Question

A liquid of density `rho` is flowing with a speed v through a pipe of cross sectional area A. The pipe is bent in the shape of a right angles as shown. What force should be exerted on the pipe at the corner to keep it fixed?

Answer 1

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

`|DeltavecP|=|vecP_(f) - vecP_(i)|=sqrt2dDeltamv`
`F = (dP)/(dt) = (sqrt2)v (dm)/(dt)`,[as `dm = rhoAdL`]
`F =sqrt2v((rho.AdL))/(dt) ,[as dL//dt =v]`
`F = sqrt2 rho Av^(2)` .