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Monday, 11 June 2018

MOMENTUM EQUATION FLUID MECHANICS

We were discussing the various basic concepts such as Euler’s Equation of motionBernoulli’s equation from Euler’s equationderivation 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.

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.

Reference:

Fluid mechanics, By R. K. Bansal
Image Courtesy: Google

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