Oil of density 800 kg m ⁻³ flows steadily through a horizontal pipe. The cross-sectional areas of the pipe at two sections A and B are 40 cm ^2 and 10 cm ^2 respectively. If the volume flow rate of the oil is 2000 cm ^3 s ⁻¹ , what is the pressure difference between the two sections?

Step-by-step solution

From the given volume flow rate Q , the velocity of oil at section A is: v_A = Q A_A = 2000 cm ^3 s ⁻¹ 40 cm ^2 = 50 cm s ⁻¹ = 0.5 m s ⁻¹ The velocity at section B is: v_B = Q A_B = 2000 cm ^3 s ⁻¹ 10 cm ^2 = 200 cm s ⁻¹ = 2 m s ⁻¹ According to Bernoulli's principle for a horizontal pipe: P_A + 1 2 v_A^2 = P_B + 1 2 v_B^2 The pressure difference is: P = P_A - P_B = 1 2 (v_B^2 - v_A^2) Substitute the values: P = 1 2 800 (2^2 - 0.5^2) P = 400 (4 - 0.25) = 400 3.75 = 1500 Pa Answer: 1500 Pa