# Branched Pipes

The application of the Bernoulli equation to Branched pipes

### Key Facts

**Gyroscopic Couple**: The rate of change of angular momentum () = (In the limit).

- = Moment of Inertia.
- = Angular velocity
- = Angular velocity of precession.

## 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.**Bernoulli**'

**s**

**principle**states that for an inviscid flow, an increase in the speed of the fluid occurs simultaneously with a decrease in pressure or a decrease in the fluid's potential energy.

**Bernoulli**'

**s**

**principle**can be applied to various types of fluid flow, resulting in what is loosely denoted as

**Bernoulli**'

**s**

**equation**.

## Branched Pipes

##### MISSING IMAGE!

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Example:

##### Example - Example 1

Problem

Water is pumped from a river to two reservoirs and . The water surface in reservoir is at the
same hight as the river whilst that in reservoir is 20 ft. higher.
Pumping from the river takes place by means of a centrifugal pump, the equation relating flow (in
cubic ft./sec.) and ft. at a constant speed being given by
From the river to a junction is a common pipe is used of 8 in. diameter and 500 ft. long. The
branch to the reservoir is 5 in. in diameter and 200 ft. long. The branch from to reservoir
is 6 in. in diameter and 200 ft. long.
Neglecting all losses other than pipe friction, calculate the

**discharge to and**. Take as 0.007 throughout.Workings

Darcy's equation can be rewritten as follows:
Applying Bernoulli at the river and reservoir :
Similarly:
But by continuity:
From equation (1)
Subtracting equation (2) from (1)
Substituting into equation (3) squared with values for from equation (4) gives:
Rearranging and collecting terms:
Squaring gives:
Treating this as a quadratic in
And:
From equation (4)

Solution