2.1. From the given data: D1 = 0.1 m, D2 = 0.15 m, V1 = 2 m/s. Using these data, the following preliminary calculations are useful: A1 = π 4 D2 1 = π 4 (0.1)2 = 0.007854 m2 , A2 = π 4 D2 2 = π 4 (0.15)2 = 0.01767 m2 Volumetric flow rate, Q, is given by Q = A1V1 = (0.007854)(2) = 0.0157 m3/s According to the continuity equation, A1V1 = A2V2 = Q → V2 = Q A2 = 0.0157 0.01767 = 0.889 m/s At 20◦C, the density of water, ρ, is 998 kg/m3 , and the mass flow rate, ˙m, is given by m˙ = ρQ = (998)(0.0157) = 15.7 kg/s 2.2. From the given data: D1 = 0.2 m, D2 = 0.3 m, and V1 = 0.75 m/s. Using these data, the following preliminary calculations are useful: A1 = π 4 D2 1 = π 4 (0.2)2 = 0.03142 m2 , A2 = π 4 D2 2 = π 4 (0.3)2 = 0.07069 m2 (a) According to the continuity equation, A1V1 = A2V2 → V2 = A1V1 A2 = (0.03142)(0.75) 0.07069 = 0.333 m/s (b) The volume flow rate, Q, is given by Q = A1V1 = (0.03142)(0.75) = 0.02357 m3/s = 23.6 L/s