A liquid of density `rho` is flowing with a speed V through a pipe of cross sectional area A. What force does the liquid stream exert on wall in x direction if it splashes in the form of a circle after it hits the wall?

Options

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

Answer

A

Explanation

Consider a small element of dm in the direction of flow `dm = rho xx A xx dx`
Momentum in direction of flow `= dm xx V`
final velocity in X direction = 0
Change in momentum per second `= rho A ((dx)/(dt)) (v - 0)` ` = rho A v^(2)`
`:.` Force in x direction = change in momentum in x direction `= rho A v^(2)`

`dm = A xx dx xx rho`