Case Study: Toricelli's Law: Quiz

Problem 4

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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