Determination of Friction Factor for Pipes of Different Diameter and Loss Coefficient for Various Pipe Fittings

Learning Objectives: i. To investigate the behavior of incompressible fluid in piping network, especially

fluid friction loss ii. To investigate the behavior of incompressible fluid in piping network, especially

fluid head loss across pipe fittings iii. To become familiar with use of mercury/water manometer for measurement of

head loss across pipes and pipe fittings List of Required Equipment & Accessories: It includes the following

i. Fluid Circuit Friction Experimental Apparatus (Figure 1) Equipment

Figure 1: Equipment for used for the Experiment

Theory When a fluid flows through a pipe, there is a loss of energy (or pressure) in the

fluid. This is because energy is dissipated to overcome the viscous (frictional) forces exerted by the walls of the pipe as well as the moving fluid layers itself. In addition to the energy lost due to frictional forces, the flow also loses pressure as it goes through fittings, such as valves, elbows, contractions and expansions. The pressure loss in pipe flows is commonly referred to as head loss. The frictional losses are referred to as major losses while losses through fittings etc, are called minor losses. Together they make up the total head losses.

The Reynolds number Re is a dimensionless number that gives a measure of the ratio of inertial forces (V) to viscous forces (/L). It is a very useful quantity and aids in classifying fluid flows.

where, = density of the fluid, (kg/m3) .

V = average velocity of flow inside the pipe, (m/s). Lc= characteristic dimension = D for pipe flows, (m). = dynamic viscosity of the fluid, (Pa .s).

For flow through a pipe experimental observations show that laminar flow occurs when Re < 2300 and turbulent flow occurs when Re > 4000. In the between 2300 and 4000, the flow is termed as transition flow where both laminar and turbulent flows are possible. The average velocity of flow can be found out by measuring the actual discharge and dividing it by cross-sectional area of the pipe. The head loss due to friction in pipe flows can be calculated using the Darcy- Weisbach equation. It is a phenomenological equation, which relates the head loss due to friction along a given length of pipe to the average velocity of the fluid flow.

where, hf = head loss due to friction, (m of fluid).

V = average velocity of flow inside the pipe, (m/s). L/D= length to diameter ratio of the pipe, (m). f = a dimensionless coefficient called the Darcy friction factor.

The Darcy friction factor f is not a constant and depends on the parameters of the pipe and the velocity of the fluid flow. It may be evaluated for given conditions by the use of various empirical or theoretical relations, or it may be obtained from Moody diagrams. The Darcy friction factor for laminar flow (Re < 2300) is given by the following formula:

The value of the Darcy friction factor may be subject to large uncertainties in the transition flow regime and so here the equation for turbulent flow is assumed to be valid. For turbulent flow Colebrook equation has to be used to find f.

where, /D is the relative roughness of the pipe.

The head loss due to friction in pipe fittings (minor losses) can be calculated using following expression

where, K is the loss coefficient in the fittings. Procedure

i. Close all air vent valves and drain valves. Open all flow control valves, glove valve and cock for water to flow.

ii. Start the circulate water pump. iii. Adjust flow rate to the desired value. iv. Measure the differential pressure in all pipes and fittings related to fluid friction

loss for water flow rate by means of water inverse U tube manometer and mercury U tube manometer. Measure actual flow rate using rotameter.

v. Change the flow rate and collect the same data as in step iv. Collect this data for at least five different values of flow rate for all the pipes and fittings.

Precautions i. Remove air from mercury manometer before taking readings. ii. Fill the water in water tank to proper level before starting the experiment. iii. Read the reading from manometers and rotameter by keeping the eyes at the

level of mercury, water or weight. iv. After changing the flow rate, allow sufficient time to system to reach steady state. v. From manifold, carefully open the valves corresponding to pipes or fitting under

observation and close the valves before opening the valves for next pipe/fitting.

Observations and Calculations Pipe Diameters: 1, , Pipe Length: 2 m

Table 1 : Experimental Data for Friction Factor in Pipes mm H2O = mm Hg x 12.55

Diameter of pipe containing fittings= 1 Fittings: 90o elbow, Gradual expansion, Gradual contraction,

Gate Valve, Globe valve, Ball valve, 90o bend, Sudden expansion, Sudden contraction

1" 3/4" 1/2" 1" 3/4" 1/2" 1" 3/4" 1/2" 1" 3/4" 1/2" 1" 3/4" 1/2" 1" 3/4" 1/2"

Lit/min m3/s mH2O mH2O mH2O m/s m/s m/s

12345

fmoodySr.No.

Discharge

Q

Velocityinpips Re ln(Re)hf f=hfxD/Lx2g/V2

Table 2 : Experimental Data for Loss Coefficient of Fittings

Results and Inference

i. The Darcy friction factor for the three different pipes for different values of Reynolds number have been found out experimentally and compared with the theoretical results.

ii. The loss coefficients for various fittings for different values of Reynolds number have been found out experimentally and compared with the results in literature.

Report: i. Plot the friction factor f vs ln (Re) for all the pipes from data obtained and moody

chart. ii. Plot loss coefficient K vs ln (Re) for all the fittings. iii. Discuss the above trends and justify them from theory.

hm Velocity Re ln(Re) K=hmx2g/V2

Fitting V

Lit/min m3/s mH2O m/s

12345

QSr.No.

Discharge