Calculating Pressure in Liquids: What Formula Can You Use?

In summary, to calculate the pressure in fluids, such as water, you can use the formula P = d * density of liquid * g + atmospheric pressure, where d is the depth, g is the acceleration due to Earth's gravity, and the density of the liquid depends on its temperature. However, this formula does not take into account the effects of turbulence. To find the pressure as a function of density and temperature, you can refer to the "Thermodynamic & Transport Properties of Water" or steam tables, which provide data and equations for various fluid conditions. Alternatively, there are constitutive models available, but there is no first-principles formula for any liquid.
  • #1
TriKri
72
0
How do you calculate the pressure in fluids, for example water? With gases, you can use the ideal gas law, is there some similar formula to calculate the pressure for liquids?
 
Physics news on Phys.org
  • #2
The pressure a fluid exerts upon a surface at depth, d, below the surface of a liquid, [itex]\gamma[/itex] is the density of the fluid times d, [itex]d\gamma[/itex]. That comes from calculating the weight of a column of water of base area [itex]\Delta A[/itex] and height d (that is, of course, [itex]\gamma\Delta A d[/itex]). The pressure is that force divided by the area: [itex]\gamma\Delta A d/\Delta A= \gamma d[/itex].

To be exact, you should add the air pressure on the surface of the liquid but that is typically much smaller than the pressure of the liquid itself.
 
  • #3
Thanks, but I'm more looking for the pressure of the liquid as a function of the density and the temperature, and then some liquid dependent variables. Is there such a formula? This of course supposes that no liquid is really incompressible.

HallsofIvy said:
To be exact, you should add the air pressure on the surface of the liquid but that is typically much smaller than the pressure of the liquid itself.

Really? The air pressure at sea level corresponds to going down 10 meters in the water, I think that is quite much!
 
  • #4
The pressure at a depth d is given by P=d*densityof liquid* g+atmospheric pressure
(g=acceleration due to Earth's gravity).Of course the density depends upon the liquid and its temperature.
 
  • #5
That is not what I mean. At deeper levels, the density is higher; this is what causes the higher pressure. When you do flow calculations, you need to be able to calculate the pressure as a function of the density, since the pressure is different in different locations at the same depth if the water is turbulent.
 
  • #6
You will find some charts that may be useful if you google Density of Fluids-Changing Pressure and Temperature.
 
  • #7
I'm not sure I see just what you are trying to do, but maybe what you're looking for is the "Thermodynamic & Transport Properties of Water" aka the steam tables. You'd need the subcooled portion (as opposed to the saturated tables). Using the tables, if you know two values (say pressure & temp, or pressure & enthalpy, or temperature & density) you can look up the others. There are several free versions on the internet, and proprietary versions by NIST and ASME.
 
  • #8
TriKri said:
That is not what I mean. At deeper levels, the density is higher; this is what causes the higher pressure. When you do flow calculations, you need to be able to calculate the pressure as a function of the density, since the pressure is different in different locations at the same depth if the water is turbulent.
Under what fluid conditions is one interested?

Is one looking for pressure in the atmosphere, for which there is ample data and equations?

Is one looking for pressure in a body of water such as a lake, river, sea or ocean? In this case, the pressure at sea level is taken at 1 atm (~14.7 psia, 0.101325 MPa) absolute. In the water, the pressure increases with depth due to the overlying mass. Similarly, in the atmosphere, pressure decrease with altitude as the overlying mass decreases with altitude.

One can also have a closed (forced convection) system, e.g. a pressurized coolant system in a power plant which might operate at 3000-3500 psia, or 2250 psia (typical of a pressurized water reactor primary system), or 1050 psia (typically of a boiling water reactor primary system). Usually the pressure is regulated by an accumulator. Within the closed loop the differential pressure might be something like 25-30 psid (differential pressure).

The composition of the fluid, the thermodynamics of the system and boundary conditions determine the pressure. Equations or models are availablel for a wide range of fluids (liquids and vapors/gases).
 
  • #9
TriKri said:
That is not what I mean. At deeper levels, the density is higher; this is what causes the higher pressure. When you do flow calculations, you need to be able to calculate the pressure as a function of the density, since the pressure is different in different locations at the same depth if the water is turbulent.

Are you asking for constitutive relationships [tex]\rho(P,T)[/tex]? I don't think there is a first-principles one for any liquid, but there are several models:

http://pubs.acs.org/doi/abs/10.1021/ie50574a048
http://www.engineeringtoolbox.com/fluid-density-temperature-pressure-d_309.html
http://www.springerlink.com/content/w568745842053865/
 
  • #10
Ok, thanks! That was some useful links.
 

What is the formula for calculating pressure in liquids?

The formula for calculating pressure in liquids is P = ρgh, where P is pressure, ρ is density, g is acceleration due to gravity, and h is the depth of the liquid.

How is pressure in liquids different from pressure in gases?

Pressure in liquids is caused by the weight of the liquid above a specific point, while pressure in gases is caused by the collisions of gas molecules with the walls of the container.

What units are typically used to express pressure in liquids?

Pressure in liquids is typically expressed in units of pascals (Pa) or newtons per square meter (N/m^2).

How does temperature affect pressure in liquids?

In liquids, temperature does not have a significant effect on pressure. However, as temperature increases, the density of liquids typically decreases, resulting in a slight decrease in pressure.

Can pressure in liquids be greater than atmospheric pressure?

Yes, pressure in liquids can be greater than atmospheric pressure. This occurs when the liquid is under a greater depth or when an external force is applied to the surface of the liquid.

Similar threads

Replies
27
Views
2K
Replies
2
Views
6K
Replies
19
Views
1K
  • Mechanics
Replies
4
Views
2K
Replies
4
Views
1K
Replies
31
Views
9K
Replies
6
Views
2K
Replies
10
Views
961
Back
Top