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
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?