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Tuesday, 19 June 2018

MOMENT OF MOMENTUM EQUATION IN 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 as well as resultant force exerted by flowing fluid on a pipe bend, in the subject of fluid mechanics, in our recent posts.

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

Moment of momentum equation

According to the concept of moment of momentum equation, Resulting torque acting on a rotating fluid will be equal to the rate of change of moment of momentum.

Let us consider that we have a rotating fluid and let us consider two sections in rotating fluid i.e. section 1 and section 2.

V1 = Velocity of fluid at section 1
r1 = Radius of curvature at section 1

V2 = Velocity of fluid at section 2
r2 = Radius of curvature at section 2

Q = Rate of fluid flow
ρ = Density of fluid

Let us find the momentum of fluid at section 1
Momentum of fluid per second at section 1 = Mass x velocity
Momentum of fluid per second at section 1 = ρ Q x V1
Moment of momentum per second at section 1 = ρ Q x V1 x r1

Similarly, Moment of momentum per second at section 2 = ρ Q x V2 x r2
Rate of change of moment of momentum = ρ Q x V2 x r- ρ Q x V1 x r1
Rate of change of moment of momentum = ρ Q [V2 x r- V1 x r1]

According to the concept of moment of momentum equation, Resulting torque acting on a rotating fluid will be equal to the rate of change of moment of momentum.

Resultant Torque = Rate of change of momentum

T = ρ Q [V2 x r- V1 x r1]

Above equation will be termed as moment of momentum equation.

Applications of moment of momentum equation

Moment of momentum equation will be applied in following cases.
1. To determine the torque exerted by water on sprinkler
2. For analysis of flow problems in centrifugal pump and turbine

We will now find out the "Momentum equation"and Free liquid jet, 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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