Bernoulli/Continuity, Water flowing at different heights/radii

mknob001

1. 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.

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

3. 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?

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Chestermiller

Mentor
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:
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I'm guessing this is why I can't solve this, but is there something I'm missing?

Chestermiller

Mentor
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!

"Bernoulli/Continuity, Water flowing at different heights/radii"

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