A liquid of density `rho` flows along a horizontal pipe of uniform cross - section A with a velocity v through a right angled bend as shown in Fig. What force has to be exerted at the bend to hold the pipe in equilibrium ?

Explanation

Change in momentum of mass `Deltam` of liquid as it passes through the bend

`dP=P_(f)-P_(i)=sqrt2d Delta mv`
`F=(dP)/(dt)=(sqrt2)v(dm)/(dt),["as dm "=rho A dL]`
`F=sqrt2v((rho. AdL))/(dt),["as "dL//dt=v]`
`F=sqrt2rhoA v^(2)`