Glycerine of density 1.25 10^3 ~kg / m ^ 3^4 is flowing in conical shaped horizontal pipe. Crosssectional area of the pipe at its both ends is 10 ~cm ^2 and 5 ~cm ^2 respectively. Pressure difference at both the ends is 3 ~N / m ^2 . Rate of flow of liquid in the pipe is

Step-by-step solution

Using Bernoulli's equation, aligned & P₁+ 1 2 v₁^2+ g h₁=P₂+ 1 2 v₂^2+ g h₂ & P₁+ 1 2 v₁^2=P₂+ 1 2 v₂^2 & P₁-P₂= 1 2 ( v₂^2- v₁^2 ) & v₂^2-v₁^2= 2 3 1.25 10^3 =4.8 10⁻³ ...(i) aligned From equation of continuity, aligned & A ₁ v ₁= A ₂ v ₂ & v ₁ v ₂ = A ₂ ~A ₁ = 5 10 =0.5 & v ₁=0.5 v ₂ ..(ii) aligned Substituting (ii) into (i), aligned 0.75 v ₂^2=4.8 10⁻³ v ₂ & =0.08 ~m / s Rate of flow of glycerine & =A₂ v ₂ & =5 10⁻⁴ 0.08 & =4 10⁻⁵ ~m ^3 / s aligned