K approaches infinity.

The following plot shows the opening angle of each of the valves vs the respective K values for

each of the valves. Each valve type shows a similar loss coefficient at small openings up to open. For

much of that time the globe valve has a slightly higher K value than the butterfly or the gate valve. This

is most likely due to the irregular geometry in the globe valve versus the other valves geometry. At a

larger opening the data becomes a little more spread. The butterfly valve becomes the highest K value

toward the more open positions as the globe valves geometry starts get out of the way. The

butterflies geometry still has an obstruction down the middle to add to the K value.

Figure 11: Shows the loss coefficients for the three valves at each opening.

0.0000

20.0000

40.0000

60.0000

80.0000

100.0000

120.0000

140.0000

160.0000

180.0000

200.0000

0 1/8 1/4 3/8 1/2 5/8 3/4 7/8 1

LossCoeffecientK

Valve Opening (step)

Loss Coefficients vs Opening

Gate Valve

Globe Valve

Butterfly Valve


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configuration 1 2 3 4

[patm-ps] (volts) 7.31 7.24 7.24 7.26

[patm-ps] (in. H2O) 4.149156 4.109424 4.109424 4.120776

[patm-ps] (psf) 21.57561 21.369 21.369 21.42804

[pT-ps] (volts) 4.2 4.05 4.85 3.21

[pT-ps] (in. H2O) 2.38392 2.29878 2.75286 1.821996

[pT-ps] (psf) 12.39638 11.95366 14.31487 9.474379

V (ft/s) 103.1758 101.3166 110.8725 90.19981

Q (ft^3/s) 2.250946 2.210385 2.418864 1.967855

K 1.740476 1.787654 1.492784 2.261682

Table 7: The results from experiment 2.

In most calculations the gravitational constant is ignored especially when the experiment is

being conducted with a fluid that is quite light like air. The gravitational constant contribution the

pressure differential across a system can be given by the following equation: The term of the equation gives the height differential between the input and output. The height differential

in this experiment for set up number two was 0.75 ft. This made the pressure differential due to gravity

about 0.108 inches of water. In this experiment it can be seen that by including the gravitational

pressure differential was quite trivial and made a very little impact on the solution. Therefore unless the

height of the structure was much higher the gravitational portion can be ignored in calculations.


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Conclusions

After examining the results for the experiments the conservation of energy principles that were

introduced in the introduction were analyzed, measured, and confirmed. A characteristic load curve

was be examined in detail in addition to a system load curve that determined the operation point.

Pressure drops across valves and tubes were examined in detail to look at the losses associated with

these flows. Three separate experiment were done with the brief following results.

Each of the experiments was approached with an experimental mind set but also a predictive,

mathematical mindset that will challenge the experimental results. Prior to the first experiment the

operating point will be predicted using the parallel combined system model. This will be compared with

the measured operation point found in the first experiment using the pressurized flow system. The

predicted operation point and the measuring point calculated out to be within 5% of each other giving a

high confidence in the accuracy of the experiment. The flow rate measured versus predicted values

came out much worse. This was most likely due to an error in collecting data.

In the second experiment the FLL unit was used in conjunction with several DMM units to

measure the pressure drop across 3 given valves. Those valves are the gate valve, globe valve, and

butterfly valve. Each valve has a unique internal geometry that caused losses. The valve that causes the

lowest pressure differential is the gate valve due the non-intrusive nature of the gate mechanism.

Following the gate valve was the butterfly and globe valve in that order. The valve that caused the most

losses was the globe valve.

In the last experiment the loss values were calculated for a plumbing structure made up of

individual components that all added to the K value. The effects of gravity were also examined and

found to be negligible for plumbing structures with a delta z that is not extremely large. This is due to

the density of air being extremely light in comparison to most fluids.


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31

Appendix

See attached output plots from labview.


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Conservation of Energy Long Form Final