Oil enters the bend of a pipe in the horizontal plane with velocity 4 ~ms ⁻¹ and pressure 280 10^3 Nm ⁻² as shown in the figure. The pressure of oil at the point Q is 86 . Find the value of . ( KNm ⁻² ) . (Take specific gravity of oil as 0.9 and 37^ =0.6 )

Step-by-step solution

Let A₁ and A₂ be the cross-sectional area of the pipe at points P and Q respectively. Let v ₁ and v ₂ be the velocities of oil at the points P and Q respectively. By conservation of mass, Q = A ₁ ~V ₁= A ₂ ~V ₂ v₂= ( A₁ A₂ ) (v₁ )=4 v₁ Applying Bernoullis's equation between points P and Q , we have P₁+ 1 2 v₁^2=P₂+ 1 2 v₂^2P₂=P₁+ 1 2 p (v₁^2-v₂^2 )=P₁+ 1 2 0.9[16-256] 10^3=280 10^3+(-108) 10^3P₂=172 10^3 Nm ⁻²P₂=172 ( KN m ⁻² ) .