Bernoulli's principle: Incompressible water flows out of a large reservoir through a pipe that opens to the atmosphere 5.70 m below the level of the water in the reservoir. What is the speed of the water as it comes out of the pipe?
A) 1.72 m/s
B) 7.47 m/s
C) 55.8 m/s
D) 10.6 m/s
E) 27.9 m/s

Question

Quizplus · Accepted Answer

According to Bernoulli's principle, the total energy of a fluid is conserved along a streamline. This means that the sum of the potential energy, kinetic energy, and pressure energy must remain constant.

At the surface of the reservoir, the water has only potential energy given by:

$PE = mgh$

where $m$ is the mass of the water, $g$ is the acceleration due to gravity, and $h$ is the height of the water above the opening of the pipe.

At the exit of the pipe, the water has only kinetic energy given by:

$KE = \frac{1}{2}mv^2$

where $v$ is the speed of the water.

Since there is no change in pressure energy, we can set the potential energy at the surface of the reservoir equal to the kinetic energy at the exit of the pipe:

$mgh = \frac{1}{2}mv^2$

Simplifying this expression gives:

$v = \sqrt{2gh}$

Plugging in the given values gives:

$v = \sqrt{2(9.81~m/s^2)(5.70~m)} = \boxed{10.6~m/s}$

Bernoulli's Principle: Incompressible Water Flows Out of a Large Reservoir