Water bottle pressure problem with hole at bottom

[ntsai91]

Homework Statement

Suppose a bottle filled with water, which has a hole close to the bottom
as shown in the figure. Express your answer with y₁ , y₂, and P_o
(atmospheric pressure). Assume A₁ << A₂.

1) When a cap is closed, find the condition, where no water leaks out form the hole; v1=0

2) Now consider the cap is open, estimate the velocity of the water flowing out from the hole.

Homework Equations

P₁ + ρgy₁ + 1/2 ρv₁² = P₂ + ρgy₂ + 1/2 ρv₂²

The Attempt at a Solution

1) Zero-d out the two terms with velocity. Got up to

P1 - P2 = ρg (y2-y1)

not sure what the question is really looking for...

2) I got v₁ = √(2g(y1-y2)/((A₁²/A₂²)-1))

is this right?

 

[rude man]

question 1: what are p1 and p2? Your answer must be an expression of one or more of
p0, (y2-y1), A1 and A2.

question 2: how did you arrive at your answer for #2? (It's not what I got.)