Answer to Question #290836 in Mechanics | Relativity for Shiu

Question

a styrofoam cylinder, filled with water, sits on a table. you then poke a small hole through the side of the cylinder, 20 cm below the top of the water surface. what is the speed of the fluid emerging from the hole?

Answer 1

Solution:

Let's write the Bernoulli equation (indexes 1 and 2 corresponds to the top and bottom, respectively):

$$\dfrac{\rho v_1^2}{2}+\rho gh_1+p_1=\dfrac{\rho v_2^2}{2}+\rho gh_2+p_2.$$

Since $v_1=0$, $h_2=0$ and $p_1=p_2$, we get:

$$\rho gh_1=\dfrac{\rho v_2^2}{2},$$ $$v_2=\sqrt{2gh_1}=\sqrt{2\cdot9.8\ \dfrac{m}{s^2}\cdot0.2\ m}=2.0\ \dfrac{m}{s}.$$