Water flows out of a large reservoir through an open pipe, as shown in the figure. What is the speed of the water as it comes out of the pipe?
A) 8.9 m/s
B) 9.9 m/s
C) 13 m/s
D) 14 m/s
E) 16 m/s

Question

Water flows out of a large reservoir through an open pipe, as shown in the figure. What is the speed of the water as it comes out of the pipe? 
A) 8.9 m/s 
B) 9.9 m/s 
C) 13 m/s 
D) 14 m/s 
E) 16 m/s

Quizplus · Accepted Answer

Using the Bernoulli's equation, we can equate the pressure at the surface of the reservoir (where the height is 29 m) with the pressure at the pipe end (where the height is 0 m), and assume that the velocity at the surface is negligible compared to the velocity at the pipe end:
\begin{align*}
P_1+\frac{1}{2}ho v_1^2+ho gh_1 &= P_2+\frac{1}{2}ho v_2^2+ho gh_2 \
P_1 &= P_2 \
\frac{1}{2}ho v_1^2+ho gh_1 &= \frac{1}{2}ho v_2^2+ho gh_2 \
v_2 &= \sqrt{v_1^2+2gh_1} \
&= \sqrt{2(9.81\ \mathrm{m/s^2})(29\ \mathrm{m})} \
&\approx 13\ \mathrm{m/s}
\end{align*}
Therefore, the answer is (C) 13 m/s.

Water Flows Out of a Large Reservoir Through an Open