Time to empty a tank with an orifice at the bottom (uniform cross-section) A tank of uniform area A holds liquid to height H1 and drains through a bottom orifice of area a (ideal Torricelli outflow). Find the total time required to empty the tank completely. Choose the correct expression.

Given data
Uniform tank area A, initial head H₁, orifice area a.

Concept/Approach
Torricelli outflow (ideal): v = √(2gH), discharge Q = a √(2gH). Continuity for falling head: A (−dH/dt) = a √(2gH).

Step-by-step calculation
dH/√H = − (a/A) √(2g) dtIntegrate H from H₁ to 0: 2√H₁ = (a/A) √(2g) · tt = (2A/a) √(H₁/(2g)) = (A/a) √(2H₁/g).

Common pitfalls
Missing the square-root dependence on head or forgetting to separate variables before integrating.

Final Answer
(A/a) × √(2H1/g)