For the arrangement shown, the water jet ceases to cross the wall after a time t = α³ s. The tank cross-sectional area is A = 5 m² and the orifice area is a = 32 cm². Assume the container remains fixed and take g = 10 m s⁻². Find α. Image
Physics · Fluid Mechanics
JEE Advanced Practice

Question

For the arrangement shown, the water jet ceases to cross the wall after a time t = α³ s. The tank cross-sectional area is A = 5 m² and the orifice area is a = 32 cm². Assume the container remains fixed and take g = 10 m s⁻². Find α. 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 5. Final answer: 5.