Experiment 2 Head Loss in Pipe and BendsObjective:1. To determine the head loss in pipe flow for different diameters.2. To estimate the friction factor for difference pipe diameters.3. To determine the head losses in bends.

Learning Outcome:Upon completion of the experiment, students should be should be able to determine the head loss in pipe flow for different pipe diameters. Besides that, students are able to plot the graph of friction factor against Reynolds number. Students should be able to determine the head losses in each bend and find the pressure drop along the pipe. Besides that, they should be able to plot the graph of against to obtain K for all the four bends.

Introduction:In fluid dynamics, head is a concept that relates the energy in an incompressible fluid to the height of an equivalent static column of that fluid. From Bernoulli's Principle, the total energy at a given point in a fluid is the energy associated with the movement of the fluid, plus energy from pressure in the fluid, plus energy from the height of the fluid relative to an arbitrary datum. Head is expressed in units of height such as meters or feet. To move a given volume of liquid through a pipe requires a certain amount of energy. An energy or pressure difference must exist to cause the liquid to move. A portion of that energy is lost to the resistance to flow. This resistance to flow is called head loss due to friction.Losses of head is also incurred by fluid mixing which occurs at fittings and by frictional resistance at pipe wall. For a short pipe with numerous fittings, major part of the head loss occurred because of the local mixing near the fittings. Where else for long pipes, the surface friction at the pipe wall will predominate because of the length. When a fluid flows through a pipe, the internal roughness of the pipe wall can create local eddy currents within the fluid adding a resistance to flow of the fluid. The velocity profile in a pipe will show that the fluid elements in the center of the pipe will move at a higher speed than those closer to the wall. Therefore friction will occur between layers within the fluid. This movement of fluid elements relative to each other is associated with pressure drop, called frictional losses. Pipes with smooth walls such as glass, copper, brass and polyethylene have only a small effect on the frictional resistance. Pipes with less smooth walls such as concrete, cast iron and steel will create larger eddy currents which will sometimes have a significant effect on the frictional resistance. Rougher the inner wall of the pipe, more will be the pressure loss due to friction. As the average velocity increases, pressure losses increase. Velocity is directly related to flow rate:

Where Q is the volumetric flow rate and A is the cross-sectional are of the pipe. Fluids with a high viscosity will flow more slowly and will generally not support eddy currents and therefore the internal roughness of the pipe will have no effect on the frictional resistance. This condition is known as laminar flow.Laminar flow generally happens when dealing with small pipes, low flow velocities and with highly viscous fluids. At low velocities fluids tend to flow without lateral mixing,and adjacent layers slide past one another like playing cards. There are neither cross currents nor eddies. Laminar flow can be regarded as a series of liquid cylinders in the pipe, where the innermost parts flow the fastest, and the cylinder touching the pipe isn't moving at all. In turbulent flow, the fluid moves erratically in the form of cross currents and eddies. Turbulent flow happens in general at high flow rates and with larger pipes.For this experiment in part 2, the energy loss in pipe network with bends and fittings has two components major loss due to shear stress between the water and the pipe surface and minor loss, energy loss caused by sudden changes in either direction or velocity as stated by Strothman (2006). Bends are provided in pipes to change the direction of flow through it. An additional loss of head, apart from that due to fluid friction, takes place in the course of flow through pipe bend. The fluid takes a curved path while flowing through a pipe bend as shown in figure: When a fluid flows in a curved path, there must be a force acting inwards on the fluid to provide the inward centripetal acceleration. This result in an increase in pressure near the outer wall of the bend, starting at some point A and rising to a maximum at some point B. There also a reduction of pressure near the inner wall giving a minimum pressure at C and a subsequent rise from C to D. Therefore between A and B and between C and D the fluid experiences an adverse pressure gradient which the pressure increases in the direction of flow. Fluid particles in this region, because of their close proximity to the wall, have low velocities and cannot overcome the adverse pressure gradient and this leads to separation of flow from the boundary and consequent losses of energy in generating local eddies. Losses also take place due to a secondary flow in the radial plane of the pipe because of a change in pressure in the radial depth of the pipe. This flow, in conjunction with the main flow, produces a typical spiral motion of the fluid which persists even for a downstream distance of fifty times the pipe diameter from the central plane of the bend. This spiral motion of the fluid increase the local flow velocity and the velocity gradient at the pipe wall, and therefore results in a greater frictional loss of head than that which occurs for the same rate if flow in a straight pipe of the same length and diameter.

Apparatus and Materials:Hydraulic Bench, Losses in Bends Apparatus, Pipe Friction Apparatus, stopwatch.

Safety Precautions:1. Make sure there are no air bubbles in the manometer before taking the readings.2. The readings on the manometer are taken when the flow rate is steady.3. The eyes of the observer must be perpendicular to the readings to prevent parallax errors.

Procedures:Part A. Head loss in pipes of different diameters.1. The LS-18001-15 Pipe Friction Apparatus is placed on the hydraulic bench.2. The water inlet and outlet nipples are connected with flexible hoses.3. The quick coupling is connected to the copper wire which has 11mm diameter.4. The water pump is switched on and the overflow valve of the hydraulic bench is closed slowly.5. The valves at the copper pipe are opened and the air gap in the manometer is removed by pressing the relief valve which is located on top of the manometer. The water flow rate is measured using the flow meter on the hydraulic bench and a stopwatch.6. The reading at the manometer is recorded.7. Steps 4 to 6 are repeated with different flow rates and the readings of the manometer is taken.8. Steps 3 to 7 are repeated for diameters of 8.3mm and 5.3mm.

Results:Part A. Head loss in pipes of different diameters.EM201 Fluid MechanicsLab Report 2

6

11mmFlow rate, Q (Ls-1)Height, h (mm Hg)

0.29635

0.25529

0.24022

0.20315

0.1388

0.0503

8.3mmFlow rate, Q (Ls-1)Height, h (mm Hg)

0.289128

0.243104

0.20884

0.19661

0.14139

0.08817

5.3mmFlow rate, Q (Ls-1)Height, h (mm Hg)

0.136278

0.131236

0.120204

0.100161

0.088123

0.06975

Calculations:Length of the pipe, The Reynolds number for the pipe is calculated by the equation

Where is the velocity, the diameter of the pipe.Coefficient of kinematic viscosity of the fluid at 25The friction factor for the pipe is then calculated from the equation

Where is the difference of height of the manometer,

, length of the pipe, diameter of the pipe, velocity of the fluid, gravitational accelerationFlowrate, (10-4 m3/s)Velocity, (m/s)Reynolds numberh (m Hg)Friction factor,

2.960.77994790.0350.029

2.550.67181650.0290.033

2.400.63176780.0220.028

2.030.53464980.0150.027

1.380.36344170.00800.031

0.500.13216060.00300.087

Table 1.1. Flow rate, velocity, reynolds number, head loss and friction factor for pipe with diameter 11mm.

Flowrate, (10-4 m3/s)Velocity, (m/s)Reynolds numberh (m Hg)Friction factor,

2.891.33122480.1280.028

2.431.12103110.1040.032

2.080.9608814.00.08400.035

1.960.9068318.00.06100.028

1.410.6515977.00.03900.035

0.880.4073737.00.01700.039

Table 1.2. Flow rate, velocity, reynolds number, head loss and friction factor for pipe with diameter 8.3mm.

Flowrate, (10-4 m3/s)Velocity, (m/s)Reynolds numberh (m Hg)Friction factor,

1.361.5490350.2780.029

1.311.4887000.2360.026

1.201.3679730.2040.027

0.9901.1265780.1610.031

0.8800.99758450.1230.030

0.6900.78245850.07500.030

Table 1.3. Flow rate, velocity, reynolds number, head loss and friction factor for pipe with diameter 5.3mm.

Procedures:Part B. Head loss in bends1. The inlet valve is connected to the hydraulic bench supply.2. The inlet and outlet valves are fully opened and the water flow rate is controlled from the hydraulic bench.3. The flow rate of water is measured by using the flow meter on the hydraulic bench and a stopwatch. The water flow rate is set to a suitable value.4. After the flow rate is steady, the air relief valve which is located at the top of the manometer is pressed if the water levels in the manometer are too low.5. The water level of every tube in the manometer is recorded.6. Steps 4 and 5 are repeated for different flow rates.

Results:t(s)24.827.9438.9841.88

Water Collected (L)5555

Volumetric Flow rate (Ls-1)0.2020.1790.1280.119

Velocity, (ms-1)0.9220.8170.5840.543

Tube 1555465397360

Tube 2 509435377346

Tube 3450395350326

Tube 4420375335315

Tube 7334320297289

Tube 8 263275270269

Tube 9185224235245

Tube 1050137177217

Table 2.1

Calculations:From the equation in part A, the Reynolds number can be calculated,

Given the diameter of the pipe, is 16.7mm, is Also given from the graph, the friction factor, can be found.

Flowrate, (10-4 m3/s)Velocity, (m/s)Reynolds numberFriction factor,

2.020.92217033

1.790.81715093

1.280.58410789

1.190.54310032

Table 2.2. Value of flow rate, velocity, Reynolds number and friction factor.Given

90 large radius bend

Flow rate, (Ls-1)h (m)h (m)

0.9220.0460.0220.024

0.8170.0300.0180.012

0.5840.0200.0090.011

0.5430.0140.0080.006

Flow rate, (L/s)h (m)Velocity head, Lost Coefficient, K

0.9220.0240.0430.558

0.8170.0120.0340.353

0.5840.0110.0170.647

0.5430.0060.0150.400

90o small radius bend

Flow rate, (Ls-1)h (m)h (m)

0.9220.0300.0160.014

0.8170.0200.0130.007

0.5840.0150.0060.009

0.5430.0110.0060.005

Flow rate, (L/s)h (m)Velocity head, Lost Coefficient, K

0.9220.0140.0430.326

0.8170.0070.0340.206

0.5840.0090.0170.529

0.5430.0050.0150.333

90 elbow

Flow rate, (Ls-1)h (m)h (m)

0.9220.0510.0100.041

0.8170.0450.0080.037

0.5840.0270.0040.023

0.5430.0200.0040.016

Flow rate, (L/s)h (m)Velocity head, Lost Coefficient, K

0.9220.0410.0430.953

0.8170.0370.0341.088

0.5840.0230.0171.353

0.5430.0160.0151.067

Two 45 bends

Flow rate, (Ls-1)h (m)h (m)

0.9220.1350.0100.125

0.8170.0870.0080.079

0.5840.0580.0040.054

0.5430.0280.0040.024

Flow rate, (L/s)h (m)Velocity head, Lost Coefficient, K

0.9220.1250.0432.907

0.8170.0790.0342.324

0.5840.0540.0173.176

0.5430.0240.0151.600

With reference from Table 2.2, the velocity head is calculated with

The frictional head loss, is thus

=Piezometric head - , where the piezometric head is obtained from the manometer readings.Loss coefficient,

Discussion:With reference to Part A of this experiment, it is observed that the flow velocity and head losses were higher as the diameter of the pipe decreases. In a straight uniform pipe, there exists shear stress along the wall of the pipe and this produces resistance to the flow. Generally, as the cross-sectional area increases in the pipe, the flow rate of the fluid will decrease, the velocity is then reduced hence head losses reduce also. Based on the graphs from Part A, as the Reynolds number increases, the friction factor decreases. Reynolds number, a dimensionless parameter can be used to determine the type of fluid flow. The fluid flow for all diameters are turbulent flow in this experiment because the flow is laminar when Re < 2000 which has high viscosity with low inertia, transient when 2000 < Re < 4000 and turbulent when Re > 4000.

On the other hand, results from Part B of the experiment shows head losses occurs when fluids flow through different types of bends, too. Analyzing the graph of against for the four types of bends shows that generally when the velocity increases, head loss due to bends increases also. We are able to interpret that the head loss in the two 45 bends is the highest among all the pipe bends, followed by the 90 elbow, 90 large radius bend and finally 90 small radius bend.Lastly, the accuracy of the results of this experiment can be increased if parallax errors could be prevented when taking the readings. Most fluids are turbulent flows and the viscosity of the fluid itself can affect the results of the experiment.

Conclusion:In part A of this experiment, Reynolds number can be used to identify the type of flow of the fluid, which is turbulent as all the data obtained showed Reyolds number of higher than 4000. The higher the Reynolds number the lower the friction factor. Part B of this experiment proves that head loss occurs when fluid flows through bends. Different bends produced different pressure drops and through the plotting of graphs, it is determined that the 90 small radius bend has the lowest head loss for different flow rates.Reference:

Douglas, J.F. Gasiorek, J.M and Swaffield, J.A. (2001) Fluid Mechanics. 4th ed. London: Prentice Hall.Head Loss Darcy - Weisback Equation - Fluid Flow Hydraulic and Pneumatic, Engineers Edge. 2015. Head Loss Darcy - Weisback Equation - Fluid Flow Hydraulic and Pneumatic, Engineers Edge. [ONLINE] Available at: http://www.engineersedge.com/fluid_flow/head_loss.htm. [Accessed 11 June 2015].Losses in Pipes. 2015. Losses in Pipes. [ONLINE] Available at: http://me.queensu.ca/People/Sellens/LossesinPipes.html. [Accessed 11 June 2015].Reynolds Number. 2015. Reynolds Number. [ONLINE] Available at: https://www.grc.nasa.gov/www/BGH/reynolds.html. [Accessed 11 June 2015].11