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Difference in pressure?
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:
The answer is 7.15 x 10^4 Pa with the main line at the higher pressure.
1. How did they get this answer?
I used the equation P1-P2=.5ρv2²+ρgy2-.5ρv2²-ρgy1²
and I got 9.11x10^4 Pa
2. Why is the main line at a higher pressure if it has a larger diameter?
2 Answers
- JullyWumLv 71 decade agoFavorite Answer
It looks like the answer calculation has mistakenly assumed the height to be 5.0m instead of 7.0m. (that gives a pressure diff. of 7.15^4 Pa)
I agree with your calculation .. 9.11^4 Pa
Pressure is greatest where the flow rate is slowest (in widest pipe) .. and reduced in the narrower pipe where flow rate is fastest.
- Anonymous1 decade ago
There is 7 metres head of water difference between the tap and the mains pipe and you have to assume that all the flow in the mains is going into the riser. If the tap was shut off and no water was flowing in either pipe the mains pipe would be at7*9.8*1e3 kg/m^2 higher pressure than the tap end. With water moving at constant speed in laminar flow in both pipes there's an extra 5m/s velocity differential which has to be made up by some acceleration at the junction - you don't seem to have enough information to calculate friction losses so I suspect that it is this change in kinetic energy / cross-sectional area that you need to factor in.
