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Wednesday, 12 December 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. 

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 continuity equation and Bernoulli’s 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. 

Compressible flow is basically defined as the flow where fluid density could be changed during flow. 

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 continuity equation, 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. 

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. 

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 [V2-V1

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 

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