Water flows through a horizontal tube of variable cross section. The cross-sectional areas at A and B are 4 mm ^2 and 2 mm ^2 respectively. If 1 cc of water enters through A per second, calculate the pressure difference P_A - P_B .

Step-by-step solution

Given volume flow rate, Q = 1 cm ^3 /s = 10⁻⁶ m ^3 /s Cross-sectional area at A , A_A = 4 mm ^2 = 4 10⁻⁶ m ^2 Cross-sectional area at B , A_B = 2 mm ^2 = 2 10⁻⁶ m ^2 From the equation of continuity, the velocities at A and B are: v_A = Q A_A = 10⁻⁶ 4 10⁻⁶ = 0.25 m/s v_B = Q A_B = 10⁻⁶ 2 10⁻⁶ = 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 density of water = 1000 kg/m ^3 : P_A - P_B = 1 2 1000 (0.5^2 - 0.25^2) P_A - P_B =