# Surge Tanks

**Contents**

## Introduction

When the rate of flow of a fluid passing down a pipe-line changes, there is a change in pressure. The severity of this effect depends upon the rate of change in the flow rate, the length of the pipe and its diameter. In small bore pipes there is no real problem other than maybe an annoying hammering sound. In large water mains the rate of change in flow is carefully controlled to avoid damage to pipes and valves. Unfortunately this solution will not work with Turbines where a sudden change in load requires a rapid change in water demand.**Surge Tanks**or

**Stand Pipes**are used to reduce the pressure surges. When the flow to the turbine is reduced, water flows into the surge tank and conversely for increased load , the initial extra water required is from the surge tank.

**surge tank**(or

**surge drum**) is a standpipe or storage reservoir at the downstream end of a closed aqueduct or feeder pipe to absorb sudden rises of pressure as well as to quickly provide extra water during a brief drop in pressure.

**valve**is a device that regulates, directs or controls the flow of a fluid by opening, closing, or partially obstructing various passageways.

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## Instantaneous Closure Neglecting Friction

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- Surge tank area / Pipe line area
- = the initial velocity of water in the pipe.
- = the instantaneous velocity in the pipe line t secs. after the change in load.
- = The height of the surge level above the surface of the reservoir t secs. after the change in load.
- = density of water.
- be the periodic time of the oscillation in the Surge Tank.

**By Newtons second Law**The pressure force on the water column in the pipe line = Mass multiplied to Acceleration ( is called the Acceleration or Inertia head )

**By Mass Continuity**Flow in the surge tank = Flow in the pipe, i.e. Or this can be written as: Differentiate: Substituting equation (4) in equation (3) But this is the equation for simple harmonic motion whose solution is: When , and by inspection .

Hence: Differentiate the above equation: But from equation (3) when : And also: Substitute in equation (7) If is the period of a complete oscillation:

When: From equation (5)

And since From equation (6) The following two graphs show the variation of both and with time.

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**Notes:**

- The maximum surge height occurs at time , i.e.

- A large value of i.e. a large surge tank area, means a small but a longer periodic time .
- Changes in reservoir level and the inertia of the water column in the surge tank have been neglected.

## A Sudden Complete Valve Closure Allowing For Friction

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**maximum surge**can then be found by putting and in the following equation. This equation can only be solved by trial and error but a first approximation neglecting friction and using will save work!

And for the first

**minimum surge**Note that in the theory is measured positively upwards from the reservoir level. is positive or negative depending upon whether the surge level is rising or falling. is positive or negative depending whether the flow is towards the surge tank or away from it. is added when the flow is towards the surge tanks and is subtracted if the flow is towards the reservoir.

From the

**Darcy equation**the friction head lost is: This is usually written as where is a constant for the pipe line. At a time secs, after closure let the surge level be at a height above the reservoir level and let the pipe velocity be . For steady flow at velocity the level in the surge tank would be below the reservoir level. Thus the excess pressure head at causing the deceleration of the water column is from

**Newton'**

**s second Law**:

Pressure force = Mass multiplied to Acceleration But by continuity: Hence: Substituting from equations (10) and (11) in (9) i.e. This is insoluble as it stands since we can not deal with the friction term.

To eliminate : But: Substitute in equation (8) Or: The solution of this equation is: It is now necessary to evaluate the constant :

When: , and The height of the first

**maximum surge**can then be found by putting and in the above equation. The equation can then only be solved by trial and error but a first approximation neglecting friction and using will save work!

**First Minimum Surge.**

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Equation (8) now becomes: And by continuity: Or: NOTE: the net effect of the flow reversal on the above equations is to change the sign of the term, so the equations generated, during the consideration for sudden complete closure are modified as follows.

Eliminating equation (13) becomes: Eliminating : Putting when : The following graphs show the variations of and with time.

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is positive or negative depending whether the flow is towards the surge tank or away from it.

is added when the flow is towards the surge tanks and is subtracted if the flow is towards the reservoir.

## Gradual Valve Closure

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**Continuity equation**: Or: After the valve has closed in a time remains zero and the equation becomes: as before

This can only be dealt with by numerical integration and even then the variation of with time must be known. It is usual to assume that decreases uniformly from to zero in a time i.e. at a time .

## Sudden Valve Opening On Increased Load.

**Note**: Assume that the velocity at the valve increases instantaneously to the final steady velocity

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##### Example - Example 1

Show that if the friction head is proportional to velocity squared , the oscillatory motion of the level in the Surge tank following a sudden complete shut down of then turbines is given by the equation taking the form: in which is the height at any instant of the Surge Tank level with reference to the reservoir level, and are constants, the former having positive values when the flow along the pipe-line is towards the Surge Tank and negative when reversed.

Find and if the Surge Tank diameter is 100 ft. pipe line diameter 15 ft. and the

**length**of the pipe-line from reservoir to Surge Tank 2,400 ft. At the instant when the turbines are completely shut down, the flow along the pipe-line from reservoir to surge tank is and the level in the Surge Tank is stationary, 3 ft. below the level in the reservoir.

### Variable Area Chamber

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**23287/Surge-Tanks-017.png**cannot be found in /users/23287/Surge-Tanks-017.png. Please contact the submission author.The object is to limit the extremes of the surges. This arrangement provides a quick initial response followed by a slower change in levels and almost constant pressure in the larger chamber. Note that:- Chamber caters for sudden valve closure.
- Gallery assists demand for more water caused by an increased load on the turbine.

### Throttled Surge Tank

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### Johnson Differential Surge Tank

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**23287/Surge-Tanks-019-a.png**cannot be found in /users/23287/Surge-Tanks-019-a.png. Please contact the submission author.On a change of load the Surge level will change rapidly in the riser thus causing a rapid deceleration or acceleration in the pipe.The main chamber level lags behind. The net flow into or out of the Surge Tank is thus less than in the simple design.

**Note:**There are various other designs of Surge Tank with Air tight Chambers, Conical shapes and multiple chambers. In some designs where the height of the Tank is limited , it is common to have chambers with an overflow spill way.