Glycerin of density 1 . 25 × 10 3 kg m – 3 is flowing through the conical section of pipe. The area of cross-section of the pipe at its ends are 10 cm 2 and 5 cm 2 and pressure drop across its length is 3 N m – 2 . The rate of flow of glycerine through the pipe is x × 10 – 5 m 3 s – 1 . The value of x is _____.

Step-by-step solution

It is given that A 1 = 10   cm 2 ;   A 2 = 5   cm 2 ∆ P = 3   N   m - 2 By continuity equation, A 1 v 1 = A 2 v 2 ⇒ v 1 = A 2 v 2 A 1       . . . ( i ) By Bernoulli's equation, 1 2 ρ v 2 2 - 1 2 ρ v 1 2 = ∆ P       . . . ( i i ) Using equation (i) in (ii) ∆ P = ρ 2 ( v 2 2 - A 2 v 2 A 1 2 ) ⇒ ∆ P = ρ v 2 2 2 1 - A 2 A 1 2 ⇒ 3 = 1 . 25 × 10 3 × v 2 2 2 1 - 1 4 ⇒ v 2 2 = 6 × 4