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Unit 2 FSH

By

Nakul Mahalle

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Loss in pipe and fitting

A. Major Energy Losses

This loss is due to friction.

B. Minor Energy Losses

These losses are due to :

1. Sudden enlargement of pipe,

2. Sudden contraction of pipe,

3. Bend of pipe,

4. Pipe fittings, etc.

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  • MAJOR ENERGY LOSSES

These losses which are due to friction are calculated by :

1. Darcy-Weisbach formula

2. Chezy’s formula

  1. Darcy-Weisbach formula
  2. The loss of head (or energy) in pipes due to friction is calculated from Darcy-Weisbach formula

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where,

hf = Loss of head due to friction,

f = Co-efficient of friction, (a function of Reynolds number, Re)

h = 0.0791/ Re^1/4, for Re varying from 4000 to 10^6

h = 16/Re For Re < 2000(Laminar or viscous flow)

V = Mean velocity of flow, and

D = Diameter of the pipe.

L = Length of the

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  • Loss of Head due to Sudden Enlargement

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Loss of Head due to sudden Contraction

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Flow through compound pipe

Let,

D1, D2, D3 = Diameters of pipes 1, 2 and 3 respectively,

L1, L2, L3 = Lengths of pipes 1, 2 and 3 respectively,

V1, V2, V3 = Velocities of flow through pipes 1, 2 and 3 respectively

f1, f2, f3 = Co-efficients of friction for pipes 1, 2 and 3 respectively, and

H = Difference of water level in the two tanks.

As the rate of flow (Q) of water through each pipe is same, therefore,

Q = A1V1 = A2V2 = A3V3

Also, The difference in liquid surface levels = Sum of the various head losses in the pipes

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Equivalent Pipe

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Bernoulli’s Theorem

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Assumptions:

It may be mentioned that the following assumptions are made in the derivation of Bernoulli’sequation:

1. The liquid is ideal and incompressible.

2. The flow is steady and continuous.

3. The flow is along the stream line, i.e., it is one-dimensional.

4. The velocity is uniform over the section and is equal to the mean velocity.

5. The only forces acting on the fluid are the gravity forces and the pressure forces.

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  • APPLICATIONS OF BERNOULLI’S EQUATION

Although Bernoulli’s equation is applicable in all problems of incompressible flow where there is involvement of energy considerations but here we shall discuss its applications in the following measuring devices:

1. Venturimeter

2. Orificemeter

3. Rotameter and elbow meter

4. Pitot tube.

  • Venturimeter
  • A venturimeter is one of the most important practical applications of Bernoulli’s theorem. It is an instrument used to measure the rate of discharge in a pipeline and is often fixed permanently at different sections of the pipeline to know the discharges there.
  • Types of venturimeters:

1. Horizontal venturimeters.

2. Vertical venturimeters.

3. Inclined venturimeters

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Orifice Meter or Orifice plate

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