Water flows through a horizontal tube as shown in the figure. The difference in height between the water columns in vertical tubes is 5 cm and the area of cross-sections at A and B are 6 ~cm ² and 3 ~cm ² respectively. The rate of flow will be _ _ _ _ cm ³ / s . (take g=10 ~m / s ² )

Step-by-step solution

Given: h = 5 cm, A₁ = 6 cm², A₂ = 3 cm², g = 1000 cm/s² By continuity: A₁v₁ = A₂v₂ v₂ = 2v₁ By Bernoulli's equation: P₁ - P₂ = 1 2 (v₂^2 - v₁^2) Since P₁ - P₂ = gh : gh = 1 2 (4v₁^2 - v₁^2) = 3 v₁^2 2 v₁ = 2gh 3 = 2 1000 5 3 = 100 3 cm/s Rate of flow Q = A₁v₁ = 6 100 3 = 200 3 cm³/s