Application of Pascal's Law in a tall vertical pressurized pipe with water as in Fire Standpipe 3

[solidspaces]

According to Pascal’s Law, the pressure inside a chamber that is full and pressurized with a fluid is constant.
Does this imply that the static pressure at the base of the pressurized chamber like a very tall column of pipe (in the vertical position) is the same as the static pressure measured at the top of the pipe?
Should the pressure be measured at the top or the bottom of these pressurized pipes to conduct the leakage test which is usually done at about 14 bar pressure as per NFPA?

 

[LittleInch]

You've radically misunderstood the law / principle - see

https://www.grc.nasa.gov/

http://www/k-12/WindTunnel/Activities/Pascals_principle.html

what is says is that the pressure AT A SINGLE POINT is exerted equally in all directions

As per the attachment, the pressure at the base of a vertical column on earth needs to take account of the gravitational forces exerted on the fluid.

I don't know what NFPA says about where you conduct the pressure, but if the words "minimum" or "highest point" are in there, then measure at the top, noting that the pressure at the base of the column could be much higher, depending on the height of your standpipe.

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

 

[bimr]

No, the static pressure is not the same at the top and bottom. The static pressure is zero at the top and equal to the height of the water at the bottom. The pressure of the fluid is added to the static pressure.

You should be using Bernoulli’s equation instead of Pascal's. Bernoulli’s equation relates the fluid pressure, density, speed, and height at different points:

The pressure should be measured at the location where the pressure is highest in the tank. That would be the base. Otherwise, you would over-pressurize the tank.

Most tanks in this service are gravity.

 

[zdas04]

If ever there was a place where you would not use Bernoulli's Equation this is certainly it.

No velocities here, so dynamic pressure (1/2*ρ*v²) would be zero, but the equation that bimr showed would then be quite wrong since the total pressure at the top would not ever equal the total pressure at the bottom. The nomenclature is quite lame as well since P₁ and P₂ are actually "Static Pressure" (a component of total pressure) not "Pressure on the fluid" (which implies total pressure).

Pascal's law (a manifestation of Archimedes' Principle) says that an applied force is transmitted throughout the fluid, not that the applied force is the only force acting on the fluid. The proper fluid statics equation is:

P= ρgh+P_applied (with the reference plane for "h" usually taken at the surface of the fluid and positive is down)

For your hydrostatic testing question, the test pressure applies to each section of the vessel and piping under test. If I'm doing a 900 psig pipeline test on a pipe that drops over a 1,000 ft cliff (and I've done that), then I know that with a water test the pressure at the bottom of the hill is going to be 433 psig higher than the pressure at the top of the hill. When I apply 467 psig to the top of the hill, the welds and piping at the bottom are under test pressure and can be considered tested if they don't fail during the test duration. The piping and welds at the top of the hill are at about half of test pressure. If I raise the applied pressure at the top of the hill to 900 psig, then I've tested the whole system, but the piping on the bottom of the hill has been subjected to 1333 psig and I have to start being concerned about yield and work hardening.

In your exact case you have to ask "how tall is tall?". Every meter of height is almost 0.1 bar. A 10 m vessel would have 14 barg at the top and 15 barg at the bottom. If the MAWP of the vessel is 100 barg (ASME B16.5 Class 600), then this is exactly the way to do your 14 barg leak test. If the MAWP of the vessel is 20 bar (Class 150) then you'd still do it this way. If the MAWP were 8 barg, then I'd probably split the difference and do the test with an applied pressure of 13.5 barg.

David Simpson, PE
MuleShoe Engineering

In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual. Galileo Galilei, Italian Physicist

 

[bimr]

Thanks for the long, but quite confused and wrong review of my post above.

As clearly stated above, P = pressure and y = height. Don't understand the reasoning where you lamely mislabel P as static pressure.

To obtain static pressure, knowledgeable engineers multiply the height times the fluid density and acceleration due to gravity, again, as clearly stated above.

If you reread the post, you will clearly see that it states "pressure of the fluid", not "pressure on the fluid" as you posted.

Perhaps your confusion will end if you change the label for the height to h instead of y. In the future to avoid additional confusion, you should also note that some people prefer to use the letter z.

h’s, y’s and z’s can be a bit confusing.

 

[zdas04]

My review of your post was 4 lines, not terribly long, and anything but wrong.

Bernoulli's equation is actually (I actually can successfully translate "y" or "Z" for the "h" that Daniel Bernoulli used in his derivation):

Dynamic pressure + static pressure + head pressure = Total pressure = constant = (1/2)ρ*v²+P_static+ρ*g*h

So in a flowing stream, I can use Bernoulli to calculate (at velocities greater than zero and less than about 0.1 Mach) how a varying cross sectional flow area will trade velocity for pressure and vice versa. It does good describing sub-sonic lift on airfoils. With velocity equal to zero, then this equation does not equal a constant for all positions within the fluid and doesn't work.

Your implication that "pressure of the fluid" has a meaning other than static pressure in this context confuses me.

The reason for the tone of my last post was that I am sick to death of people thinking that Bernoulli's Equation is the Universal Solution to any fluid problem. To derive that equation, you have to assume a long list of things from Density is constant with both time and position; to friction is zero; to zero heat transfer from or to the fluid; to the flow must lack either rigid body rotation or swirl. This is a very limiting list that means that Bernoulli's equation is only occasionally useful (when it is useful, it is very useful, but it isn't often useful) and it should not be the go-to arithmetic for every problem that involves fluids of any kind either at rest or in motion. You cannot use it for fluid statics problems. You cannot use it in situations where upstream density is more than about 1-2% different from downstream density. You cannot use it in any situation where pressure change due to friction are not trivial.

The OP is asking a fluid statics problem and the Bernoulli Equation has nothing to contribute to a fluid static problem.

David Simpson, PE
MuleShoe Engineering

In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual. Galileo Galilei, Italian Physicist

 

[skdesigner]

Skipping directly to the OP's last question:

NFPA 14-2013 11.4.2 states "The hydrostatic test pressure shall be measured at the low elevation point of the individual system or zone being tested." So, you use the gauge reading at the bottom of the standpipe when doing your hydro test.

Don't forget about all the other acceptance tests in NFPA 14.

R M Arsenault Engineering Inc.

http://www.rmae.ca

 

[solidspaces]

To: skdesigner (Mechanical):
1) If as you have stated, that as per NFPA 14-2013 11.4.2, the standpipe is tested as follows: "The hydro static test pressure shall be measured at the low elevation point of the individual system or zone being tested.", So, you use the gauge reading at the bottom of the standpipe when doing your hydro test", but doing so would not subject the pipe joints above the bottom of the standpipe will be tested at much lower pressure than the specified test pressure of 225 psi (13.8 bars). Is this acceptable as per NFPA?
2) Your second point is that: Don't forget about all the other acceptance tests in NFPA 14. Please let us know which other acceptance test requires the network to be retested at 225 psi and which section of NFPA stipulates this repeat pressure test?
3) If the additional acceptance tests do indeed require you to retest the standpipe at 225 psi, we are back at square one, namely whether to subject the standpipe to a pressure of 225 psi at the top of the riser or not.

 

[bimr]

This is supposed to be a site for engineers.

According to Bernoulli:

Total Energy =

Bernoulli’s equation is the sum of the pressure, dynamic pressure and hydrostatic pressure. Since there is no dynamic pressure, Bernoulli's equation simplifies to:


Total Energy =

Golly! That is agrees exactly with what you posted above.

 

[solidspaces]

So should the 225 psi be achieved at the top or the bottom of the tall standpipe?

 

[zdas04]

bimr,
Snarky nonsense aside, what I DID NOT post was

P₁+ρ*g*h₁=P₂+ρ*g*h₂ because it doesn't.

If you don't see the difference then you might want to question your own expertise.

David Simpson, PE
MuleShoe Engineering

In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual. Galileo Galilei, Italian Physicist

 

[solidspaces]

The 6 inch standpipe is 75 meters tall. Subjecting it to the code test pressure of 225 psi at the top of the standpipe will impose excessive pressure at the base of the riser.
Any suggestions of how it could be tested without such pressures.
Thanks

 

[zdas04]

Is this a leak test or a strength test? If it is a leak test like the OP said, you could document your problem and apply engineering judgement to the problem. In a similar situation (a 30 m standpipe), I put the test gauge at the bottom and pressurized the system to the required pressure on that gauge (just like the NFTA quote you included called for). For your 75 m standpipe that would require an applied pressure around 6.5 bar which is actually plenty for a leak test (would be a problem for a strength test, in your system the only way to do a strength test is with a pneumatic test).

David Simpson, PE
MuleShoe Engineering

In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual. Galileo Galilei, Italian Physicist

 

[flexiblycool]

Thanks zdas04
The only problem with achieving the test pressure of 225 psi at the base of the riser is that the pipe joints at higher elevations will see much lower pressures, which seems to circumvent the stringent test requirements. My concern is that are we really interpreting the NFPA code correctly.

 

[LittleInch]

What NFPA 14 section 11 says is that the test needs to be not less than 200psig or not less than maximum pressure plus 50psi, when the max pressure is more than 150 psi, whichever is greater. it then states this pressure is taken at the lowest point. There is little room for error here.

Assuming that someone has done the sums right, the maximum pressure for a fire system will be the maximum pump discharge pressure (normally at zero flow, plus any height difference from the lowest point minus the elevation of the pump discharge nozzle. The important point here is that this max pressure is at no flow. The pressure seen by any point higher than the lowest point will be reduced compared to the lowest point, but in operation it cannot realistically see any pressure higher than the test pressure

At flowing conditions, two things would act to reduce this pressure:
1) The pump discharge pressure would reduce as flow increases, assuming a centrifugal pump is used
2) The friction drop along the line will reduce the pressure at any point from the pump

Therefore although a higher point in the standpipe would not be tested to the same pressure as the lowest point due to hydrostatic head, given that in operation it would never see anything higher than this pressure, the test is valid and makes sense.

75 metres is quite a significant height, but so long as you have enough pressure from your pump to give you whatever pressure you need at the top at full flow, the testing is quite straightforward.

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

 

[bimr]