Water hammer in pipes

1) Suppose there is a tank which consists of water and consider a pipe (long) ABas shown in the figure, connected to this tank at a height of 'H' from the centre of the pipe.

2) on the other end of the pipe there is a valve which is provided to regulate flow of water.

3) when this valve is open the water flows with a velocity V in the pipe. But when this valve is closed suddenly, it disturbs the momentum of the flowing water and consequently leads to the formation of a high-pressure wave.

4) This high-pressure wave has got an effect of hammering on the walls of the pipe and hence it is called a water hammer.

Following cases of water hammer in pipes are considered:-

1) gradual closure of the valve,

2)The sudden closure of the valve, ( pipe is considered rigid)

3)sudden closure of valve, (pipe is considered elastic)

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Water Hammer

Hardy cross method:-

The procedure of Hardy cross method is as follows:-

1)In this, a trial distribution of discharges is made arbitrary but in such a way that continuity equation is satisfied at each node.

2) with the help of assumed values of Q, head lost in each pipe is calculated.

3) consider any circuit ( loop). The algebraic sum of head losses round each loop must be zero.

4) now calculate the net head loss around each loop considering the head loss to be positive in clockwise flow and to be negative in an anticlockwise flow.

(If the net head loss due to assumed values of Q round the loop is zero, then assumed values of Q in that loop is correct. But if the assumed values of Q is not zero then assumed values of Q are corrected by introducing $\Delta Q$ for flow till the circuit is balanced.)

$\Delta Q=\dfrac {-\sum r Q_0^n}{\sum r n Q_0^{n-1}}$

For turbulent flow the values of n = 2 and hence above correction factor becomes,

$\Delta Q=\dfrac {-\sum r Q_0^2}{\sum 2r Q_0}$

5) If the value $\Delta Q$ comes out to be positive, then it should be added to the flows in the clockwise direction and subtracted from the flows in the anticlockwise direction.

6) some pipes maybe common to two circuits then the two corrections are applied to these pipes.

7) after the corrections have been applied to each pipe in a loop and to all loops, a second trial calculation is made for all loops. The procedure is repeated until '$\Delta Q$' becomes negligible.

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