Mumbai University > Civil Engineering > Sem 5 > Applied Hydraulics 1

Marks: 10M

Year: Dec 14, May 15, Dec 15

Moment of momentum equation is derived from moment of momentum principle which states that the resulting torque acting on a rotating fluid is equal to the rate of chance of moment of momentum.

Let $V_1$ = velocity of fluid at section 1

$r_1$ = radius of curvature at section 1

Q = rate of flow of fluid

$\rho$ = density of fluid

and $V_2$ and $r_2$ = velocity and radius of curvature at section 2

Momentum of fluid at section 1 = mass x velocity = $P Q \times V_1 /s$

Moment of momentum per second at section 1 = $PQ \times V_2 \times r_2$

Rate of change of moment of momentum = $PQ V_2 r_2 - PQV_1 r_1 = PQ[v_2r_2 - v_1r_1]$

According to moment of momentum principle

Resultant torque = rate of change of moment of momentum

$T = PQ [V_2r_2 - V_1r_1]$ ----- (1)

Eq (1) is known as moment of momentum equation.