Is the pressure used in the Bernoulli Principle is the pressure of the particular location? 2

[Loo Kian Sing]

When we want to apply the Bernoulli Principle, we cannot use the pressure of the fluid, but using the pressure at that particular location?

If yes, how we measure or know the pressure at that particular location? By any calculation from the pressure of the fluid?

If not, the pressure at the surface of the water should be zero in an open tank? Then why we need to use the atmospheric pressure in the calculation by Bernoulli Principle?

 

[BigInch]

Use the pressure at a known location. From there you can try to calculate the pressure elsewhere by considering fluid density and elevation change plus friction head lost between the reference point and

Technology is stealing American jobs. Stop H1-Bs for robots.

 

[zdas04]

Loo Kian Sing,
Before you try to apply the equations derived from the Bernoulli Principle, you need to review the underlying assumptions in the derivation of those equations:
[ul]
[li]Inviscid: No friction at all[/li]
[li]Incompressible: No change in density from one measurement point to the other (for gases, people often assume that 1-2% change in density is the maximum allowable, the Fanno-flow compressible flow equations support this magnitude of change)[/li]
[li]Irrotational[/li]
[li]Reversible: Again, losses to friction are not reversible[/li]
[li]Isothermal[/li]
[li]Isentropic:[/li]
[li]Adiabatic: No heat transfer from or to the environment[/li]
[li]Isenthalpic: No work done on or by the fluid[/li]
[/ul]
If friction is not zero then there is simply no way to derive the equations. If the fluid does as much work as turning a turbine meter, then the equations don't work.

The energy equation says that static pressure plus dynamic pressure plus hydrostatic pressure equals total pressure. This works everywhere. The (valuable) addition that the Bernoulli Principle makes is that in conditions where the assumptions are satisfied, the three kinds of pressure add up to a constant and the energy simply moves from one term to the others. That lets you calculate dynamic pressure and therefore velocity through an orifice, or velocity and pressure change through a change in duct diameter, or the lift on an airplane wing. Dang useful things to know. If there is friction then the total pressure is not constant and that is also useful to know, but it makes the relationship between static pressure an velocity unpredictable relative to each other.

Assuming that you can legitimately use the equations, then I have a hard time understanding the distinction between "pressure of the fluid" and "pressure at a particular location". The term "pressure" only has physical meaning relative to the fluid within the volume. Remove the fluid and pressure is zero.

Finally, what do you want to "apply the Bernoulli Principle" to? It sounds like you might have a solution in search of a problem. The pressure at the surface of the water in a tank is not "zero" it is "local atmospheric pressure" which tends to be somewhere between 11.2 and 15.1 psia depending on elevation. Most tank calculations that I've ever done have had a velocity term that was very very small so dynamic pressure was insignificant and the analysis becomes a fluid statics problem instead of a fluid dynamics problem that might utilize the Bernoulli equations.

[bold]David Simpson, PE[/bold]
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

 

[LittleInch]

Great post Dave.

The other factor people seem to neglect is that especially for liquids is that the velocity term is so low that it is often ignored in real life applications. Low pressure high speed gas yes, low speed high pressure liquids no.

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

 

[3DDave]

"If not, the pressure at the surface of the water should be zero in an open tank?"

The pressure at the surface is probably not zero. Unless this is in a complete vacuum. Having worked on a fluid system where that condition was true, I can say that neglecting atmospheric pressure is not a good idea. Most of the time the pressure there is balanced by the same pressure exerted elsewhere or the pressure there is too small a component to matter, but it's value should not be generally neglected.

 

[zdas04]

3DDave,
No, the GAUGE pressure at the surface of the liquid in a vented tank actually is zero gauge. I don't think anyone was ignoring atmospheric pressure in this discussion, Bringing it back into that paragraph just didn't add any value.

[bold]David Simpson, PE[/bold]
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

 

[Loo Kian Sing]

Thank you.