Water flow througyh a horizontal pipe whose internal diameter is `2.0 cm` at a speed of `1.0 ms^(-1)` What should be the diameter of the nozzle, If the water is to emerge at a speed of `4.0ms^(-1)`?

Explanation

Here `D_(1) = 2.0 cm = 0.02m`
`v_(1) = 1.0ms^(-1), D_(2) = ? , v_(2) = 4.0ms^(-1)`
Fromequation of continuity `a_(1) upsilon_(1) = a_(2) upsilon_(2)`
`or (pi D_(1)^(2))/(4) xx upsilon_(1) = (pi D_(2)^(2))/(4) xx upsilon_(2)`
`orD_(2)^(2)= (upsilon_(1))/(upsilon_(2))= D_(1)^(2) = (1)/(4) xx (0.2)^(2) = (0.01)^(2)`
`or D_(2) = 0.01 m = 1.0 cm`