Experimental Friciton Coefficient Vs Reynold`s Number
Reynolds Number
Friction Coeffiicient (f)
LAB REPORT
EXPERIMENT # 3
HEAD LOSS IN PIPES
PNGE 211: AN INTRODUCTION TO FLUID MECHANICS
Made By: Nabeel Ahmed Khan
Submitted To: Doruk Alp
Date of Submission: 13/05/16
AIM OF THE EXPERIMENT
The aim of the experiment is to find the friction factor and the minor and major head loss in three different types of flow pipes including Long Pipes, Expansion and constriction pipes and elbow.
THEORY
Viscosity of a fluid is its resistance that is produced when the fluid flows. It is based on the Reynold`s number and is given by the following ratio
Re= ρVDμ
Where, Re is the Reynold`s Number, ρ is the density, Vis the Velocity , D is the Diameter and μ is the viscosity of the fluid .
The major head loss is given by the following equation h major = f(L/D) (V2/2g)
The minor head loss is given by the following equation h minor = Σ K (V2/2g)
Where f is the friction coefficient, L is the length of the pipe, D is the Diameter, V is the velocity of the fluid, g is the gravitational acceleration constant and K is the loss coefficient.
EQUIPMENTS TO BE USED
The system is set on the hydraulic bench in order to make use of water supply and volumetric measurement facilities of the bench. It involves a long pipe for major head loss, an expansion and a constriction pipe and an elbow for minor head losses. The pipes are connected to manometer so as to give the pressure difference between the pipes.
The equipment is shown in figure 1.The fig 2 gives the labeled details of the experimental setup.
There were some safety precautions that had to be followed as well. Since the experiment involves the use of electricity, we needed to ensure that the experiment never comes in contact with water as it might lead to an electric shock. Moreover, we needed to make sure that we didn't use the submergible pump with the tank empty. All changes in the experimental design or procedure, if made, had to be supervised by the lab assistant.
Figure 1 Experimental Setup
Figure 2 Diagrammatic Representation of the Experimental Setup
PROCEDURE
The experiment involves a known flow of water through long and small pipes to observe the head losses. We first tried to calibrate the experimental setup before beginning. This was done by removing air bubbles from the linings of the tubes connecting the manometer and the pipes. This was followed by connecting the manometers to the long pipe and setting the flow rate in the rotameter to the required values and then the change in the height of manometers was observed in the manometers. This was followed by noting the time it takes to fill 10 liters of water in the empty tank.
We had to repeat the same procedure using the other pipes. The values of the diameter and the length of the pipes are given in the lab manual. We would find the head losses using the above given equations.
OBSERVATION AND CALCULATIONS
LONG PIPE
FLOW RATE
(m3/s)
× 10-4
CHANGE IN HEIGHT
(m)
CHANGE IN PRESSURE
(Pa)
VELOCITY
(m/s)
REYNOLD`S NUMBER
EXPERIMENT FRICTION COEFFICIEN(f)
BLASIUS FRICTION COEFFICIEN
(fblasius)
H major
(m)
4.44
0.16
1569.6
1.96
33320
0.0170
0.0234
0.0159
3.88
0.14
1373.4
1.71
29070
0.0199
0.0242
0.0140
3.33
0.11
1079.1
1.47
24990
0.0212
0.0252
0.0110
2.78
0.08
784.8
1.22
20740
0.0220
0.0264
0.0080
2.22
0.05
490.5
0.98
16660
0.0217
0.0278
0.0050
UNITS CONVERSIONS AND CALCULATIONS
Flow rate in L/h is converted to m3/s by multiplying by 2.7778 ×10-7
Change in pressure = ρg( h) where ρ is the density of water that is 1000kg/m3, g is the gravitational acceleration constant and h is the change in height in meters.
Reynold`s number Re= ρVDμ , D is the diameter (0.017m), μ is 1×10-3kg·m 1·s 1.
Velocity = (Flow rate/ Area ); area is 2.27×10-4 m2
Experiment friction coefficient (f) = ( p/ ρ)(D/L)(2/V2) , L is the length of the pipe (0.8m)
F blasius = 0.3164/Re1/4
h major = f(L/D) (V2/2g)
LONG PIPE
REYNOLD`S NUMBER
EXPERIMENT FRICTION COEFFICIEN(f)
BLASIUS FRICTION COEFFICIEN
(f Blasius)
MOODY`S FRICTION COEFFICIEN
(f Moody`s)
% error
(fBlasius –f)/ fBlasius
% error
(f Moody`s –f)/ f Moody`s
33320
0.0170
0.0234
0.023
27.4
26.1
29070
0.0199
0.0242
0.025
17.8
20.4
24990
0.0212
0.0252
0.027
15.9
21.5
20740
0.0220
0.0264
0.028
16.7
21.4
16660
0.0217
0.0278
0.029
21.9
25.2
f Moody`s is the value of the friction coefficient that is read from the Moody`s chart at the particular values of the Re No.
UNITS CONVERSIONS AND CALCULATIONS FOR EXPANSION AND CONTRACTION PIPES
EXPANSION PIPE
FLOW RATE
VELOCITY
REYNOLD`S
NUMBER
CHANGE IN HEIGHT
(m)
CHANGE IN PRESSURE
(Pa)
FRICTION COEFFICIENT
F
BLASIUS FRICTION COEFFICIENT
(FBLASIUS)
K
H MINOR
(m)
Inlet
4.44
1.96
19880
0.08
784.8
0.0454
0.027
3.2
0.08
Outlet
4.44
0.70
inlet
3.88
1.71
17324
0.06
588.6
0.043
0.028
3.2
0.06
outlet
3.88
0.61
inlet
3.33
1.47
15052
0.05
490.5
0.047
0.029
3.2
0.046
outlet
3.33
0.53
inlet
2.78
1.22
12496
0.035
343.3
0.048
0.030
3.2
0.032
outlet
2.78
0.44
inlet
2.22
0.98
9940
0.02
196.2
0.044
0.032
3.2
0.02
outlet
2.22
0.35
Flow rate in L/h is converted to m3/s by multiplying by 2.7778 ×10-7
Change in pressure = ρg( h) where ρ is the density of water that is 1000kg/m3, g is the gravitational acceleration constant and h is the change in height in meters.
Reynold`s number Re= ρVDμ , D is the diameter (D is 0.0284 , μ is 1×10-3kg·m 1·s 1).
Velocity = (Flow rate/ Area ); inlet area is 2.27×10-4 m2 ,outlet area is 6.33 ×10-4 m2
Experiment friction coefficient (f) = ( p/ ρ)(D/L)(2/V2) , L is the length of the pipe (0.125m)
F blasius = 0.3164/Re1/4
K is the loss coefficient given as K = (D22/D12 -1)2 where D2 is greater than D1
CONSTRICTION PIPE
FLOW RATE
VELOCITY
REYNOLD`S
NUMBER
CHANGE IN HEIGHT
(m)
CHANGE IN PRESSURE
(Pa)
FRICTION COEFFICIENT
F
BLASIUS FRICTION COEFFICIENT
(FBLASIUS)
K
H MINOR
(m)
Inlet
4.44
0.70
33320
0.24
2354
0.28
0.0234
6.46
1.3
Outlet
4.44
1.96
inlet
3.88
0.61
29070
0.20
1962
0.30
0.0242
6.47
0.96
outlet
3.88
1.71
inlet
3.33
0.53
24990
0.15
1471.5
0.31
0.0252
6.48
0.71
outlet
3.33
1.47
inlet
2.78
0.44
20740
0.10
981
0.30
0.026
6.47
0.49
outlet
2.78
1.22
inlet
2.22
0.35
16660
0.0650
638
0.30
0.028
7.67
0.375
outlet
2.22
0.98
Flow rate in L/h is converted to m3/s by multiplying by 2.7778 ×10-7
Change in pressure = ρg( h) where ρ is the density of water that is 1000kg/m3, g is the gravitational acceleration constant and h is the change in height in meters.
Reynold`s number Re= ρVDμ , D is the diameter( D is 0.017m , μ is 1×10-3kg·m 1·s 1.)
Velocity = (Flow rate/ Area ); inlet area is 2.27×10-4 m2 ,outlet area is 6.33 ×10-4 m2
Experiment friction coefficient (f) = ( p/ ρ)(D/L)(2/V2) , L is the length of the pipe (0.125m)
K is the loss coefficient given as K = (H2-H1)(2g/V22)+6.34
h minor = K (V2/2g)
ELBOW PIPE (readings)
FLOW RATE
MANOMETER HEIGHT(1) /m
MANOMETER HEIGHT(2) /m
4.44
60
96
3.88
66
94
3.33
71
92
2.78
75
90
2.22
79
89
The readings for the elbow pipe were taken by connected the manometer tubes to the elbow and setting the rotameter as we had set for other pipes.
Figure 3 Moody`s Chart
The graph shows that generally with the increase in Reynolds number, the friction in the long pipe decreases.
CONCLUSIONS
The values for friction that we obtained for the long pipe are almost consistent with the values in the literature(Moody`s Chart). We learned through this experiment that there is an head loss in each pipe due to internal friction of the pipes. The experiment is accurate and gives us a good idea of the head loss in pipes.
