Bernoulli/Continuity, Water flowing at different heights/radii

[mknob001]

Homework Statement

Water flows in the pipe below as an ideal fluid where:
P1 = 1.95*10^5 Pa ; Rad @ P1 = 3cm
P2 = 1.20*10^5 Pa ; Rad @ P2 = 1.50 cm
P2 is above P1, but the height difference is UNKNOWN.

Questions:
1. What are the velocities at P1 and P2?
2. Find volume flow rate through the pipe.

I don't have a diagram, but it's pretty simple - known pressures with known radii at UNKNOWN heights.

Homework Equations

P1 = P2 + dgh -- doesn't this assume the areas are the same? (which they aren't)
Bernoulli's.
A1V1 = A2V2

The Attempt at a Solution

1. I used A1V1 = A2V2 to solve the ratio between V1 and V2 (since rad can be used to find A) and solved for v1.

2. I substituted answer for v1 into v1 of bernoulli's equation. This way I can get v2.
BUT, I can't solve Bernoulli's eq. without knowing the heights, h1 and h2.

3. I though P1 - P2 = dgh could work, but I thought this was only for change in height with the same area. Am I wrong?

Help would be much appreciated. I'm so stuck on this whole different areas/heights/pressures thing and my brain is shutting down a bit from the frustration. Haha help?

 

[Chestermiller]

Sometimes people us a capital P to represent the sum of the pressure p (lower case) plus ρgz:

P = p + ρgz

Is it possible that that is the case here? Even then, you still need to know the density in order to get the kinetic energy per unit volume.

 

[mknob001]

thanks for responding -- sorry that i used dgh, it's just what my teacher uses

Anyway, I don't think so, she definitely means p1 and p2 being the pressure at the bottom and top of the pipe. And we're allowed to use d = 1000 kg/m3 for water so I know the density. I'm just not sure if I can solve for the height (z) with the information given.

I'm thinking that she needs to give us that in order to solve it.

I found a problem that uses the same diagram and all the same information, except this one has a height difference given:
q1376760"]http://www.chegg.com/homework-help/questions-and-answers/water-moves-constricted-pipe-steady-ideal-flow-lower-point-pressure-171-105-pa-pipe-radius-q1376760
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I'm guessing this is why I can't solve this, but is there something I'm missing?

 

[Chestermiller]

I agree with you. You need to know the height difference.

Chet

 

[mknob001]

Thanks, once I know that this problem will be pretty easy. Thanks!