A tank has a small hole of area of cross-section A at the bottom. Water from a pipe of inner cross-section area 2A is entering the tank with a velocity of 5 m/s. Calculate the height (in m) up to which the water will be filled inside the tank at steady state?
Physics · Mixed Chapter
JEE Mains

Question

A tank has a small hole of area of cross-section A at the bottom. Water from a pipe of inner cross-section area 2A is entering the tank with a velocity of 5 m/s. Calculate the height (in m) up to which the water will be filled inside the tank at steady state?

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1: Inlet volume-flow rate is Qᵢₙ=(2A)(5 m/s)=10A m/s. Step 2: At steady level, outlet flow rate through the bottom orifice is Qₒᵤₜ=A√(2gh). Step 3: Equate inflow and outflow: 10A=A√(2gh), so √(2gh)=10 m/s. Step 4: h=100/(2g)=5 m for g=10 m/s². Therefore the steady-state height is 5 m.