Branched Pipes

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Contents
  1. Introduction
  2. Branched Pipes
  3. Worked Example

The application of the Bernoulli equation to Branched pipes

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Engineering Fluid Mechanics Pipes

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Introduction

It is common for a pipeline to be branched and for the system to be feeding more than one reservoir. This page examines this situation.

Branched Pipes

23287/branched_pipes_1.png

Applying Bernoulli's equation to the whole system but neglecting both the entry head and the junction head.

H_1=\frac{4fl_1{v_{1}}^{2}}{2d_1g}+\frac{4fl_2{v_{2}}^{2}}{2d_2g}+\frac{{v_{2}}^{2}}{2g}
(1)
H_2=\frac{4fl_1{v_{1}}^{2}}{2d_1g}+\frac{4fl_3{v_{3}}^{2}}{2d_3 g}+\frac{{v_{2}}^{2}}{2g}
(2)

It most cases it is possible to neglect the last terms of \frac{v^2}{2g}

Applying the continuity equation:-

a_1v_1=a_2v_2+a_3v_3
(3)

Or

{d_{1}}^{2}v_1={d_{2}}^{2}2v_2+{d_{3}}^{2}v_3
(4)

Worked Example

Water is pumped from a river to two reservoirs A and B. The water surface in reservoir A is at the same hight as the river whilst that in reservoir B is 20 ft. higher.

Pumping from the river takes place by means of a centrifugal pump, the equation relating flow Q (in cubic ft./sec. and H ft. at a constant speed being given by H=75-10\;Q^2

From the river to a junction J is a common pipe is used of 8 in. diameter and 500 ft. long. The branch J to the reservoir A is 5 in. in diameter and 200 ft. long. The branch from J to reservoir B is 6 in. in diameter and 200 ft. long.

Neglecting all losses other than pipe friction, calculate the discharge to A and B. Take f as 0.007 throughout. (B.Sc. Part 2)

To view the workings, please click on the red button