What Determines the Maximum Height for Water Flow in a Faucet?

[alaa410]

The main water enters a house on the first floor. the line has a gauge pressure of 1.9x10^5Pa
a) A faucet on the second floor 6.50 meters above the first floor is turned off. what is the gauge pressure of this faucet? b)how high could a faucet be before no water would flow from it even if the faucet were open.

iv figured the first part is solved with P2= p1+densitygh

but I am very unclear about what would matter with the faucet being open in part two please help :)

 

[Astronuc]

The main water enters a house on the first floor. the line has a gauge pressure of 1.9x10^5Pa
a) A faucet on the second floor 6.50 meters above the first floor is turned off. what is the gauge pressure of this faucet? b)how high could a faucet be before no water would flow from it even if the faucet were open.

iv figured the first part is solved with P2= p1+densitygh

but I am very unclear about what would matter with the faucet being open in part two please help :)

When water is not flowing, the pressure is 'static'. When a liquid is flowing through a pipe, there is a pressure drop associated with the viscosity of the liquid.

In a vertical pipe, in order for the fluid to flow out the upper end, the pressure must exceed the static head ρgh. So what is the gauge pressure of the liquid at the top end of an open vertical pipe when the liquid does not flow? Then relate that to p1 + ρgh, and solve for h.

 

[alaa410]

gh=p1+pgh?

 

[haruspex]

gh=p1+pgh?

That can't be right because it mixes dimensions. LHS is accn*distance = L²T^-2. RHS is pressure, ML^-1T^-2.
Also, it's confusing to use p1 for a pressure and p for a density. ρ for density would be better.
To answer your original question, obviously there can be no flow if the faucet is closed. With the faucet open, there will be some flow as long as the pressure supplied overcomes the head of water in the up pipe. The rate of flow will depend on by how much extra pressure there is (and a few other things). The wording of the question is intended to make it clear that they don't care about the rate of flow, so it is not a hydrodynamics question. All they are asking for is what supply pressure will just balance the head of water.

 

[alaa410]

its asking how high the faucet should be so that no water would reach it from the pressure gauge at the bottom of the house that much i understand. but I am still not getting how i would solve for that. i got the pressure of water coming out of the faucet at 6.5 but i don't see how that number will help me find part b

 

[haruspex]

its asking how high the faucet should be so that no water would reach it from the pressure gauge at the bottom of the house that much i understand. but I am still not getting how i would solve for that.

At the height at which no water would come out, the water pressure would be, what?

i got the pressure of water coming out of the faucet at 6.5 but i don't see how that number will help me find part b

It doesn't, but the same formula does.

 

[alaa410]

p1/ρg=h ? some one give me a solution for gods sake :p

 

[alaa410]

well look at that... it worked haha thanks guys :D