A ball of weight `W` is supported on a vertical jet of water. If the stream of water flowing from the nozzle has a diameter `D` and velocity `u`, determine the value of `H`. Assume that no loss of energy takes place.

Answer

`1/(2g)`

Explanation

Applying continuity equation at nozzle end at a top position
`a_(1)u=a_(2)v`
`v=(a_(1)u)/(a_(2))`…..i
`v^(2)-u^(2)=-2gH`
`implies H=1/(2g) {u^(2)-[W/(rhoa_(1)^(2)u)]^(2)}`…….ii
`implies rhoa_(2)v^(2)=Wimplies v=W/(rhoa_(1)u)`
`implies (rhoa_(2)u)/W=1/vimpliesv^(2)=W/(rhoa_(1)u)`
`impliesH=1/(2g) {u^(2)-[W/(rhoa_(1)^(2)u)]^(2)}`
`=1/(2g){u^(2)-[(4D)/(rhopiD^(2)u)]^(2)}`