Water flows m a horizontal tube (see figure). The pressure of water changes by 700 N m - 2 between A and B where the area of cross section are 40 c m 2 and 20 c m 2 , respectively. Find the rate of flow of water through the tube. (density of water = 1000 k g m - 3 )

Step-by-step solution

Using equation of continuity 40 V A = 20 V B ⇒ 2 V A = V B Using Bernoulli’s equation P A + 1 2 ρ V A 2 = P B + 1 2 ρ V B 2 ⇒ P A - P B = 1 2 V B 2 - V A 2 ⇒ Δ P = 1 2 1000 V B 2 - V B 2 4 ⇒ Δ P = 500 × 3 V B 2 4 ⇒ V B = Δ P × 4 1500 = 700 × 4 1500 m s Volume flow rate = 20 × 100 × V B = 2732   c m 3 / s