True or False: When liquid is released through a hole in a tank and the hole is some distance above the bottom of the tank, the velocity of the liquid released decreases as the tank empties.

True or False: When liquid is released through a hole in a tank and the hole is some distance above the bottom of the tank, the velocity of the liquid released decreases as the tank empties.

• A. True
• B. False
• C. Not enough information
• D. Always decreases

Answer: (B)

The main idea here is that the speed at which liquid exits through a hole under gravity is set by the height of liquid above the hole, not by how full the tank is in general. This is Torricelli’s law: v = sqrt(2 g h), where h is the vertical distance from the liquid surface to the hole. As the tank drains, the liquid surface falls, so h decreases. Because v depends on h, the exit velocity gets smaller as the tank empties, eventually approaching zero when the tank is empty. This assumes typical conditions like a small hole and negligible viscous losses.

The main idea here is that the speed at which liquid exits through a hole under gravity is set by the height of liquid above the hole, not by how full the tank is in general. This is Torricelli’s law: v = sqrt(2 g h), where h is the vertical distance from the liquid surface to the hole. As the tank drains, the liquid surface falls, so h decreases. Because v depends on h, the exit velocity gets smaller as the tank empties, eventually approaching zero when the tank is empty. This assumes typical conditions like a small hole and negligible viscous losses.