Question

a)Discuss Darcy Weisbach equation for loss of head due to friction in a pipe line

b)Discuss Nikuradse's experiment on flow through pipes

Answer 1

Ans A : Darcy Weisbach Equation is used to calculate the loss of head due to friction in the pipe. It is an empirical equation in mechanics which was named after Henry Darcy and Julius Weisbach. In the Darcy Weisbach Equation the loss of pressure or head loss which is due to friction along the given length of pipe to the average velocity of the fluid flow for an incompressible fluid.

Darcy Weisbach equation ,  

Where, H_F is the head loss or pressure loss,

g is the acceleration due to gravity.

v is the velocity of incompressible fluid.

f is the coefficient of friction or friction factor.

d is the diameter.

L is the length of the pipe.

ASSUMPTIONS USED :

• A uniform horizontal pipe with fixed diameter d and area A, which allow a steady flow of incompressible fluid.
• Their will be the loss of energy due to friction for the application of Bernoulli’s principle.
• Then we have to apply Bernoulli’s principle.
• After that we are finding frictional resistance .

Application of Darcy Weisbach Equation:

It is used to calculate the loss of head due to friction in the pipe.

B) Nikuradze’s experiment is still considered very brilliant and is rated in the gold standard for the effect of roughness on the inside of a pipe. In this experiment he used water and sand roughened pipes. And thereafter he classified spherical particles into narrow particle size ranges and which he glued them onto the inside parts of the various pipes having different diameters.Afterwars he started flowing water through those pipes with varying flow rates and then he measured the pressure which was different across the ends of the pipe.In the end by varying the size of the internal diameter of the pipes he was successful in making various range of Reynolds number flow.The results he got from that experiment were brilliant for the roughened pipes . The ranges which he used was :

• In RANGE 1 , Those having small reynolds number, the resistance factor is the same for rough and smooth pipes . The projections of the roughening are completely within the limits of laminar layer .
• In RANGE 2 , which is also known as transition range , there was slight increases in the resistance factor for progessive reynold numbers . The thickness of the laminar layer coresponds to the projections .
• In RANGE 3 , In this range the resistance factor is independent of the reynolds number . In this all the projections of the roughening exceeds the laminar layer .

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