## Sunday, 14 October 2018

We were discussing the basics of shear stress in turbulent flowminor head losses in pipe flowhydraulic gradient and total energy line, basic concept and working of syphonflow through pipes in seriesflow through pipes in parallel, flow through branched pipes, power transmission through pipes and flow through nozzle, in the subject of fluid mechanics, in our recent posts.

Now we will go ahead to see the concept of water hammer in pipes, in the subject of fluid mechanics, with the help of this post.

### Water hammer in pipes

A sudden change of fluid flow rate in a large pipeline, due to sudden closing of valve or pump, may involve a great mass of water moving inside the pipe.

Pressure will be increased in the pipe, due to sudden change of flow rate, greater than the normal static pressure in the pipe.

Excessive pressure may fracture the pipe walls or cause other damage to the pipe line system. This phenomenon will be termed as water hammer phenomenon.

### Let us understand the basic concept of water hammer in pipes

Let us consider, as displayed here in following figure, one tank filled with water and a pipe AB which is connected with water tank at one end. Let us think that water is filled in tank up to a height of H from the centre of pipe AB.

One valve is provided at the other end of pipe in order to regulate the flow of fluid. Let us assume that valve is fully open and water is flowing at a velocity of V through the pipe.

If valve is closed suddenly, momentum of flowing water will be destroyed and consequently a wave of high pressure will be set up. This wave of high pressure will be transmitted along the pipe with a velocity equal to the velocity of the sound wave and may create noise called knocking.

There will be also hammering action over the pipe walls due to this wave of high pressure and hence this phenomenon will be termed as water hammer.

### Pressure rise due to water hammer will be dependent over the following factors as mentioned here

• Velocity of water flow in pipe
• Pipe length
• Time taken for closing the valve
• Elastic properties of the material of the pipe

The sudden rise of pressure due to water hammer may be viewed as the result of the force developed in the pipe required to stop the flowing water column. Let us think that water column has a total mass M and it is changing its velocity at the rate of dV/dT.

Now according to the Newton’s law of motion, we will have following equation as mentioned here
F = M dV/dT

If the velocity of entire water column is reduced to zero instantly then we will have following case

F = M dV/dT = M (V0 – 0)/0 = ∞
F = Infinite

The resulting force and hence pressure will be infinite, but it is not possible because mechanical valve will take a certain amount of time for complete closure of valve.

In addition, neither the pipe walls nor the water column involved are perfectly rigid under large pressure. The elasticities of the material of the pipe and water column will also play an important role in the phenomenon of water hammer.

Further we will go ahead to find out the concept of boundary layer theoryin the subject of fluid mechanics, with the help of our next post.

Do you have any suggestions? Please write in comment box.

### Reference:

Fluid mechanics, By R. K. Bansal