Consider a very small hole in the bottom of a tank that is 17.0 cm in diameter and filled with water to a height of 90.0 cm. Find the speed at which the water exits the tank through the hole.
A) 44.1 m/s
B) 17.64 m/s
C) 48.3 m/s
D) 4.20 m/s

Question

Consider a very small hole in the bottom of a tank that is  17.0 cm in diameter and filled with water to a height of  90.0 cm. Find the speed at which the water exits the tank through the hole.
A)  44.1 m/s
B)  17.64 m/s
C)  48.3 m/s
D)  4.20 m/s

Quizplus · Accepted Answer

The speed at which water exits the tank can be found using Torricelli's law, which states that the speed $v$ of efflux of a fluid under the force of gravity from a hole is given by the equation $v = \sqrt{2gh}$, where $g$ is the acceleration due to gravity (approximately $9.8 \, \text{m/s}^2$) and $h$ is the height of the fluid above the hole. Plugging in the given height of $90.0 \, \text{cm} = 0.9 \, \text{m}$, we get $v = \sqrt{2 \times 9.8 \, \text{m/s}^2 \times 0.9 \, \text{m}} = \sqrt{17.64} \, \text{m/s} \approx 4.20 \, \text{m/s}$.

Consider a Very Small Hole in the Bottom of a Tank