A liquid of density 600 kg/m ^3 flowing steadily in a tube of varying cross-section. The cross-section at a point A is 1.0 cm ^2 and that at B is 20 mm ^2 . Both the points A and B are in same horizontal plane, the speed of the liquid at A is 10 cm/s. The difference in pressures at A and B points is ________ Pa.

Step-by-step solution

Using the equation of continuity: A_A v_A = A_B v_B (1.0 10⁻⁴) 0.1 = (20 10⁻⁶) v_B v_B = 10⁻⁵ 2 10⁻⁵ = 0.5 m/s Using Bernoulli's equation for a horizontal tube: P_A + 1 2 v_A^2 = P_B + 1 2 v_B^2 P_A - P_B = 1 2 (v_B^2 - v_A^2) Substituting the given values: P_A - P_B = 1 2 600 (0.5^2 - 0.1^2) P_A - P_B = 300 (0.25 - 0.01) P_A - P_B = 300 0.24 = 72 Pa Answer: 72