Hydraulic System
December 12, 2018

## MOMENTUM EQUATION FOR COMPRESSIBLE FLOW

We were discussing the basics of drag
force &lift force and drag and lift coefficient in the subject of fluid
mechanics, in our recent posts.

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We will discuss now a new topic i.e. compressible fluid
flow, in the subject of fluid mechanics, with the help of this post. Before
going in detail discussion about compressible flow, we must have basic
knowledge about various equations associated with the compressible flow.

Till now we were discussing the various concepts and
equations such as continuity equation, Euler equation, Bernoulli’s equation and
momentum equation for incompressible fluid flow. In same way we will have to
discuss above equations for compressible fluid flow too.

We have already seen the derivation of

**and***continuity equation***for compressible fluid flow in our previous post. We will start here our discussion about the compressible fluid flow with the basics of momentum equation for compressible fluid flow.***Bernoulli’s equation*
Compressible flow is basically defined as the flow
where fluid density could be changed during flow.

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**Momentum
equation for compressible fluid flow**

The momentum per second of a flowing fluid will be
equal to the product of mass per second and the velocity of flow.

The momentum per second of a flowing fluid = Product
of mass per second x Velocity of flow

The momentum per second of a flowing fluid = ρ A V x
V

ρ A V = Mass per second

As we have already seen during discussion of

**, term ρ A V will be constant at each section of flow. Therefore, the momentum per second of a flowing fluid will be equal to the product of mass per second which is a constant quantity and the velocity of flow.***continuity equation*
Therefore, we can say that momentum per second will not
be affected due to compressible effect as term ρ A V is constant. In simple, we
can say that momentum equation for incompressible and compressible fluid will
be same.

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*Momentum
equation for compressible fluid for any direction will be given as mentioned
here *

*Momentum equation for compressible fluid for any direction will be given as mentioned here*

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.

Net force in a direction = Rate of change of
momentum in same direction

Net force in a direction = Mass per second x change
of velocity

Net force in a direction = ρ AV x [V

_{2}-V_{1}]
Further we will go ahead to find out the pressure wave and sound wave, 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