2 replies to this topic

[bag]

Hi Professionals

 

Is there any formula which explains the relationship of liquid mass and liquid pressure in a fixed volume?

 

For example, a metering pump (PD pump) is pumping against a closed outlet. Pressure at discharge will increase as the pump injects liquid into the discharge pipe. When the discharge pipe pressure reaches a certain value, how do I check what is the mass inside the discharge pipe? i assume an adiabatic process.

 

Thanks.

[samayaraj]

Hi bag,

 

In general, liquid are incompressible. But, liquid will compress a little on subjected to pressure. But this volume change is negligible.

 

Hence If you know the cross section area (CSA) of container and the height of liquid, you can calculate volume and you can calculate weight by multiplying volume with density.

 

In PD pumps, discharge pressure will rise suddenly if the outlet is closed and it may lead to failure of pump/ trip the pump. For this, a safety valve is provided upstream of discharge isolation valve to avoid such consequence. You should not operate PD pumps in this manner. As I said above, the liquid hold up is CSA X length of discharge pipe. Once you know the liquid holdup, you can calculate weight of liquid inside the pipe.

 

Do you meant the liquid is being pump to a closed vessel where inert gas blanket is provided as cover gas for cushioning? If so, the pressure in the discharge will increase gradually based on the flow rate of pump. 

 

 

#Samayaraj

Edited by samayaraj, 09 December 2014 - 09:12 AM.

[MrShorty]

Is there any formula which explains the relationship of liquid mass and liquid pressure in a fixed volume?

Not only is there a formula that explains the relationship between mass in a volume (=density, correct?) and pressure, there are many equations. We call these equations "equations of state" (EOS). From the simplest "ideal gas law" (which cannot describe liquid behavior at all) through van der Waals equation (and other cubic EOS) to multiparameter complex EOS specific to certain fluids. Wikipedia's entry on EOS's http://en.wikipedia....uation_of_state

 

The usual approach, then, to your question would be: 1) Select a suitable EOS for the fluid of interest, 2) Solve that EOS for volume or density at your specified T and P, and 3) compute mass from density and known pipe volume.

 

Of course, there are other, simpler equations available, too. As samayaraj indicated, sometimes it is adequate to assume the liquid is perfectly incompressible. In this case, you can calculate the saturated liquid density from whatever source you have, then assume the compressed liquid density is the same. The usual equation I see used here is the Rackett equation, or some variation on the Rackett equation.

 

There are also isothermal compressibility equations (http://en.wikipedia....Compressibility ). If you have saturated liquid density and a tabulated "compressibility factor" for the fluid and temperature in question (symbol beta, usually), then one can calculate density at pressures other than saturation. As noted in the Wikipedia article, this is where your assumption of "adiabatic" may be most applicable, because the compressibility factor will be different depending on whether you are assuming a constant temperature or a constant entropy process.