We were
discussing the various basic concepts such as Euler’s Equation of motion, Bernoulli’s equation from Euler’s equation, derivation of discharge through venturimeter,
derivation of discharge through Orifice meter and Pitot tube with the expression of velocity
of flow at any point in the pipe or channel in the subject of fluid mechanics,
in our recent posts.

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Today we
will see here the concept of the momentum equation, in the subject of fluid
mechanics, with the help of this post.

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**Momentum
equation**

Momentum
equation is based on the law of conservation of momentum or on the momentum
principle.

According
to the law of conservation of momentum, net force acting on a fluid mass will
be equivalent to the change in momentum of flow per unit time in that direction.

Force
acting on a fluid mass (m) will be given by Newton’s second law of motion and
we will have following equation as mentioned here.

F = m x a

Where, a
is the acceleration of the fluid flow acting in the same direction as force F.

As we know
that acceleration could be defined as the rate of change of velocity or we can
write as mentioned here.

Above
equation is termed as the law of conservation of momentum or on the momentum
principle.

We can
also write the law of conservation of momentum or on the momentum principle as
mentioned here.

F. dt = d
(mv)

Above
equation will be termed as the impulse-momentum equation.

After
considering above equation we can say that impulse of a force F acting on a
fluid of mass m in a short duration of time dt will be equal to the change of
momentum in the direction of force.

We will
now find out the force exerted by a flowing fluid on a pipe bend, in
the subject of fluid mechanics, in our next post.

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

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**Reference:**

Fluid
mechanics, By R. K. Bansal

Image
Courtesy: Google