In flow through parallel pipes of the same material

By Mohit Uniyal|Updated : July 18th, 2022

In flow through parallel pipes of the same material

(a) The head loss for all pipes is same
(b) the total discharge is equal to the sum of discharges at various points
(c) The total head loss is the sum of head loss in the various pipes
(d) Both (a) and (b)

Answer- (d) - Both (a) and (b)

In flow through parallel pipes of the same material, the head loss for all pipes is the same, and total discharge is equal to the sum of discharge at various points.

Solution:- When the fluid flow through pipes, it consists of two types of losses:

  1. Major losses
  2. Minor losses

The major loss is due to pipe wall friction, which is given by the ‘Darcy Weisbach equation

Δp = fD (L/D) (ρV2/2)

Where,

  • Δp = Pressure loss in N/ m2
  • fD = Darcy friction factor
  • L = Pipe length in m
  • D = hydraulic dimeter in m 
  • V = Average fluid flow velocity in m/s 
  • ρ= Fluid density in kg/m3

As the material of the pipe is the same, then the Darcy friction factor is the same of all pipe 

Apart from this, all other parameters are the same, i.e., pipe length, hydraulic diameter, the velocity of fluid flow, and density of fluid flow. So the head loss will be the same for all the pipes.

When the fluid flows in parallel pipes, the discharge rate is equal to the sum of the discharge rate of individual pipes.

i.e Q = Q1 +Q2 + Q3  +..............+ Qn

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