Abstract
The main purpose of this try things out was to show how the chaffing factor may differ with Reynolds number by simply manipulating the flow rate of the liquid in a tube. The main rule used in the experiment was your Bernoulli’s formula, taking significant head deficits into account. These kinds of major head losses were normally because of wall scrubbing in the pipe and viscous forces among layers within a fluid.
Usually the results obtain from the try things out do believe the assumptive prediction plus the discrepancy from the points since shown inside the moody data was relatively small.
Inside the laminar movement and violent flow place where the frictional factor beliefs are similar to the values inside the moody data.
The relative roughness benefit obtained for the water line was zero. 0008, depending on the details plotted around the moody graph. There were a lot of options for errors from this experiment just like systematic mistakes, human errors, equipment constraints and some elements that were not really taken into consideration during analysis with the data.
The key errors engaged human and equipment limitations, which brought on the data items obtained to alter from the expected theoretical beliefs. The factors and presumptions made had been that the small head failures were negligible, which might not have been the truth. The thickness and viscosity values from the data piece might have as well introduced error into the benefits.
Introduction
Theory and Principles
In this research, the theory and principles in used is definitely the loss of strength and total head of fluid as a result of frictional resistance of genuine or viscous fluid. In fully produced straight tube flow, energy loss or head failures occurs as a result of wall chaffing. These loss are usually known as the major brain losses (hLmajor).
Other than significant head loss, minor mind losses (hLminor) too arise due to loss due to bends, contractions, valves, and others. To calculate main head damage, the solution in used is
In which is known as the friction aspect
May be the length of the water line
To determine the kind of flow whether in alisar or thrashing region, Reynolds number can now be used. For a laminar flow, the Reynolds number could be up to 2k while for a whole turbulent stream, the Reynolds number could be up to 4,000. Reynolds amount can be determined using the formula, Re =
In which Ï= denseness of the substance
V=average fluid speed flowing through pipe
D= size of pipe
= dynamic viscosity of the liquid
Next, to determine the friction element for laminar flow, this can be a function of Reynolds’s quantity and the method used can be f= For turbulent location, f is a function of Reynolds’s quantity and family member roughness (ï¥/D or k/D) and these kinds of values can be discovered from the Moody Chart and Table almost eight. 1 (Munson et. ‘s., 2006) Background
The Darcy-Weisbach equation started and given its name two wonderful hydraulic engineers of the middle 19th hundred years.
One of them is usually Julies Weisbach, a German engineer who also proposed in 1845 the equation inside the form we are using today where. Yet , he would not provide satisfactory data for the variance in f with velocity. Thus, his equation performed poorly in comparison to the empirical Prony equation, which was widely used at that time, where a and b are empirical scrubbing factors pertaining to the velocity and velocity squared.
Before Weisbach, in about 1770, Antoine Chezy, released an equation for flowin open programs but Chezy’s work was lost until 1800 the moment his ex – student, Prony published a merchant account to describe this. Darcy, who will be Prony’s pupil, then released new relations for the Prony rapport. The equation is
In which c, m and elizabeth are empirical coefficients to get a given form of pipe. Darcy thus released the concept of the pipe roughness scaled by diameter; which is known as the comparable roughness when ever applying the Moody Chart today. Ways of Reducing Water pipe Losses
Making use of the equation of major brain losses, Pipe losses could be reduced by various ways these kinds of asIncreasing how big is pipe or perhaps using a water pipe with greater diameter. A larger diameter can cause the hL to be smaller sized while additional parameters stay constant. Small size of water pipe will often play a role in higher tube loss because the water line size is reduced, the pressure at the pump inlet increases.
Reducing the flow price of the fluid. By reducing flow rate, the variable V in the equation is going to reduced which will result in a smaller hL.
Using a smoother water pipe which is also an alternative to reduce head loss as smoother tube means smaller sized f. Using a smaller farrenheit the substance will encounter less friction when going in the tube and thus head loss can be reduced. Apart from that, the surface of the water line can also be waxed to reduce the friction between your fluid as well as the pipe.
Trial and error Procedures
1) Firstly, the water is usually fed by using a straight tube.
2) The flow charge of normal water is then controlled using a circulation control device facing the volumetric tank and measured by collecting the water inside the tank after which divide how much water collected over time taken.
3) The inlet tube is then linked directly to table supply intended for higher flow rates and a Hoffman clamp is definitely clamped with each of the water manometer
connection pipes.
4) Test rig movement control control device is then closed and zero flow reading is obtained from mercury manometer. The flow control valve is then opened fully and head loss shown by simply mercury manometer is then scored.
5) The flow rate and the temperatures of normal water are after that measured.
6) For decrease flow costs, the outlet pipe can be connected to the outlet at the bottom of the regular head fish tank while the outlet to the reservoir is coupled to the beach supply. The pressure drop is then measured applying water manometer instead of mercury manometer.
7) The experiment is then repeated six moments to get six diverse flow prices for each high and low flow costs with cheapest value of around 30mm elevation difference in the manometer studying.
Pictures of Experimental Machine
Inlet Pipe
Drinking water Manometer (For small
Pressure drop, low flow rates)
Mercury Manometer (For larger
Pressure distinctions, high flow
Rates)
Stream control control device
Measuring Cyndrical tube
Thermometer
Stopwatch
Results
Step 1 : The following formula have been used to estimate Re and friction element for every remark
/ kg/m3 value obtain from furniture of drinking water properties at t/ occitan value obtain from tables of normal water properties in t/oC
Diameter from the pipe, D/m (0. 003m)
Speed of circulation in the water pipe, V/ ms-1
Exactly where velocity of the flow, V/ ms-1= Price of flow / Area of pipe
=
Calculation of head reduction, hL on every observation
While and (due to arrangement of the manometer which cancel out the height difference)
Pressure transform for normal water monometer
Pressure modify for mercury manometer
; where M is the length of pipes in meters, meters (0. 5m)
Tables of result
For low flow charge
Volume of water, Versus
Period, t/s
Temperature, T/oC
V1/ml
V2/ml
average V/m3
t1
t2
tave
T1
T2
Tave
water
148. 00
149. 00
1 ) 49×10-4
30. 13
30. 15
30. 18
28. 00
27. 00
twenty seven. 00
134. 00
134. 00
1 . 34×10-4
35. 15
30. 25
35. 20
27. 00
twenty-eight. 00
27. 40
126. 00
124. 00
1 . 25×10-4
30. 20
40. 10
30. 12-15
twenty-eight. 00
27. 00
27. 50
112. 00
113. 00
1 . 13×10-4
30. 12
31. 30
30. 20
twenty-eight. 00
27. 00
twenty seven. 50
96. 00
ninety six. 00
9. 60×10-5
40. 20
30. 35
30. 25
28. 00
28. 00
27. 60
sixty six. 00
65. 00
6th. 55×10-5
30. twenty-five
35. 10
30. 18
twenty eight. 00
27. 00
27. 50
hi/mm
hf/mm
change in elevation, †h/m
h1
h2
average hi there
h1
h2
typical hf
210. 00
210. 00
210. 00
89. 00
fifth there’s 89. 00
89. 00
zero. 12
200. 00
2 hundred. 00
200. 00
93. 00
93. 00
93. 00
0. 10
195. 00
195. 00
195. 00
96. 00
ninety six. 00
96. 00
zero. 10
188. 00
one-hundred and eighty-eight. 00
188. 00
ciento tres. 00
103. 00
103. 00
0. 09
one hundred and eighty. 00
180. 00
180. 00
109. 00
109. 00
109. 00
0. ’07
173. 00
173. 00
173. 00
125. 00
a hundred and twenty-five. 00
125. 00
0. 05
denseness of water, Ïwater
viscosity of water, water
thickness of atmosphere, Ïair
996. fifty nine
almost eight. 520E-04
1 . 23
996. 45
8. 610E-04
1 ) 23
996. 45
8. 610E-04
1 . 3
996. 45
8. 610E-04
1 . 23
996. forty-five
8. 610E-04
1 . 23
996. forty five
eight. 610E-04
1 . twenty three
Diameter of pipe, m = zero. 003 meters; Length of water line, L sama dengan 0. 50 m Volumetric flow level, m3s-1
Velocity, V/ms-1
Lso are
Pressure change, †P/Pa
Brain loss, HL/m
frictional factor, n
5. 93E-06
0. seventy
2445. 96
1181. 55
0. 12
0. 0293
4. 44E-06
0. 63
2179. 41
1044. 66
zero. 11
0. 0319
four. 15E-06
0. 59
2036. 40
966. fifty-five
0. twelve
zero. 0338
3. 73E-06
0. 53
1829. 73
829. 86
0. ’08
0. 0360
3. 17E-06
0. 45
1558. seventy nine
693. 18
0. 07
zero. 0414
2 . 17E-06
zero. 31
1066. 19
468. 63
0. 05
zero. 0598
Gravitational speed, g = 9. seventy eight m/s2; Part of pipe, A = πd2/4 = six. 07×10-6 m2 For high flow rate
Volume of normal water, V
Time, t/s
Temperature, T/oC
V1/ml
V2/ml
average V/m3
t1
t2
Tave
T1
T2
Tave
mercury
156. 00
one hundred and fifty six. 00
1 . 56E-04
five. 19
5. 20
five. 20
28. 00
twenty-eight. 00
28. 00
174. 00
174. 00
1 . 74E-04
6. 20
six. 20
6. twenty
28. 00
28. 00
28. 00
186. 00
187. 00
1 . 87E-04
several. 15
7. twenty
several. 18
28. 12
twenty-eight. 10
28. 10
157. 00
156. 00
1 . 57E-04
six. 20
7. twenty
six. 20
28. 00
twenty-eight. 00
28. 00
143. 00
141. 00
1 ) 42E-04
8. 20
almost 8. 06
8. 13
twenty nine. 00
29. 00
29. 00
137. 00
136. 00
1 . 37E-04
15. 30
15. twenty
12-15. 25
29. 10
twenty nine. 10
29. 15
hi/mm
hf/mm
change in height, †h/m
h1
h2
average hi
h1
h2
average hf
362. 00
362. 00
362. 00
twenty-one. 00
21. 00
twenty one. 00
0. thirty four
345. 00
345. 00
345. 00
36. 00
thirty six. 00
36. 00
0. 31
323. 00
323. 00
323. 00
57. 00
57. 00
57. 00
0. twenty seven
287. 00
287. 00
287. 00
92. 00
92. 00
92. 00
zero. 20
256. 00
256. 00
256. 00
122. 00
122. 00
122. 00
0. 13
209. 00
209. 00
209. 00
166. 00
166. 00
166. 00
0. ’04
density of water, Ïwater
viscosity of drinking water, water
density of air, Ïair
density of mercury, Ïmercury
996. thirty-one
8. 330E-04
1 . twenty-three
13559. 53
996. 31
almost 8. 330E-04
1 . 3
13559. 53
996. twenty-eight
almost eight. 483E-04
1 . 3
13559. 29
996. 23
8. 483E-04
1 . 23
13559. 53
996. 02
8. 100E-04
1 . 23
13557. twelve
995. 99
8. 133E-04
1 . 23
13556. eighty six
Diameter of pipe, g = 0. 003 meters; Length of tube, L sama dengan 0. 50 m Volumetric flow price, m3s-1
Velocity, V/ms-1
Re.
Pressure change, †P/Pa
Brain loss, HL/m
frictional factor, n
3. 00E-05
some. 25
15243. twenty-four
42026. 62
4. 30
zero. 0280
2 . 81E-05
several. 97
14246. 10
38082. 77
3. 85
0. 0291
2 . 60E-05
3. sixty-eight
12956. 20
32782. 67
3. 35
0. 0292
2 . 17E-05
3. 08
10834. 67
24032. 82
installment payments on your 46
0. 0306
1 . 75E-05
2 . 47
9115. 27
16512. ’04
1 ) 69
0. 0326
almost 8. 95E-06
1 . 27
4652. 17
5298. fifty five
0. 54
0. 0398
Gravitational acceleration, g = 9. 81 m/s2; Area of tube, A sama dengan πd2/4 sama dengan 7. 07×10-6 m2
Step 2: Plotting from the f above Re graph (Refer to moody graph) Does low Re benefit matches together with the theoretical line? ()
Yes, usually the laminar and turbulent movement matches with all the theoretical collection in the moody graph. Will the high Lso are value circumstance matches with a particular comparable roughness, series? Yes, the high Re case fits with a particular relative roughness line inside the moody chart. What do you imagine the family member roughness, value is for the pipe in your experiment? The relative
roughness worth for the pipe through this experiment is 0. 0008.
The friction factor in the turbulent regime estimated)
From desk 8. 1-Introduction Fluid Mechanics MYO, the value if relative roughness, ε = zero. 0015mm
The diameter, D in the pipe= 3mm
Which means relative roughness value ε/D= (0. 0015)/(3)
= 0. 0005
From the moody data, the chaffing factor worth relative to the Reynolds’s number in the turbulent regime is as follow: Reynolds’s No .
Friction component form theoritical data
Friction Factor of fresh data
Percentage error, %
15243. 24
0. 029
zero. 0280
3. 45%
14246. 10
0. 030
zero. 0291
3. 00%
12956. 20
0. 031
0. 0292
5. 81%
10834. 67
0. 032
zero. 0306
4. 38%
9115. 27
0. 035
zero. 0326
6. 86%
4652. 17
0. 038
0. 0398
-4. 74%
The proportion error is definitely calculated by applying the following formulation: (ftheory-fexperimental)/ftheory times 100%
Step four
Assuming that the value of viscosity,. The value of viscosity, can be determined foundation on pertaining to the situations where there is known as a low Lso are value. a) Use info taken high is a low Re worth. ()
Velocity, V/ms-1
Re
Pressure change, †P/Pa
0. 63
2179. 41
1044. 66
zero. 59
2036. forty
966. 55
0. 53
1829. 73
829. eighty six
0. 45
1558. 79
693. 18
0. 23
1066. 19
468. 63
b); because
c) Storyline the graph of pressure change, (P1- P2) vs . velocity, V
d) Find the lean of the graph, the viscosity value, could be determine based on the gradient of the graph The gradient of the graph is 1634 Pa/ms-1
Where gradient of the collection =
as duration of pipe, L/m and diameter of water pipe, D/m are pipe geometries
Therefore the value of determined in the graph is usually:
value form data sheet sama dengan 8. 610 x 10-4 kg/m. h
value contact form gradient with the plotted graph = on the lookout for. 19125 x 10-4 kg/m. s
The percentage of difference between viscosity, value gets from the info sheet as well as the value obtains from the plotted graph is usually:
Discussion
The causes of errors had been mainly due to human mistake, and tools limitations. Human error could have occurred as a result of shaking of our hands when holding the pipe. This may have influenced the fluid flow that might cause the reading for the manometer to fluctuate regarding the actual worth. Besides that, the time assessed using the stop watch might be wrong due to reaction of human when using the stop watch. A period lag or perhaps excess period could have quickly been launched into the time recorded.
The amount of drinking water collected could possibly be more because of human response time in taking away the measuring cylinder away from the pipe. Besides that parallax error could have happened when choosing reading in the manometer plus the volume of drinking water in the computing cylinder. Gear limitations cannot be neglected since it would have induced significant errors to the outcomes obtained. One of many possible errors was that minor losses inside the pipe due to pipe fixtures were presumed to be minimal.
However , the truth is, these slight losses will be significant. As a result, errors were introduced in our computations which might affect the outcomes of the test. Other than that, atmosphere bubbles were seen to develop in the pipe. This may have resulted in fluctuations with the liquid level in the manometer. The value taken might have diverse from the actual value. Furthermore, the temperature measured may also be erroneous, and could have given rise to incorrect estimations to get the beliefs of denseness and viscosity of normal water. In performing the try things out, the pipe was not kept straight and at a constant level.
This means that the assumption produced in using the Bernoulli’s equation that both ends of the pipewere at the same level was erroneous. It was as well assumed that the fluid was incompressible pertaining to the Bernoulli’s equation to become used. The equation, used in the computations was a rough estimate; and this could have released some problem into the calculations.
The information recorded to get the alisar flow was shown to be quite accurate since all the details only deviated slightly from your laminar flow line around the moody data. However , a number of the points documented a Reynolds number in the transition range. With that said, the information recorded intended for the transition stage from the flow did not agree with the thing that was expected.
The friction component for your data points in the trasition level was expected to increase a bit, before an additional rise when the flow sooner or later becomes thrashing. This consequence could have been due to the problem in the viscosity at selected temperatures, ultimately causing an error in the Reynolds number calculated. The information recorded pertaining to the turbulent flow showed precision. Almost all of the points, aside from one, were lying about the same line which usually correspond to a relative roughness of 0. 0008.
As we have no idea of the actual family member roughness in the pipe employed in the experiment, we were unable to make reviews between this kind of theoretically calculated value as well as the actual value. The viscosity calculated is usually 9. 19×10-4 and the value from data sheet is usually 8. 610 x 10-4. The percentage error calculated was about 6. 75%.
This disparity could be due to the slight problem in heat recorded in which the experiment was conducted. Apart from that, the rolling up of ideals throughout the calculations might have intorduced a certain percentage error for the final results. The error between the estimated chaffing factor in the turbulent program and the info from the experiment might be cause by the above error once conducting the experiments besides that inside the moody graph and or chart the values plotted taken into account the viscosity effect which in turn causes the mistakes of 3%-6% between the a couple of datas.
Summary
This experiment was conducted to analyze the resistance from flow in a pipe and establish a essential Re benefit for the flow in the pipe. Through the plotting in the first set of information on the moody charts, it was shown the flow was laminar up to and including Reynolds number of about 2446. This was near the expected critical Reynolds volume of 2300. From the second group of data, the relative roughness of the pipe was believed to be 0. 0008.
Employing, theviscosity of water determined was on the lookout for. 19×10-4 kg/ms. This benefit has an error of 6th. 75% from the value succumbed the data sheet. Slight differences in the beliefs were expected as there have been a few errors associated with the undertaking of the research. Some of the problems involved in the try things out include man errors in taking measurements, equipment restrictions and finely-detailed and the reliability of the assumptions and basis on which the equations and analysis were based.
References
N. R. Munson, D. Farrenheit. Young, Capital t. H. Okiishi, Fundamentals of Fluid Mechanics, 5th Male impotence., 2006, Steve Wiley and Sons Incorporation.
Darcy-Weisbach formula 2008. Gathered October three or more, 2008, from http://en.wikipedia.org/wiki/Darcy-Weisbach_equation
Glenn Brown (2000), The History in the Darcy-Weisbach Formula. Retrieved March 4, 08, from http://biosystems.okstate.edu/darcy/DarcyWeisbach/Darcy-WeisbachHistory.htm
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