Objectives 1. To investigate the head loss due to friction across bends and elbows. 2. To find the bend/elbow constant for given pipe.
Introduction Minor loss is caused when there is additional component os added to the straight pipe such as tees, elbows and bend. This minor loss will contribute to head loss due to the friction across bends and elbows. Bernoulli’s equation relates pressure, velocity and elevation between any two points in the flow. But since the equation have some restriction, a new term must be introduce. P1/ρg + V1/2g + z1= P2/ρg + V2/2g + z2 + hL Head loss is added because in real life situation there are losses. The head loss will increase when the fluid flow through fittings (elbows or bends) due to the friction effect that caused by the viscosity. This situation can be proved by calculation of the drop in the flow rate. Minor losses expressed in terms of loss coefficient, Kι and defined as: Kι = hι / (V²/ (2g). The values of Kι are related to the pipe friction factors by a constant which is dependent on the ratio of the bend radius to the pipe diameter R/D.
Procedures 1. Start the pump and wait till there is water flow. 2. Raise the swivel tube. 3. Adjust the bench regulating valve to provide a small averflow through both inlet tank and overflow pipe. 4. Set a series of condition as in Table 1. 5. Measure flow rate at each condition using stopwatch and volumetric tank.
6. Repeat steps 1-5 for pipe with elbows.
Results Required volume of water, V = 3 liter = 0.003m3 Diameter for both pipes, D = 0.003m3 Temperature of water = 24 ºC
#
Outlet head (cm)
1 2 3 4 5
35 30 25 20 15
#
Outlet head (cm)
1 2 3 4 5
35 30 25 20 15
BENDS Inlet head, h1 (cm) 385 366 336 314 288 Table 1 ELBOWS Inlet head, h1 (cm) 426 420 410 400 390
Inlet head, h2 (cm) 121 97 80 70 60
Time, t (second) 42 32 29 27 25
Inlet head, h2 (cm) 115 92 78 64 50
Time, t (second) 64 56 48 44 38
Calculated data: Table 3 BENDS #
Volumetric flow rate Q (m3/s)
Average velocity V (m/s)
1
7.143 x 10-5
2
9.375 x 10-5
3
1.034 x 10-4
0.132
4
1.111 x 10-4
0.141
5
1.200 x 10-5
0.153
0.909 1.193
Re # (dimensionles s)
Total head loss hL (m)
Friction factor, f (dimensionless)
Head loss due to a single bend, hb (m)
Bend constant, Kb
10171.41
2.64
0.74
0.44
10.43
13315.71
2.69
0.44
0.45
6.23
14658.47
2.56
0.34
0.43
4.92
2.44
0.28
0.41
4.05
2.28
0.22
0.38
15777.44 17120.20
3.18
Table 4 ELBOWS #
Volumetric flow rate Q (m3/s)
Average velocity V (m/s)
Re# (dimensionles s)
Total head loss hL (m)
Friction factor, f (dimensionless)
Head loss due to a single bend, hb, (m)
Bend constant, KB
1
4.688 x 10-5
0.60
6713.80
3.11
0.97
0.54
29.43
2
5.357 x 10-5
0.68
7608.98
3.28
0.80
0.57
24.19
3
6.25 x 10-5
0.80
8951.74
3.12
0.55
0.54
16.55
4
6.818 x 10-5
0.87
9735.02
3.36
0.50
0.58
15.03
5
7.895 x 10-5
1.01
11301.57
3.40
0.38
0.58
11.16
Bend /Elbow constant, Kb
%diff
From experiment
Table A
Bend
10.43
6.6
58.03
Elbow
29.43
29.10
1.13
CALCULATION:
1. Volumetric flow 3L=0.003 m3 Q (m3/s) = Volume (m3) / Time= (0.003m3) /42= 7.1428 x 10-5m3/s
2. Average velocity Area of pipe= π (D²/4) = π (0.01²/4) = 7.854x10-5 m2 V (m/s) = Q/A= (7.1428 x 10-5m3/s)/ (7.854x10-5 m2) = 0.909 m/s
3. Reynolds # _ Reynolds # = ρ (kg/m3) x V (m/s) x d (m) µ (Ns/m2) = (997.0x0.909x0.01)/ (0.891x10-³) = 10171.41
4. Frictional head loss hf (m)
hf= h1(m) – h2(m) = 0.385m – 0.121m = 0.264m
5. Friction factor, f (dimensionless) ƒ = 2gDhf
=
2(9.81 m2/s) (0.007m) (0.264m)
LV2
0.36m x (1.856m/s) 2
6. hf = f x (L/D) x (V2/2g) = 0.74 x (0.288m/0.010m) x (0.91m/s) 2/2x9.81m/s = 0.9m for bends
Head loss due to a single bend hb = (hL – hf) / N = (0.120m – 0.0373m) / 4 = 0.0207 m
Elbow constant, Kb = (2ghb)/V2
= [2(9.81m/s2) (0.0207 m)] / (0.659m/s) 2
= 0.9352
Kb from table A = 30f = 30(0.0312) = 0.936
%diff = [(0.9352– 0.9360) / 0.9360] x 100% = 0.09%
= 0.0543
Discussion For this experiment, we are using bend and elbows pipe the investigate the head loss in the pipe. Different from previous experiment when we use straight pipe, bends and elbows pipe will contribute to minor loss in the head loss. The losses in the bends and elbows are caused by the flow seperation on the inner side of the pipes. And just like the previous experiment, we find that the fluid flow is also turbulent flow as the Reynold Number shows high values. This is because in real situation such as home piping it is impossible to have laminar flow since the velocity will be very low and the materials will be too expensive. We also realize that the time taken for the bends is shorter than the elbows for the fluid to rise until 3L. This is because bends will allow the fluid to make turn easily rather than elbows that will restric the fluid to move fast. It is recommended to reduce head loss we use bends rather than elbows to have lower head loss To avoid any parallax error we must take reading from the height of the inlet. We also must take the reading immediately when the volumetric tank flow stop. Also make sure to connects the pipe correctly and make sure there is no leakage anywhere in the connection.
Conclusion Alhamdulillah, we manage to carry out the experiment without any problem. The percentage error also is very small about 1% error which is acceptable. We also managed to observe the effect of bends and elbows pipe to the flow of fluid.
References: 1.
2.
Fluid Mechanics Laboratory Guidelines for Biotechnology Engineering Lab 1, 3rd edition (Jan 2007), Syed Abu Bakar Al-Saggoff. Fluid Mechanics Fundamental and Applications, Yunus A. Cengel, John M. Cimbala
QUESTIONS:
1.
Derive Extended Bernoulli Equation and Modified Bernoulli Equation from the First Law of Thermodynamics. What are the different between the 2 equations?
Extended Bernoulli Equation:
where
&
Modified Bernoulli Equation:
with
Therefore, difference between these 2 equations is that Modified Bernoulli Equation have no shaft work,
2.
.
What are major losses, minor losses and head losses? Major losses - the total head loss in a pipe
Minor losses – losses caused by additional component such as elbows abd bends in the straight pipe system.
Head loss:
3.
What is the equation to determine head loss for straight pipe?
Hf = h1 – h2
4.
For a system with a constant diameter of straight pipe and not involving any pump work, how can we determine the head loss?
By using piezometer. The head lost is the difference of inlet head and outlet.
5.
What is the friction factor? How we can determine it experimentally? How it change with Reynolds Number?
Friction factor: ƒ=
2gDhf
LV2
Reynolds Number:
Reynolds Number is inversely proportional with the friction factor.
6.
What is Moody Diagram? What we can obtain from it?
Moody Diagram is a graph that relates the friction factor, f for fully developed pipe flow to the Reynolds Number, Re and relative roughness of a circular pipe. Thus, for turbulent flow, that is Re>2300, we could find its friction factor, f.
7.
What is equation to determine head loss for minor losses? hL = kLV2/ 2g
8.
For a system with 1 bend and not involving any pump work, how can we determine the head loss for the bend?
Apply the head loss equation.
9.
What is loss coefficient? What is equivalent length? How the 2 relates?
Loss coefficient - expression of minor loss or also called as resistance coefficient, KL.
Equivalent length - also expression of minor losses, Eequiv. = DKL/f.
Loss coefficient is relates to determine equivalent length by multiplying KL with D/f.
10.
For a system in horizontal plane consists of 2 similar elbows and 3 straight pipes with a constant diameter and having same length. Explain how we can determine the head loss for the system and show that we can determine the friction factor for the system if we apply the Modified Bernoulli Equation to the system.
Head loss for this system could be determined by comparing the height of the 1st and 3rd straight pipe, and friction factor could be found by using equation
.
11.
How we can determine pressure drop from the head loss? From the equation
12.
, pressure drop is,
By using all answers for the questions above, explain what you should do in the experiments in order to achieve the objectives.
Identify the type of piping system being used, whether it is straight pipe, bend or elbow. Then, we find its head loss and pressure drop.
