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.

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

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