Asked in ETEA MDCAT 2015 2015Moderate

A larger water tank open at the top has small hole in the bottom when the water level is 30m above the bottom of the tank the speed of the water leaking from the hole is:

Correct answer: B. 24m/s

  • A. 2.5m/s
  • B. 24m/s
  • C. 4.44m/s
  • D. Cannot be calculated unless the area of the hole is given

Explanation

The problem can be solved using Torricelli's Theorem, which states that the speed of efflux, v, of a fluid under the force of gravity through a small hole in a container is given by V = √(2gh), where g is the acceleration due to gravity (approximately 10 m/s²), and h is the height of the fluid above the hole. In this case, with g = 10 m/s² and h = 30 m, we calculate V = √(2×10×30) = 24.49 m/s, which approximates to 24 m/s.Option A (2.5 m/s) and Option C (4.44 m/s) are significantly lower than the correct value and result from incorrect calculations. Option D is incorrect because, according to Torricelli's Theorem, the speed does not depend on the hole's area, only the height of the water column.

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About Bernoulli's Equation

Bernoulli’s equation applies conservation of energy to steady flow of an incompressible, non-viscous fluid along a streamline: pressure, kinetic and gravitational terms have a constant total. It explains pressure-speed changes in narrow pipes, Venturi meters and lift, and differs from continuity because it relates pressure as well as velocity and height.

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