# MOMENTUM EQUATION

It is based on the law of conservation of momentum or on the momentum principle, which states that the net force acting on a fluid mass equal to the change in the momentum of the 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 × a

Where ‘a’ is the acceleration acting in the same direction as force

F. dt = d(mv) Is known as the impulse momentum equation.

It states that the impulse of a force F acting on a fluid mass m in a short interval of time dt is equal to the change of momentum d(m v) in the direction of force.

## Force exerted by a flowing fluid on a pipe-bend:

The impulse momentum equation is used to determine the resultant force exerted by a flowing fluid on a pipe bend.

Consider two sections (1) and (2) as above Let v1 = Velocity of flow at section (1)

P1= Pressure intensity at section (1)

A1 = Area of cross-section of pipe at section (1)

And V2, P2, A2 are corresponding values of Velocity, Pressure, Area at section (2)

Let Fx and Fy be the components of the forces exerted by the flowing fluid on the bend in x and y directions respectively. Then the force exerted by the bend on the fluid in the directions of x and y will be equal to FX and FY but in the opposite directions. Hence the component of the force exerted by the bend on the fluid in the x – direction = – Fx and in the direction of y = – Fy. The other external forces acting on the fluid are p1 A1 and p2 A2 on the sections (1) and (2) respectively. Then the momentum equation in x-direction is given by