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 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.

V

_{1}= Velocity of fluid at section 1
r

_{1}= Radius of curvature at section 1
V

_{2}= Velocity of fluid at section 2
r

_{2}= 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 V

_{1}
Moment of momentum per second at section 1 = ρ Q x V

_{1}x r_{1}
Similarly, Moment of momentum per second at section
2 = ρ Q x V

_{2}x r_{2}
Rate of change of moment of momentum = ρ Q x V

_{2}x r_{2 }- ρ Q x V_{1}x r_{1}
Rate of change of moment of momentum = ρ Q [V

_{2}x r_{2 }- V_{1}x r_{1}]
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 [V_{2} x r_{2 }- V_{1} x
r_{1}]

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