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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