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Moment of Momentum Equation

Moment of momentum equation states, “The resulting torque acting on a rotating fluid is equal to the rate of change of moment of momentum.

Let v1 and v2 are the velocity at nozzle 1 and 2.

Moment of fluid at a section 1

= mass x velocity = ρ Q x v1

Moment of momentum per second of fluid at section 1

= ( ρ Q v1) r1

Similarly moment of momentum per second of fluid at section2

= ( ρ Q v2)r2

Rate of changes of momentum

= ρ Q v2 r2 – ρ Q v1 r1 = ρ Q (v2 r2 – v1 r1)

According to the moment of momentum principle.

Resultant torque = rate of change of moment of momentum

T = ρ Q (v2 r2 – v2 r1)

This equation is known as moment of momentum equation.

Application of Moment of Momentum Equation:

(1)    To determine torque exerted by water on sprinkler
(2)    To analyze problems in turbines and centrifugal pumps

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