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 cm² and 3 cm² respectively. The rate of flow will be ____ cm³/s. (take g=10 m/s² )

Solution

Physics sir · 4 steps

The 5 cm gap is a pressure difference: tie it to the speeds with Bernoulli and continuity.

1. Pressure difference. Each vertical tube shows the pressure at its point. The column at A stands h = 5 cm = 0.05 m higher, so P_A - P_B = ρ g h.
2. Continuity. The same volume passes every section each second, so A_A v_A = A_B v_B. With 6 v_A = 3 v_B, you get v_B = 2v_A.

   ρ g h = 1/2ρ(v_B² - v_A²) = 1/2ρ(4v_A² - v_A²) = 3/2ρ v_A²

3. Find the speed. The tube is horizontal, so Bernoulli has no height term. Then v_A² = 2gh/3 = (2 × 10 × 0.05)/3 = 1/3 m²s⁻², which gives v_A = 1/√3 m s⁻¹ = 100/√3 cm s⁻¹.
4. So. Rate of flow Q = A_A v_A = 6 × 100/√3 = 600/√3 = 200√3 cm³s⁻¹, which is option (d).

The idea to keep. In a venturimeter, the height difference gives P₁ - P₂ = ρ g h. Continuity fixes the ratio of the speeds. Then use the area that matches the speed you found when you compute Q = Av.

Answer from the NTA final answer key. Solution by PrepWiser.