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## Homework Statement

A hole is punched in a full milk carton, 10cm below the top. What's the initial velocity of outflow?

## Homework Equations

P2 = P1 + ρgh

Conservation of energy of fluids: P2 + 1/2ρv

_{2}

^{2}+ ρgy

_{2}= P1 + 1/2ρv

_{1}

^{2}+ ρgy

_{1}

## The Attempt at a Solution

Set the top of the carton as P1, and the point 10cm below the surface as P2.

Assume that milk has the same density as water: 1000kg/m3

P1 = atmospheric pressure = 101325Pa

P2 = 101325 + 1000(9.8)(0.1) = 102305Pa

P2 + 1/2ρv

_{2}

^{2}+ ρgh

_{2}= P1 + 1/2ρv

_{1}

^{2}+ ρgy

_{1}

The milk doesn't have kinetic energy at the top of the carton, so K=1/2ρv

_{2}

^{2}=0

At 10cm below the surface, y=0 (although this is still elevated above the ground, we're trying to find the change in energy between the top of the carton and hole punched in it); therefore U = ρgy

_{1}= 0

P2 + ρgh

_{2}= P1 + 1/2ρv

_{1}

^{2}

102305 + 1000(9.8)(0.1) = 101325 + 1/2(1000)v

_{1}

^{2}

103285 - 101325 = 500v

_{1}

^{2}

V1 = 1.98m/s

Is my method correct? The actual answer is V=1.4m/s, but perhaps it's because I assumed that the density of milk is the same as water....