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Head Losses in Pipes, Bends and Fittings Notes for Mechanical Engineering

By BYJU'S Exam Prep

Updated on: September 25th, 2023

Energy loss is categorized as:

  • the sudden expansion of the pipe
  • sudden contraction of the pipe
  • bend in pipe
  • any obstruction in the pipe                        
 

Major Loss: It is calculated by Darcy Weisbach’s formulas

Loss of head due to friction: Head Losses in Pipes, Bends and Fittings Notes for Mechanical Engineering

where:

L = Length of pipe

V = Mean velocity of flow

d = Diameter of pipe

f = friction factor

friction factor (f) = 4 ×coefficient of friction (f’)

For Laminar flow: Head Losses in Pipes, Bends and Fittings Notes for Mechanical Engineering and coefficient of friction: Head Losses in Pipes, Bends and Fittings Notes for Mechanical Engineering.

For turbulent flow, the coefficient of friction: Head Losses in Pipes, Bends and Fittings Notes for Mechanical Engineering

Chezy’s Formula: In fluid dynamics, Chezy’s formula describes the mean flow velocity of steady, turbulent open channel flow.

Head Losses in Pipes, Bends and Fittings Notes for Mechanical Engineering

Average velocity V is given by: Head Losses in Pipes, Bends and Fittings Notes for Mechanical Engineering

Where: Head Losses in Pipes, Bends and Fittings Notes for Mechanical Engineering

i = Loss of head per unit length of pipe 14-Head-losses (8) (hydraulic slope tan θ)

Head Losses in Pipes, Bends and Fittings Notes for Mechanical Engineering

Relation between Coefficient of Friction and Shear Stress:

Head Losses in Pipes, Bends and Fittings Notes for Mechanical Engineering

 14-Head-losses (11)

where: f = Coefficient of friction

τ0 = Shear stress

Minor Loss: Another type of head loss in minor loss is induced due to the following reasons

Loss due to Sudden Enlargement:

Head loss: 14-Head-losses (12)

Loss due to Sudden Contraction:

Head loss: 14-Head-losses (13)

Remember v1 is the velocity at a point that lies in the contracted section.

Loss of Head at Entrance to Pipe:

Head loss: 14-Head-losses (14)

Loss at Exit from Pipe

Head loss: 14-Head-losses (15)

Note: In cases 1 and 2, flow occurs from pipe to pipe, while in cases 3 and 4, flow occurs between tank and pipe. We are taking entry or exit w.r.t. pipe. So, be careful.

Combination of Pipes: Pipes may be connected in series, parallel, or in both. Let’s see their combinations.

Pipe in Series: As pipes are in series, the discharge through each pipe will be the same.

Head Losses in Pipes, Bends and Fittings Notes for Mechanical Engineering

In series pipes:

(i). Q = A1v1 = A2v2 = A3v3

(ii). The total head loss will be the sum of the head losses of each individual pipe.

Head Losses in Pipes, Bends and Fittings Notes for Mechanical Engineering

Major loss = Head loss

Due to friction in each pipe:

Head Losses in Pipes, Bends and Fittings Notes for Mechanical Engineering

While, minor loss = Entrance loss + Expansion loss + Contraction loss + Exit loss

Head Losses in Pipes, Bends and Fittings Notes for Mechanical Engineering

If minor losses are neglected then:

Head Losses in Pipes, Bends and Fittings Notes for Mechanical Engineering

Pipes in Parallel: In this discharge in the main pipe is equal to the sum of discharge in each of the parallel pipes.

Head Losses in Pipes, Bends and Fittings Notes for Mechanical Engineering

For Parallel pipes:

(i). Total discharge: Q = Q1 + Q2

(ii). The loss of head in each parallel pipe is the same.

i.e. Loss of head for branch pipe 1 = Loss of head for branch pipe 2

Head Losses in Pipes, Bends and Fittings Notes for Mechanical Engineering

where: hf,1 and hf,2 are head loss at 1 and 2 respectively.

Equivalent Pipe: A compound pipe that consists of several pipes of different lengths and diameters to be replaced by a pipe having a uniform diameter and the same length as that of a compound pipe is called an equivalent pipe.

(i). Series connection:

Head Losses in Pipes, Bends and Fittings Notes for Mechanical Engineering

Head Losses in Pipes, Bends and Fittings Notes for Mechanical Engineering

(where: L = L1 + L2 + L3)

If f = f1 = f2 = f3

Then: Head Losses in Pipes, Bends and Fittings Notes for Mechanical Engineering

(ii). Equivalent length for parallel connection:

Head Losses in Pipes, Bends and Fittings Notes for Mechanical Engineering

Hydraulic Gradient Line (HGL) and Total Energy Line (TEL):

Head Losses in Pipes, Bends and Fittings Notes for Mechanical Engineering

HGL → It joins a piezometric head Head Losses in Pipes, Bends and Fittings Notes for Mechanical Engineering at various points.

TEL → It joins the total energy head at various points

14-Head-losses (31)

Note:

1. HGL is always parallel but lower than TEL by velocity head.

2. For stationary bodies such as reservoirs or lakes, the EGL and HGL coincide with the free surface of the liquid.

3. A steep jump or droop occurs in EGL and HGL whenever mechanical energy is added to the fluid (by a pump or mechanical energy is removed from the fluid (by a turbine) respectively.

Head Losses in Pipes, Bends and Fittings Notes for Mechanical Engineering

Power Transmission through Pipe (P):

Head Losses in Pipes, Bends and Fittings Notes for Mechanical Engineering

Pideal = ρQgH

Pideal = ρQg(H-hf)

hf = head loss

Head Losses in Pipes, Bends and Fittings Notes for Mechanical Engineering

For maximum efficiency: Head Losses in Pipes, Bends and Fittings Notes for Mechanical Engineering

Power delivered by a given pipeline is maximum when the flow is such that one-third of the static head is consumed in pipe friction. Thus, efficiency is limited to only 66.66%

Maximum efficiency, 14-Head-losses (34)

Water Hammer: When a liquid is flowing through a long pipe fitted with a valve at the end of the pipe and the valve is closed suddenly a pressure wave of high intensity is produced behind the valve. This pressure wave of high intensity is having the effect of hammering action on the walls of the pipe. This phenomenon is known as the water hammer.

The intensity of pressure rise due to the water hammer,

14-Head-losses (35)

When the valve is closed gradually when the valve closed suddenly with a rigid pipe

14-Head-losses (36)

When the valve closed suddenly with a plastic pipe

14-Head-losses (37)

If the time required to close the valve

14-Head-losses (38) Valve closure is said to be gradual.

14-Head-losses (39) The valve closure is said to be sudden.

Where, L = Length of pipe

D = Diameter of pipe

C = Velocity of pressure wave produced due to water hammer 14-Head-losses (40)

v = Velocity of flow

K = Bulk modulus of water

E = Modulus of elasticity for pipe material.

t = Time required to choose the valve.

This topic is important for GATE MEISRO MEESE IES ME, and other Mechanical exams.

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