# Transmission of Power

The transmission of Hydraulic Power through pipelines. Includes Nozzles and Jets, the conditions for maximum Power Transmission , Jet reaction and the efficiency of transmission.

**Contents**

### Key Facts

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

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

## Introduction

The transmission of power through pipes is both common and widespread in its application. Two examples are the large diameter pipes are used in many hydroelectric schemes and the comparatively small bore pipes used to connect the various pumps; motors and rams used on earth moving plant and machine tools.

## Power Transmission In A Pipe

A

**diameter**of a circle is any straight line segment that passes through the center of the circle and whose endpoints are on the circle.**Volume**is the quantity of three-dimensional space enclosed by some closed boundary.**Power**is the rate at which work is done, expressed as the amount of work per unit time and commonly measured in units such as the watt and horsepower.Water Horse Power is given by:
Weight of water / second =
Horse Power of a jet is:
The efficiency of power transmission for the pipe is given by Horse Power at outlet/Horse Power at inlet which is:
Applying

**Bernoulli**'**s****equation**to the pipe and ignoring pipe entry losses: Thus the efficiency of Power Transmission can be written as:## The Conditions For Maximum Power Transmission

i.e. The head lost due to friction is one third of the Total Supply Head.From equations (3) and (4) the Horse Power of the Jet will be:
The weight of water per second, , passing down the pipe increases linearly with , the velocity of the water along the pipe. However decreases with velocity and there is therefore an optimum velocity which will give the maximum jet Horse Power for a given pipe and Head.
Equation (5) can be rewritten using equation (2). is replaced using the

**Darcy equation**: For Maximum Power i.e. From which it can be seen that i.e. The head lost due to friction is one third of the Total Supply Head.### The Efficiency Of Power Transmission For Maximum Power

- This is given by:
The condition for Maximum Power transmitted is rarely used in practice since:
- The efficiency of transmission is low and that means that water is wasted;
- The velocity in the pipeline is high and this can give rise to dangerous
**Water Hammer**effects when valves are closed.

## Nozzles

A

**nozzle**is a device designed to control the direction or characteristics of a fluid flow as it exits an enclosed chamber or pipe via an orifice.
It is assumed that the

**Head H**is the head behind the nozzle and that all pipeline and valve losses have been accounted for elsewhere. There are, of course, losses in the nozzle itself and the actual velocity of discharge will be less than the theoretical value by one to five percent. This is catered for by the use of the coefficient of velocity, , the coefficient of contraction, and the coefficient of Discharge,:## The Nozzle Diameter For Maximum Power Transmission

In the following calculations the losses in the nozzle are ignored. Two proofs are given. The first uses the previous result for the power transmission through a Pipe Line and the second is from first principles.
Diagram from notes.

- a) It has been shown that the maximum Power transmission through a pipe lie occurs when the head lost due to friction is a third of the total head.

Hence:

- b) from first principles

**Bernoulli**'**s equation**across the nozzle and neglecting losses: And using the**continuity equation**: The power output of the nozzle is given by: The nozzle diameter for the maximum power transmission will occur when i.e. Multiply both sides by Or:## Jet Reaction

The jet reaction is the backward force exerted on the nozzle and the pipe and is equal and opposite to the force exerted by the jet on a fixed plate. i.e. The jet reaction = the mass of fluid passing through the jet per second the change in velocity.Therefore the Jet Reaction will be

### The Efficiency Of Power Transmission For Maximum Jet Reaction

- The efficiency,

Example:

[imperial]

##### Example - Example 1

Problem

A Nozzle discharges 175 galls per min. under a head of 200 ft. The diameter of the nozzle is 1 in.
and the diameter of the jet is 0.9 in.
Find:

- The
**coefficient of velocity**for the jet. - The
**head lost**in the nozzle. - The
**horse power**available in the jet.

Workings

- a) The Coefficient of Contraction, is given by:

- b) Using Equation (5)

- c) The horse power of the jet is dependent upon the weight of water per second and the head of water in the jet

Thus:

Horse power will be:

Solution

- a) The
**coefficient of velocity**is - b) The
**head lost in nozzle**is - c) The
**horse power**available in the jet is