Height of Water Jet from Pressure in Domestic Water Pipes

[hfatehi]

Homework Statement

The pressure in domestic water pipes is typically 60 psi above the atmospheric pressure. If the viscous effects are neglected, determine the height reached by a jet of water through a small hole in the top of the pipe.

Homework Equations

I am using the Bernoullis equation;
(P1/Rho) + gZ1 + (V1^2/2) = (P2/Rho) + gZ2 + (V2^2/2)

The Attempt at a Solution

I take
Z1 = 0 (surface of the pipe)
V2 = 0 (Max height)
P1 = Atmospheric pressure + 60 = 74.7 psi
g = 32.174 ft/sec^2
question is what should P2 be? will it be just atmospehric pressure or will it be 0

 

[mybsaccownt]

well, since you defined P1 to be absolute pressure, then so should you define P2

you could have just taken gauge pressure, it's up to you

but being consistent is the most important thing

 

[teknodude]

Homework Statement

The pressure in domestic water pipes is typically 60 psi above the atmospheric pressure. If the viscous effects are neglected, determine the height reached by a jet of water through a small hole in the top of the pipe.

Homework Equations

I am using the Bernoullis equation;
(P1/Rho) + gZ1 + (V1^2/2) = (P2/Rho) + gZ2 + (V2^2/2)

The Attempt at a Solution

I take
Z1 = 0 (surface of the pipe)
V2 = 0 (Max height)
P1 = Atmospheric pressure + 60 = 74.7 psi
g = 32.174 ft/sec^2
question is what should P2 be? will it be just atmospehric pressure or will it be 0

Let's make life easier by using gauge pressure . Also you defined Z1 and V2 incorrectly.

 

[hfatehi]

May i asked why is Z1 and V2 wrong. My understanding is that at the surface of pipe where the hole is we take that point as Z1 and the height of the water at MAX as Z2. hence Z1 will be our reference point of 0. Also i thought that the velocity of the particle at its highest point in the trejactory is 0. please correct me

 

[mybsaccownt]

Bernoulli's equation (in that form) has to be applied between two points in a steady flow (with the exception of obtaining an approximate answer for 'quasisteady' flows) , I don't believe that any point in the jet besides the very base of it can be considered steady (since it diffuses).

So you will have to use bernoulli's equation to find the velocity of the water at the point where it leaves the pipe, then apply the kinematics equations to find the maximum height.