Find the height of the water

In summary, the problem involves finding the height reached by a jet of water through a small hole in a domestic water pipe with a pressure of 60 psi above atmospheric pressure, neglecting viscous effects. Using Bernoulli's equation and the kinematics equations, the velocity of the water at the point where it leaves the pipe can be found, and from there, the maximum height can be calculated.
  • #1
hfatehi
5
0

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
 
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  • #2
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
 
  • #3
hfatehi said:

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.
 
  • #4
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
 
  • #5
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.
 

1. How do you find the height of the water in a container?

To find the height of the water in a container, you will need to use a measuring tool such as a ruler or measuring tape. Place the measuring tool at the bottom of the container and measure up to the surface of the water.

2. What is the equation to calculate the height of water in a container?

The equation to calculate the height of water in a container is: Height of water = Total height of container - Height of air above water - Height of container base.

3. What are some factors that can affect the height of water in a container?

Some factors that can affect the height of water in a container include the shape and size of the container, the amount of air above the water, the temperature of the water, and the amount of water in the container.

4. Can you use a measuring cup to find the height of water in a container?

Yes, you can use a measuring cup to find the height of water in a container. Simply pour the water from the container into the measuring cup and read the measurement on the cup to determine the height of the water.

5. How do you measure the height of water in a container with an irregular shape?

To measure the height of water in a container with an irregular shape, you can use the displacement method. Fill the container with water and place it on a scale. Record the weight of the water. Then, submerge the irregularly shaped object in the water and record the new weight. The difference between the two weights is the weight of the water displaced by the object, which can be used to calculate the height of the water.

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