Question

A very small hole is punched in a full milk carton, 10 cm below the top. What is the initial velocity of outflow? I used Bernoulli's equation for conservation of energy in a fluid but I don't understand why the pressures would cancel out.

Answer 1

\[P _{1} + 1/2\rho v ^{2} + \rho gy _{1}\]

Answer 2

\[\mbox{1: top}\quad,\quad\mbox{2: small hole}\]\[p_1+\rho gh_1+\frac{1}{2}\rho v_1^{2}=p_2+\rho gh_2+\frac{1}{2}\rho v_2^{2}\quad(p_1=p_2, v_1\approx 0,\Delta h=10cm)\]\[\rho gh_1-\rho gh_2=\frac{1}{2}\rho v_2^{2}\]\[\rho g\Delta h=\frac{1}{2}\rho v_2^{2}\]\[v_2=\sqrt{2g\Delta h}\]

Answer 3

Why are the pressures equal to each other?

Answer 4

Actually, there's another aproach to this problem if we think of the energy way.
Ke=1/2mv^2 and the gravitational potential energy when the milk carton is full and just before the water start to flow would be mgh=gravitational potential energy, which would be the same as the Ke, so 1/2mv^2=mgh,
1/2v^2=gh
v=(2gh)^0.5
v=(2*9.8*0.10m)^0.5
v=1.4