Question

A hole of 1 mm² is punched in a full 1-liter milk carton, 5 cm from the bottom. What is the initial speed of the outflow?

Answer 1

Use Bernoulli equation with the following assumptions.

1) velocity of the milk on the top is near 0, because the hole is so small that the level of milk will descend slowly, compared with the velocity of the outflow.

2) Pressure on the top = pressure on the bottom. This means that we consider that the top is open to the atmosphere.

Then, the terms of pressure cancel, and Bernoulli's equation leads to:

Z1 + p1/(d*g) + (V1)^2/(2g) = Z2 + p2 /(d*g) + (V2)^2 /(2g)

=> (V2)^2 = 2g (Z1 - Z2)

g = 9.8 m/s^2

Z1 - Z2 = 5cm

(V2)^2 = 2*(9.8 m/s^2)*(0.05m) = 0.98 m^2/s^2

V2 = 0.99 m/s