Table of Contents
Table of Contents
Table of Contents
Contents
Abstract. ..................................................................................................................................... 4
Introduction. ............................................................................................................................... 5
Objectives. ............................................................................................................................. 5
Hypothesis.............................................................................................................................. 5
Theory. ....................................................................................................................................... 6
Assumptions........................................................................................................................... 7
Equations................................................................................................................................ 8
Procedure. ................................................................................................................................ 13
Results. ..................................................................................................................................... 14
Raw data............................................................................................................................... 14
Conclusion ................................................................................................................................. 18
Recommendations/improvements. ........................................................................................... 18
References. ............................................................................................................................... 19
2
3
Abstract.
Problem statement.
During this experiment we are to find the head loss when a jet of water or fluid flows through
a set of joints that are used in plumbing. During the next part of the experiment we were to
find the effect of differential head devices in the measurement of flow rate and velocity of the
Short summary.
Both of the experiments were performed using the C6-MKII-10 apparatus to collect data
about the flow and all of these data was recorded and noted using a computer software. For
part b of the experiment the head loss in the pipe of different bends were found. The bends
were 90o long and short bends. The head loss over different other joints were found too. As
for part D the venture and orifice plates were used to measure the flow rate of the fluid.
4
Introduction.
Objectives.
During the first part of the experiment the objective was to measure the head loss of a jet of
For the second part of the experiment the objective was to show the use of head devices used
to measure the velocity and flow rate of the water moving through the experimental pipe.
Hypothesis
The hypothesis for the first part of the experiment is that if we know that the head loss is
proportional to the velocity of the flow then the head loss should be equal to the velocity of
the flow multiplied a constant K which represents the ‘loss factor ‘therefore if we know the
flow velocity then we can find the head loss. Provided we account for the effects of gravity
on the flow.
For the second part the hypothesis is that if we have many different methods/devices to
measure the flow rate through the pipe then if we find the flow rate/head loss using one
method this should be equal to the measurements obtained using the other methods.
5
Theory.
During the first part the head loss in a standard pipe fitting is to be measured. The head loss
of a pipe is proportional to the speed at which the water/fluid flows through the pipe. Since
the head loss is proportional to the velocity of the flow, we can say that the head loss is equal
to the velocity of the flow squared multiplied by a constant ‘k’ which represents the loss
factor and the whole thing is divide by ‘g’ which is the acceleration due to gravity multiplied
by 2.
For experiment 2 where an orifice plate or venturi is used the flow rate and the differential
head is related by Bernoulli’s equation which a small modification which is the addition of a
discharge coefficient which is used to account for the losses during the flow. When using a
pitot tube the deference of the head loss measured between the total and static tapping is
equal to the velocity of the head of the fluid moving through the pipe.
6
Free body diagrams.
Assumptions.
7
The density of water was assumed to be a constant 999kg/m^3.
Equations.
Part B
Part D
8
Sample calculations.
Part a
Part b
*all numbers used above are arbitrary numbers used for the purpose of showing how the calculations were carried out
9
Facility and apparatus.
1. barbed connector
2. Inline strainer.
3. sudden contraction
4. 45o “Y”
5. 45o elbow
6. Long radius 90o bend.
7. Roughened pipe.
8. Smooth bore pipe of different diameter
9. Smooth bore pipe of different diameter
10. Smooth bore pipe of different diameter
11. Smooth bore pipe of different diameter
12. ball valve
13. 90o “T” junction.
14. 90o sharp bend
10
15. short radius 90o bend
16. sudden enlargement
17. pipe section made of clear acrylic with a Pitot static tube
18. Venturi made of clear acrylic
19. Orifice meter made of clear acrylic.
20. Globe valve
21. Gate valve
22. 90o elbow
23. Exit tube.
24. Test pipe.
25. Control valves.
orifices.
were tested.
11
On the left is the
the fittings.
12
Procedure.
Part B
Fit the pressure sensor before and after the fitting that is being tested.
Make sure that the Data logging accessories are connected to the console and that they are
powered on.
Make sure the software for the console is up and running in the computer system.
Close all unwanted valves and open only the required valves to make sure the flow goes
Start up the hydraulics bench and let the flow go through the fitting.
Use the program that is loaded to measure the head tapping’s on each fitting using the
pressure sensor that are plugged in before and after the fitting.
Repeat the same procedure until all fitting have been tested out.
Part D
Open all the ball vales in the network to make sure that there a minimum restriction to the
flow.
Make sure the data logging equipment is properly connected and powered up.
Use the software to obtain different readings from the venturi and orifice plates.
Vary the flow rate using the hydraulics bench from the minimum tot eh maximum.
For every trial measure the head loss, the head difference and the volume flow rate across the
sensors.
Results.
Raw data.
14
Plot 1 'K' factor vs angle
Venturi orifice sensor
Pipe throat plate head flowmeter flowrate discharge inlet throat Theo flow
Device diameter diameter diameter loss flowrate (m^3/s) coefficient area area rate
Venturi 0.024 0.014 0.02 1.32 0.744 0.000744 0.98 0.000452 0.000154 0.002249187
Orifice 0.024 0.014 0.02 0.66 0.744 0.000744 0.62 0.000452 0.000314 0.000989474
Table 2 Data for part 2 of the experiment
Data analysis.
Theoretically the value for ‘K’ should be the same for one fitting irrespective of the flowrate.
From the graph shown above we can see that the value for ‘K’ is almost the same in every
fitting angle except for the contraction and enlargement fittings. In this case although the
angle is 180 in each case the k factor is significantly different from each other this is due to a
significant error. This error must have occurred during data analysis. As for the other
readings in the graph they are not the same due to minor errors that have been neglected or
assumed negligible.
15
For the second part of the experiment the theoretical value for flowrate was compared to the
experiment value for flow rate obtained by the sensors. As you can see from the table above
the only difference between the two devices are the discharge coefficients, throat area and the
head loss. As you can see from the table above the two theoretical flow rate are not even
close to the flowrate detected by the sensors. This anomaly could be dues to systematic error.
Since we don’t have an adequate amount of readings we cannot come to a conclusion about
the relationship between the flowrates and orifice /venturi plates neither can we come to a
conclusion about the relationship between the theoretical flow rates and experimental
16
Statement of uncertainty.
The first part of the experiment was a success for the most part. As said above almost
all the values for k are the same in the 90o and 450 fittings. The only reason as to why they are
different, are because we made certain assumption such as steady flow, incompressible flow
and that the density of the fluid is a constant. These minor variations could be a result of
these assumptions combined with human error caused when rounding off certain values that
were used to analyze the data and form the graph. As for 180o fitting it’s not possible to say
which reading is the anomaly as only two readings were taken for that specific angle. There is
a possibility were both readings could be wrong. One of the main reasons that caused this
anomaly was human error that was caused when completing certain calculations.
The second part of the experiment was inconclusive mainly because there are
only two sets of data to look at. By looking at the two sets of data the experiment was not a
success. The experimental value for flowrate which was obtain from the sensors is 0.744 for
both the orifice and the venturi. At the same time the theoretical value for venturi is 0.000989
and the theoretical value for the orifice is 0.00225. Since both of these values when compared
to the experimental value for flow rate are off by a significant amount it is safe to say that the
17
Error in flow rate (15)
Conclusion .
The first part of the experiment was a success except for the 180o fitting. It was proved that
the ‘K’ factor remains constant for a fitting with the same angle irrespective of the flow rate.
As for the second part of the experiment is was inconclusive, as there was only one data set
from one device which was not enough to come to a conclusion. Although the theoretical
value for flow rate was 0.00225 m3/s and 0.000989 m3/s for the orifice plate and the venturi
Recommendations/improvements.
Velocity of the flow could have been detected using a set of sensors thus reducing human
error. The density of the fluid should have been measured at every trial to make sure it was
constant. The fluid should have no impurities to prevent this distilled water could be used.
The value for g should have been measured at the time of the experiment without assuming it
to be 9.81m/s2. The sensor should have been recalibrated after every trial to eliminate the
chance of systematic error. Certain values should not have been rounded off to certain
18
References.
Ref 1: Certain pictures were taken past labs and some during this lab.
Ref 2: Y.A. Cengel and J.M.Cimbala, Fluid Mechanics, 3rd Edition, 2014, McGraw-Hill.
Ref 3: C.S. Subramanian, MAE 3064 Fluid Mechanics Laboratory Manual, Version 5.0,2004,
Florida Tech.
Ref 4:
https://www.google.com/search?q=velocity+profile+in+pipes+with+bends&espv=2&biw=68
1&bih=652&source=lnms&tbm=isch&sa=X&ved=0ahUKEwiTgoOT7I3QAhVD32MKHSs
uDW8Q_AUIBigB#imgrc=gP8qPjETOh6gzM%3A
19