Imagine that you have been given the job of designing a fountain to be the centrepiece of a new shopping mall on the Gold Coast. The fountain will consist of a single upward jet of water, launched from a pipe of radius 2 mm and length 1.2 m. The pipe is fed by recycled water, pushed by a pump which produces a pressure difference of 50 000 Pa. How high will the water in the fountain go? The viscosity of water is 0.001 Pa s, and g = 9.8 m s-2.
A) 1.3 m.
B) 5 m.
C) 11 m.
D) 22 m.
E) 44 m.ANS

Question

Quizplus · Accepted Answer

The correct answer is D.The height of the water in the fountain can be calculated using the Bernoulli equation:$$P_1 + \frac{1}{2} ho v_1^2 + ho g h_1 = P_2 + \frac{1}{2} ho v_2^2 + ho g h_2$$where:* $P_1$ is the pressure at the bottom of the pipe* $v_1$ is the velocity of the water at the bottom of the pipe* $ho$ is the density of water* $g$ is the acceleration due to gravity* $h_1$ is the height of the water at the bottom of the pipe* $P_2$ is the pressure at the top of the pipe* $v_2$ is the velocity of the water at the top of the pipe* $h_2$ is the height of the water at the top of the pipeIn this case, we have:* $P_1 = 50 000 Pa$* $v_1 = 0 m/s$* $ho = 1000 kg/m^3$* $g = 9.8 m/s^2$* $h_1 = 0 m$* $P_2 = 0 Pa$* $v_2 = 0 m/s$Substituting these values into the Bernoulli equation, we get:$$50 000 Pa + 0 + 1000 kg/m^3 	imes 0 m/s^2 	imes 0 m = 0 + 0 + 1000 kg/m^3 	imes 9.8 m/s^2 	imes h_2$$Solving for $h_2$, we get:$$h_2 = 5.1 m$$Therefore, the water in the fountain will go 5.1 m high.

Imagine That You Have Been Given the Job of Designing