Determining Velocity of Water From a Pipe

[alibond07]

Homework Statement

I have a pipe with a capacity of 1.5 liters. Half of the pipe is filled with water and the other half air. The pressure in the pipe will be pumped to a certain value then the valve will be released. I want to determine the speed of the water as it leaves the pipe.

Variables known:

Length of Pipe:1.3m
Radius of cross-section:0.0075m
Pressure inside of pipe: 60psi
Nozzle diameter: 3mm

(Will disregard the nozzle if its makes determining the velocity too hard)

Homework Equations

Pressure*Area=Force
pΔV=Work Done

The Attempt at a Solution

Firstly I though I could approach the problem by thinking of the air in the pipe doing work against the 'piston' of water when the valve is released. However I couldn't determine the change in volume of the gas. Is there a way to do this knowing the dimensions of the pipe?

Next I tried to use Pressure*Area=Force. Then simply doing (413685*cross section)=73N

I know F=ma but I can't seem to link this to velocity.

Are my previous assumptions correct?

 

[cupid.callin]

my first guess was to use Bernoulli's eqn
bu for that we need to know if pipe is horizontal or vertical ...

isnt there any figure?

 

[alibond07]

my first guess was to use Bernoulli's eqn
bu for that we need to know if pipe is horizontal or vertical ...

isnt there any figure?

The pipe is horizontal. I had a look at Bernoulli's equation and I had 0% of an idea how to apply to my situation.

 

[cupid.callin]

can you attach the figure because i can't really understand some things about the question

 

[alibond07]

can you attach the figure because i can't really understand some things about the question

What do you mean by figure?

 

[cupid.callin]

figure i mean the diagram of pipe if given with the question ...

 

[alibond07]

figure i mean the diagram of pipe if given with the question ...

Sorry this is an experiment I carried out. I'd just like to be able to relate the pressure and the distance the water goes from the pipe. Is there information missing that you need?

 

[cupid.callin]

after increasing the pressure when you open the valve ... so at nozzle pressure will become = atmospheric pressure ...

what about the piston end ... is 60psi maintained ... or it drops slowly (which will be very hard to work with) or it is also = atmospheric pressure?

 

[alibond07]

after increasing the pressure when you open the valve ... so at nozzle pressure will become = atmospheric pressure ...

what about the piston end ... is 60psi maintained ... or it drops slowly (which will be very hard to work with) or it is also = atmospheric pressure?

I'm afraid it drops slowly. The valve releases the pressure. The nozzle after the valve release is atmospheric pressure.

I'm willing to just say that 60psi is maintained if it is easier. I will simply add it too my analysis in my lab report.

 

[olivermsun]

The pipe is horizontal. I had a look at Bernoulli's equation and I had 0% of an idea how to apply to my situation.

If you look at the first form of Bernoulli's equation as linked, you see that the LHS is constant along streamlines. That means that the expression is the same along the flow at a beginning point (take it to be the air-water surface in the pipe, where the pressure is known) and an end point (e.g., outside the nozzle, where the flow has fully accelerated and the pressure has dropped to ambient).

 

[cupid.callin]

As you know atmospheric pressure is 14.7 psi

so applying Bernoulli eqn ... (let point near piston is A and at nozzle is B)

$$P_A + \rho hg + \frac{1}{2}\rho v_A^2 = P_B + \rho hg + \frac{1}{2}\rho v_B^2$$

as pipe is horizontal so h is same

P_B = P_atmospheric
P_A = 60psi

and for relation b/w v_A, v_B use eqn of continuity

hope this helps :)

 

[RTW69]

I am not sure Bernoulli is helpful with this problem. The mass and pressure in the cylinder is changing with time and although the water is discharged to atmospheric pressure I think there is a pressure at "B". This problem resembles a water rocket problem that is fixed to a stand. These problems are typically solved using Linear Momentum equations.

 

[cupid.callin]

I am not sure Bernoulli is helpful with this problem. The mass and pressure in the cylinder is changing with time and although the water is discharged to atmospheric pressure I think there is a pressure at "B". This problem resembles a water rocket problem that is fixed to a stand. These problems are typically solved using Linear Momentum equations.

Mass is changing, so?
and according to OP, pressure is not charging ...

can you tell us how we can solve this problem with linear momentum concept?

and i'll look at the question again and see if the solution i gave is correct or not ...

 

[alibond07]

Mass is changing, so?
and according to OP, pressure is not charging ...

can you tell us how we can solve this problem with linear momentum concept?

and i'll look at the question again and see if the solution i gave is correct or not ...

I am not sure Bernoulli is helpful with this problem. The mass and pressure in the cylinder is changing with time and although the water is discharged to atmospheric pressure I think there is a pressure at "B". This problem resembles a water rocket problem that is fixed to a stand. These problems are typically solved using Linear Momentum equations.

Do you mean the simple (m1)(u1)+(m2)(u2)=(m1)(v1)+(m2)(v2)?

Can you show me how this would apply? I could work out the mass of the water but not it's initial velocity.

 

[RTW69]

Do a Google search on "Science bits water rockets" they have a good explanation of using momentum methods for analyzing water rockets. Your problem looks similar except your pipe (rocket) isn't moving. It is not clear to me that the pressure at your nozzle is atmospheric pressure.

 

[alibond07]

Do a Google search on "Science bits water rockets" they have a good explanation of using momentum methods for analyzing water rockets. Your problem looks similar except your pipe (rocket) isn't moving. It is not clear to me that the pressure at your nozzle is atmospheric pressure.

It should be atmospheric pressure? The water does not go all the way to the nozzle, only to a valve just before the nozzle.

Thanks for pointing me in the direction of that website, looks like it's going to be a great help.

 

[olivermsun]

I am not sure Bernoulli is helpful with this problem. The mass and pressure in the cylinder is changing with time and although the water is discharged to atmospheric pressure I think there is a pressure at "B". This problem resembles a water rocket problem that is fixed to a stand. These problems are typically solved using Linear Momentum equations.

Do a Google search on "Science bits water rockets" they have a good explanation of using momentum methods for analyzing water rockets. Your problem looks similar except your pipe (rocket) isn't moving. It is not clear to me that the pressure at your nozzle is atmospheric pressure.

The first page returned by that Google search gives an analysis for the rocket exit velocity that finds exactly the same expression as found using Bernoulli. I submit that this happens because Bernoulli is derived by integrating the momentum equations. :)

 

[alibond07]

Mass is changing, so?
and according to OP, pressure is not charging ...

can you tell us how we can solve this problem with linear momentum concept?

and i'll look at the question again and see if the solution i gave is correct or not ...

As you can see in my attachment I've been directed to something I think is going to help me.

I have a question. What does the $$p_{w}$$ stand for? Is it power?

Thanks