Dimensional analysis of the equation v e l o c i t y x = p r e s s u r e d i f f e r e n c e 3 / 2 × d e n s i t y - 3 / 2 , gives the value of x as _______.

Step-by-step solution

( v e l o c i t y ) x = P 3 / 2 × ρ - 3 / 2 = P ρ 2 = M L - 1 T - 2 M L - 3 3 2 = L 2 T - 2 3 / 2 = L 3 T - 3 = [ L 1 T - 1 ] 3 But L 1 T - 1 is the dimension of velocity. ⇒ x = 3