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Energy losses in pipe flow


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When a fluid is flowing through a pipe, the fluid experiences some resistance  due to which some of the energy of the fluid is lost. This loss of energy is classified as:


1) Major energy losses: The viscosity causes loss of energy in the flows, which is known as frictional loss or major energy loss and it is calculated by the following formula;

(a)Darcy-weisbach formula

   The loss of head can be measured by the following equations

   hf =4f L V2 / (2gD)

Where hf  = Loss of head due to friction

              f   = Co-efficient of friction which is a function of Reynolds number

              f = 64/Re   (for Re <2000) (laminar flow)

              L = Length of pipe

              V = mean velocity of flow

              D = Diameter of pipe

2) Minor energy losses: The loss of energy due to change of velocity of the flowing fluid in magnitude or direction is called minor loss of energy. The minor loss of energy includes the following cases


(a) Sudden expansion of pipe:


The head loss due to sudden expansion equation is he = (V1 -V2)2 /2g

 Where V1 is the velocity at section 1

              V2 is the velocity at section 2


(b)Sudden contraction of pipe:


The head loss due to sudden contraction equation is hc =k (V22 /2g)

Where    k = ((1/Cc)-1)2

                V2 is the velocity at section 2


(c) Bending in pipe:


The head loss due to bending equation is  hb=k (V2 /2g)

Where V is the velocity of the flow.

             k is the co-efficient of the bend ,which depends on the angle of the bend, radius of curvature of bend and diameter of the pipe



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