Using Bernoulli to determine pressure of equalizing flow
Using Bernoulli to determine pressure of equalizing flow
(OP)
Greetings all,
I wanted to carry out an analysis of the following scenario. A tall cylindrical container is located at depth subsea. This container is filled with water but these contents are maintained at a lesser pressure than the surrounding seawater. The interior of this container has an approximate volume 350,000 cubic feet and also features a port at the top which can be opened and closed by a valve.
The pressure differential between the local exterior & interior hydrostatic pressures is 75psi.
For the situation where the valve is open, I’ve been given a value of 60 fps for the flow velocity.
From the above, I wanted to determine what the pressure would be within the constriction formed by the valve bore. For this I made use of Bernoulli’s Equation, working between two points. The upper point, let’s call it Point A, to be a distance above the container at which the flow speed directed into the valve bore would be negligible i.e. zero. Point B, the lower point, I took this to be located at the base of the valve bore. Calculating to determine the pressure at point B gave a result that was a negative pressure.
I used absolute pressure values throughout rather than gauge so it puzzled me a little that I should end up with a negative value and a substantial one at that. Is this an indication that the flow regime in such a scenario would no longer be best explained by Bernoulli? I had in mind that the pressure drop between the static fluid and the rapid fluid flow through the valve may be resulting in cavitation, hence the calculated negative pressure. Is that a correct interpretation?
Varying both the fluid velocity through the bore and the estimated elevation of Point A above Point B gave more sensible (as in positive pressure values) with reducing the fluid velocity having the biggest effect. The element that particularly troubles me as being imprecise is having to estimate Point A. When I say estimate, I think uneducated guess is a more apt description. Could anyone point me in the direction of a better way to determine even just a very approximate distance?
Thanks in advance.
I wanted to carry out an analysis of the following scenario. A tall cylindrical container is located at depth subsea. This container is filled with water but these contents are maintained at a lesser pressure than the surrounding seawater. The interior of this container has an approximate volume 350,000 cubic feet and also features a port at the top which can be opened and closed by a valve.
The pressure differential between the local exterior & interior hydrostatic pressures is 75psi.
For the situation where the valve is open, I’ve been given a value of 60 fps for the flow velocity.
From the above, I wanted to determine what the pressure would be within the constriction formed by the valve bore. For this I made use of Bernoulli’s Equation, working between two points. The upper point, let’s call it Point A, to be a distance above the container at which the flow speed directed into the valve bore would be negligible i.e. zero. Point B, the lower point, I took this to be located at the base of the valve bore. Calculating to determine the pressure at point B gave a result that was a negative pressure.
I used absolute pressure values throughout rather than gauge so it puzzled me a little that I should end up with a negative value and a substantial one at that. Is this an indication that the flow regime in such a scenario would no longer be best explained by Bernoulli? I had in mind that the pressure drop between the static fluid and the rapid fluid flow through the valve may be resulting in cavitation, hence the calculated negative pressure. Is that a correct interpretation?
Varying both the fluid velocity through the bore and the estimated elevation of Point A above Point B gave more sensible (as in positive pressure values) with reducing the fluid velocity having the biggest effect. The element that particularly troubles me as being imprecise is having to estimate Point A. When I say estimate, I think uneducated guess is a more apt description. Could anyone point me in the direction of a better way to determine even just a very approximate distance?
Thanks in advance.





RE: Using Bernoulli to determine pressure of equalizing flow
Flow through the valve is described by the valve's CV (gpm/psi^0.5) coefficient.
As you can see by the units of CV, a 75psi differential pressure will give you the flow rate thorugh the valve.
Learn from the mistakes of others. You don't have time to make them all yourself.
RE: Using Bernoulli to determine pressure of equalizing flow
Why not Bernoulli though? The valve is of the gate type so the passage through which equalization flow takes place is essentially constant bore diameter. There isn't a published Cv value for this passage. I could attempt to calculate/estimate one though.
RE: Using Bernoulli to determine pressure of equalizing flow
Learn from the mistakes of others. You don't have time to make them all yourself.
RE: Using Bernoulli to determine pressure of equalizing flow
My motto: Learn something new every day
Also: There's usually a good reason why everyone does it that way
RE: Using Bernoulli to determine pressure of equalizing flow
Learn from the mistakes of others. You don't have time to make them all yourself.
RE: Using Bernoulli to determine pressure of equalizing flow
RE: Using Bernoulli to determine pressure of equalizing flow
Something seriously wrong with your data - either there is a lot more pressure difference or the whole is a lot lot bigger or the velocity figure is wrong.
Figure out which two elements are true (diff pressure or hole size or flow veleocity) then work out the third one...
My motto: Learn something new every day
Also: There's usually a good reason why everyone does it that way
RE: Using Bernoulli to determine pressure of equalizing flow
Learn from the mistakes of others. You don't have time to make them all yourself.
RE: Using Bernoulli to determine pressure of equalizing flow
Friday afternoon syndrome.
orifice calc gives about 75 feet/sec, previous one was giving me the velocity in the very big tube I put in - my error.
So in the end it actually looks about right.
How about putting down your calculation and see where it is going wrong?
My motto: Learn something new every day
Also: There's usually a good reason why everyone does it that way
RE: Using Bernoulli to determine pressure of equalizing flow
Since water is nearly incompressible, it will not take much water to bring water pressure up to test pressure. For example, if you had an 8 inch water main, 1,000 feet long and all of the air was removed or purged from the water line, it would only take about one cup of water to bring the pressure up to 150 PSI. For your example, that would be less than 8.3 cubic feet of water.
This is Pascal's law not Bernoulli's.
http://www.hydraulicsonline.com/hydraulic-principl...
This would not be a steady state situation. The water flow will diminish quickly over times. You also have other issues such as the flexure of the container walls and that the water pressure changes with depth, but lets not get into that.
RE: Using Bernoulli to determine pressure of equalizing flow
Learn from the mistakes of others. You don't have time to make them all yourself.
RE: Using Bernoulli to determine pressure of equalizing flow
RE: Using Bernoulli to determine pressure of equalizing flow
Learn from the mistakes of others. You don't have time to make them all yourself.
RE: Using Bernoulli to determine pressure of equalizing flow
My motto: Learn something new every day
Also: There's usually a good reason why everyone does it that way
RE: Using Bernoulli to determine pressure of equalizing flow
Regardless of the "maintained pressure" comment, the inflow and/or the outflow will be very small flow of fluid since water is not compressible; the container is full; and you are only pressurizing/depressurizing the container, not filling it.
RE: Using Bernoulli to determine pressure of equalizing flow
bimr - not quite sure how I've not fully thought the scenario out. I am describing something that exists in reality and not a hypothetical design. As LittleInch says, the how/why is immaterial, hence my omitting the detail from the OP. Pumping would not necessarily be required, just access to a lesser hydrostatic column of fluid would maintain the reduced pressure within the container.
RE: Using Bernoulli to determine pressure of equalizing flow
Your scenario can be simplified to one of continuous flow through a valve with a 75 psi pressure drop across the valve.
It is difficult or often impossible to measure the lowest pressure through a valve, for example in the Vena Contracta. Valve manufactures use a Cavitation Index to predict cavitation, not Bernoulli's equation.
http://neutrium.net/fluid_flow/cavitation-in-restr...
It is also difficult to estimate the elevation of Point A (to be a distance above the valve at which the flow speed directed into the valve bore would be negligible). A vortex equation may be used to approximate the distance.
http://www.pumpfundamentals.com/help11.html
http://en.wikipedia.org/wiki/Vortex
http://web.mit.edu/fluids-modules/www/potential_fl...