2.18 Case Study: Toricelli's Law: Quiz


Problem 4

Consider the differential equation

describing the flow of water out of the tank. What is the significance of the following?

  1. b = A
  2. b = 0
  3. Adding the condition h(0) = 0


Answers, problem 4

  1. If b = A, the water is in free fall as it empties, and the differential equation reduces to

    This is the equation describing a falling object as derived in section 2.18 of the textbook.

  2. If b = 0, there is no outlet hole, and the water does not drain out of the tank. The differential equation reduces trivially to

  3. The added condition h(0) = 0 indicates an empty tank.


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