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Consider two identical tanks with a bottom hole of diameter d. One tank is filled with water and the other tank is filled with engine oil. The height of the fluid column h is same in both the cases. The fluid exit velocity in the two tanks are \(V_{1}\) and \(V_{2}\). Neglecting all losses, which one of the following options is correct?

  • A.\(V_{2} \gt V_{1}\)
  • B.\(V_{2} = V_{1}\)
  • C.\(V_{2} \lt V_{1}\)
  • D.Insufficient data to definitively conclude the relationship between \(V_{1}\) and \(V_{2}\)

Answer: B

The exit velocities are equal: \(V_{2} = V_{1}\).

Neglecting losses, Torricelli's result from Bernoulli's equation gives the jet speed as \(V = \sqrt{2gh}\). Density cancels from both sides of the energy balance, so the velocity depends only on the head \(h\), which is the same for both tanks.

Viscosity would make the oil jet slower in reality, but the question says to neglect all losses, so \(V_{2} \lt V_{1}\) is not the answer intended. The data are sufficient, and nothing makes the oil faster.

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