Water is flowing through a horizontal tube as depicted in the figure. Given that the difference in heights of the water columns in the vertical tubes is 2 cm , and the areas of cross-section at A and B are 4 cm ^2 and 2 cm ^2 respectively, determine the rate of flow of water across any section.

Step-by-step solution

Given, area of cross-section at A , A₁ = 4 cm ^2 Area of cross-section at B , A₂ = 2 cm ^2 Difference in height of water columns, h = 2 cm Let v₁ and v₂ be the velocities of water at A and B respectively. From the equation of continuity: A₁ v₁ = A₂ v₂ 4 v₁ = 2 v₂ v₂ = 2 v₁ Applying Bernoulli's theorem for the horizontal tube: P₁ + 1 2 v₁^2 = P₂ + 1 2 v₂^2 P₁ - P₂ = 1 2 (v₂^2 - v₁^2) The pressure difference is also given by the hydrostatic pressure of the water column difference: P₁ - P₂ = g h Equating the two expre