Does Cavitation Occur in a Beer Bottle Under These Conditions?

[fayan77]

Homework Statement

$\rho$_water = 1.94
a = variable
$\gamma$ = 1.94(32.2) = 62.4
Pressure outside P₁ = 2116 lb/ft³
Temp = 75 F
Pressure at bottom P₂ = vapor pressure = 52.3 lb/ft³
Height = 6 inch = .5 ft

Homework Equations

-$\nabla{p}-\gamma\hat{j}=\rho\hat{a}$

The Attempt at a Solution

direction of change in pressure is vertical going from bottom to top so it is $\hat{j}$
I dot $\hat{j}$ with each term of -$\nabla{p}-\gamma\hat{j}=\rho\hat{a}$
then I obtain
-$\frac {dp} {dl}$ - $\gamma$ = $\rho$a
-(P₁-P₂)/.5 - $\gamma$ = $\rho$a

solving for a i get 2159.7 ft/s²
does this make sense?

 

[jedishrfu]

Great question!

I don't know the answer to it but was curious if other beers were used in the experiment.

Also how did the beer get replaced by water?