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?

Options

A. `(sqrt(2)SV)/(rho)`
B. `sqrt(2)SV^(2)rho`
C. `sqrt(3)(SV(2)rho)/(2)`
D. `sqrt(3)SV^(2)rho`

Answer

B

Explanation

Take x-axis along the flow and y-axis perpendicular to it
`V_("initial")=Vveci,V_("final")=Vvecj,|Deltavec(V)|=sqrt(V^(2)+V^(2))=sqrt(2)V`
`F=m(Deltav)/(t)=m(Deltav)/(t)=rhoxxS(l)/(t)xxsqrt(2)V=sqrt(2)SV^(2)rho`