We were
discussing the basics
of shear stress in turbulent flow, minor
head losses in pipe flow, hydraulic
gradient and total energy line, basic concept and working of
syphon, flow
through pipes in series, flow
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 theory, in
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
Image
courtesy: Google
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