A large cylindrical tank of area 1 m² contains water and has a small side hole 1 m above the bottom. A frictionless piston of mass 5 kg carries an additional 45 kg load. Find the efflux speed v when the piston is 7 m above the bottom. Take g = 10 m s⁻². Image
Physics · Fluid Mechanics
JEE Mains Advanced

Question

A large cylindrical tank of area 1 m² contains water and has a small side hole 1 m above the bottom. A frictionless piston of mass 5 kg carries an additional 45 kg load. Find the efflux speed v when the piston is 7 m above the bottom. Take g = 10 m s⁻². 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 11. Final answer: 11.