Moment Of Momentum Equation

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 = 

1$PQ\times V_1/s$

Moment of momentum per second at section 1 =PQ×V2

2$PQ\times V_2\times r_2$

Rate of change of moment of momentum = PQV2r2−PQV1r1=PQ[v2r





$P\mathrm{Q\times }{V}_2{\mathrm{r\times }}_2-P\mathrm{Q\times }{V}_1{\mathrm{r\times }}_1=PQ[v_2{\mathrm{r\times }}_2-v_1{\mathrm{r\times }}_1]$

According to moment of momentum principle

Resultant torque = rate of change of moment of momentum

T=PQ[V2r2




$T=PQ[V_{\mathrm{2\times }}{r}_2-V_{\mathrm{1\times }}{r}_1]$ ----- (1)

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

Credit:- www.ques10.com/p/15826/define-moment-of-momentum-equation-1/