The Leaking Oil Tank Mystery · AI Generator #GEN-FA667A83

Physics · fluid-mechanics

Problem

An environmental engineer discovers that a cylindrical oil storage tank has developed a small leak near its bottom. The tank has a radius of R=3.0  mR = 3.0\;\text{m} and is initially filled to a height of h0=8.0  mh_0 = 8.0\;\text{m}. The leak is a circular hole with radius r=2.0  mmr = 2.0\;\text{mm} located at a height of hhole=0.5  mh_\text{hole} = 0.5\;\text{m} above the bottom of the tank. The engineer notices something puzzling: initially, oil flows out rapidly, but as the tank drains, the flow rate decreases significantly. When the oil level drops to exactly h=2.0  mh = 2.0\;\text{m} above the bottom, she measures the volume flow rate to be Q=1.2×10−4  m3/sQ = 1.2 \times 10^{-4}\;\text{m}^3/\text{s}. Assuming the oil behaves as an ideal fluid and that the hole acts as a perfect orifice, determine the density of the oil. Take g=9.8  m/s2g = 9.8\;\text{m/s}^2.

Related theory

Browse the problem library