Bernoulli? Difference in water pressure between floors

[HeatherP]

Homework Statement

A water line enters a house 2.0 m below the ground. A smaller diameter pipe carries water to a faucet 5.0 m above the ground, on the second floor. Water flows at 2.0 m/s in the main line and at 7.0 m/s on the second floor. Take the density of water to be 1.0 x 103 kg/m3. The difference in pressure between the main line and the second floor is:

A. 7.15 x 104 Pa with the main line at the higher pressure
B. 2.65 x 104 Pa with the main line at the higher pressure
C. 7.15 x 104 Pa with the main line at the lower pressure
D. 2.65 x 104 Pa with the main line at the lower pressure
E. 9.4 x 104 Pa with the main line at the higher pressure

Homework Equations

p + 1/2ρv² + ρgy

The Attempt at a Solution

main line = second floor

p₁ + 1/2ρv²₁ + ρgy₁ = p₂ + 1/2ρv²₂ + ρgy₂

p₁ + (.5)(1000)(4) + (1000)(9.8)(0) = p₂ + (.5)(1000)(49) + (1000)(9.8)(7)

p₁ + 2000 + 0 = p₂ + 24500 + 68600

p₁ - p₂ = 24500 + 68600 - 2000

= 9.11 X 10⁴

I was told this answer was incorrect. I think I'm doing something wrong with my y (elevation). I've tried using 0 and 7 and -2 and 5 without success.

Per a search on the internet, it looks like 7.15 x 10⁴ with the main line at the higher pressure is the right answer, but I can not find an explanation why.

Any idea where I'm going wrong?

Thanks!

 

[RTW69]

I think your answer is correct. The main pressure is definitely higher or you couldn't move the water to the upstairs. I don't see any math or conversion errors.

 

[256bits]

p1 + (.5)(1000)(4) + (1000)(9.8)(0) = p2 + (.5)(1000)(49) + (1000)(9.8)(7)

What answer do you get when you use 5m as the change in elevation, rather than 7m?
A. 7.15 x 104 Pa with the main line at the higher pressure
But 5m is the elevation change between the ground and the second floor.

Your question asks for pressure difference between main line and the second floor, which is what you calculated using 7m. Your answer seems correct.

 

[GeorginaS]

Who says the answer is wrong, H?

 

[HeatherP]

Who says the answer is wrong, H?

It was a question that I had to answer in an online format so it told me that the answer was incorrect once I submitted it.

I’m going to check with my professor today to see why the answer was marked incorrect. I’ll let y’all know what I learn.

 

[HeatherP]

Well, turns out my answer was right and the computer was wrong. Who would have thought! :)

Thanks all!

 

[GeorginaS]

Wow, how cool is that? See? I didn't steer you wrong for physics advice.