MINOR HEAD LOSSES IN PIPE FLOW

We were discussing the concept of laminar and turbulent flow, Reynolds experiment, frictional loss in pipes, derivation of expression for loss of head due to friction in pipes, co-efficient of friction in terms of shear stress and also the basics of shear stress in turbulent flow, in the subject of fluid mechanics, in our recent posts.

Now we will go ahead to see minor head losses in pipe flow, in the subject of fluid mechanics, with the help of this post.

Even we have already seen earlier one post based on major and minor losses in pipes earlier. Today, we will be interested to secure the detailed information about the minor head losses in pipe flow only.

Minor head losses in pipe flow

Head loss in pipe flow system due to viscous effect i.e. due to friction will be termed as major head loss and will be indicated by h _L-Major.

Head loss in pipe flow system due to various piping components such as valves, fittings, elbows, contractions, enlargement, tees, bends and exits will be termed as minor head loss and will be indicated by h _L-Minor.

We will see here the following cases of minor head losses in pipe flow.

Loss of head due to sudden enlargement
Loss of head due to sudden contraction
Loss of head at the entrance of a pipe
Loss of head at the exit of a pipe
Loss of head due to an obstruction in a pipe
Loss of head due to bend in the pipe
Loss of head in various pipe fitting

If we want to evaluate the loss of head in long pipe, above losses will be small as compared with major loss of head i.e. loss of head due to friction. That’s why above losses are considered as minor losses and we can also neglect such losses for long pipe.

But if we want to evaluate the loss of head in small pipe, above losses must be considered as such losses will be comparable with the loss of head due to friction.

Loss of head due to sudden enlargement

Let us assume that a liquid is flowing through a pipe which has a sudden enlargement as displayed here in following figure.

Loss of head due to sudden enlargement will be given by following equation.

Where,

V₁= Velocity of fluid flow at section 1-1

V₂ = Velocity of fluid flow at section 2-2

h_e = Loss of head due to sudden enlargement

g = Acceleration due to gravity

Loss of head due to sudden contraction

Let us assume that a liquid is flowing through a pipe which has a sudden contraction as displayed here in following figure.

Loss of head due to sudden contraction will be given by following equation.

Where,

V₂ = Velocity of fluid flow at section 2-2

h_C = Loss of head due to sudden contraction

k = Minor loss co-efficient

Value of k, for different fittings or pipe components, might be secured from the post “major and minor losses in pipes”.

Loss of head at the entrance of a pipe

Loss of head at the entrance of a pipe is the loss of head when a liquid enters a pipe which is connected with a large tank or reservoir.

Loss of head at the entrance of a pipe will be given by the following equation as mentioned here.

Where,

V = Velocity of fluid flow in the pipe

h_i = Loss of head at the entrance of a pipe

Loss of head at the exit of a pipe

Loss of head at the exit of a pipe will be given by the following equation as mentioned here.

Where,

V = Velocity of fluid flow at the outlet of pipe

h_O = Loss of head at the exit of a pipe

Loss of head due to an obstruction in a pipe

Whenever there will be an obstruction in a pipe, loss of head will take place due to the reduction of area of the cross-section of the pipe at the location where obstruction is located. There will be sudden enlargement of the flow area beyond the obstruction and due to this reason there will be loss of head.

Let us consider a pipe of cross-sectional area A with an obstruction as displayed here in following figure.

Loss of head due to an obstruction in a pipe will be given by the following equation as mentioned here.

Where,

V = Velocity of fluid flow in the pipe

A = Area of pipe

a = maximum area of the obstruction

C_C = Co-efficient of contraction

Loss of head due to bend in pipe

Loss of head due to bend in pipe will be given by the following equation as mentioned here.

Where,

V = Velocity of fluid flow

h_b = Loss of head due to bend in pipe

k = Co-efficient of bend

Value of k will be dependent over angle of bend, radius of curvature of bend and diameter of the pipe.

Loss of head in various pipe fitting

Loss of head in various pipe fitting will be given by the following equation as mentioned here.

Where,

V = Velocity of fluid flow

h_b = Loss of head due to bend in pipe

k = Co-efficient of bend

Further we will go ahead to see the basics of hydraulic gradient and total energy line, in the subject of fluid mechanics, with the help of our next post.

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