Momentum Principle : It is defined as the net force acting on a fluid mass is, equal to the change in momentum of flow per unit time in that direction.

The force acting on a fluid mass 'm' is given by Newton's second law of motion.

$F = m \times a$

where, a = acceleration acting in same direction as force 'F'

But, $a = \frac{dv}{dt}$

$F = m \frac{dv}{dt}$

$\frac{d(mv)}{dt}$ [ $m = constant$ ]

$F = \frac{d(mv)}{dt}$ - - - - (1)

equation number 1 is the equation of momentum principle.

Application: Bend pipe.

Force exerted by a following fluid on a pipe bend.

The impulse momentum equation i.e. $(F.dt = d(mv)$ is used to determine the resultant force exerted by a flowing fluid on a pipe bend.

Consider two sections (1) and (2) as shown,

Let, $v_1$ = velocity of flow at section (1)

$p_1$ = pressure intensity at section (1),

$A_1$ = Area of c/s of pipe at section (1)

Let $F_x$ and $F_y$ be the components of force exerted by the flowing fluid on bend in x - and y - directions.

Then the force exerted by the bend on fluid in x and y direction will be equal to $F_x$ and $F_y$

Net force acting an fluid in the direction of X = Rate of change of momentum in X - direction.

$\therefore$ $P_1 A_1 - p_2 A_2 cos \theta - F_x = PQ (v_2 cos \theta - v_1)$

$\therefore$ $F_x = PQ (v_1 - v_2 cos \theta)$ +

$p_1 A_1 - p_2 A_2 cos \theta$ - - - - (1)

Similarly, the momentum equation in y- direction,

$0 - p_2 A_2 sin \theta - Fy = PQ (v_2 sin \theta - 0)$

$\therefore$ $Fy = PQ (-v_2 sin \theta) - p_2 A_2 sin \theta$

Now, the resultant force (FB) acting on band.

$F_R = \sqrt{fx^2 + fy^2}$

and the angle made by the resultant force with horizontal direction,

$tan\theta = \frac{fy}{fx}$