A small hole of cross-sectional area 2 mm² is near the bottom of a fully filled open water tank of depth 2 m. Taking g = 10 m/s², find the approximate volume flow rate out of the hole.
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Question

A small hole of cross-sectional area 2 mm² is near the bottom of a fully filled open water tank of depth 2 m. Taking g = 10 m/s², find the approximate volume flow rate out of the hole.

G1 Physics · Accepted Answer

Step 1: Assume the tank surface is large compared with the hole and neglect viscous losses. Step 2: Torricelli's law: outflow speed v = √(2gh) = √(2 × 10 × 2) = √40 ≈ 6.325 m/s. Step 3: Convert hole area: A = 2 mm² = 2 × 10⁻⁶ m². Step 4: Volume flow rate Q = Av = 2 × 10⁻⁶ × 6.325 ≈ 12.65 × 10⁻⁶ m³/s. Final answer: 12.6 × 10⁻⁶ m³/s (Option A).