Air flows at 120 L s⁻¹ through a horizontal pipe reducing smoothly from diameter 22 cm to 10 cm. A water manometer measures the pressure difference. Neglect losses and take air density 1.20 kg m⁻³. Find the differential water-column height in cm. Image
Physics · Fluid Mechanics
JEE Mains Advanced

Question

Air flows at 120 L s⁻¹ through a horizontal pipe reducing smoothly from diameter 22 cm to 10 cm. A water manometer measures the pressure difference. Neglect losses and take air density 1.20 kg m⁻³. Find the differential water-column height in cm. Image

Physics · Fluid Mechanics

G1 Physics · Accepted Answer

Step 1: Use continuity A₁v₁ = A₂v₂ and Bernoulli's equation P + ½ρv² + ρgh = constant; for jets use momentum flux ṁΔv. Step 2: Substitute the stated areas, levels and pressures, including Torricelli v = √(2gh) where applicable. Applying these relations to the given data gives 1.3. Final answer: 1.3.