Calculating Pressure Drop in Two-Phase Flow

[StudioSaturn]

Hi folks, my prof gave us some problems calculating pressure drop in two phase flow. She did some examples and somehow she got the density of water-liquid and water-vapor from steam tables, but she did not explain how. I have never used these. I am especially stumped on the density of water-liquid. The problem gave a pressure of 7.2 MPa, Length = 3m, Area = 1.5E-4. She got a density of liquid = 736.49kg/m^3. Thanks

 

[Astronuc]

In two phase flow, the liquid and vapor are more or less in thermodynamic equiblibrium at saturated conditions. In the two phase region, the steam and liquid are considered at the same temperature for a given pressure (see saturated temperature and pressure). The energy (enthalpy) is partioned between liquid and vapor phases.

The specific enthalpy is determined from the thermodynamic quality, x, which has a value between 0 and 1. For x=0, the fluid is all liquid, and for x = 1, the fluid is all vapor.

Specific properties are given by xp_g + (1-x)p_f, where x is the vapor fraction, p is the property, which could be specific volume (inverse of density), specific entropy, specific energy or specific enthalpy. The subscripts g and f designate vapor and fluid, respectively.

Some discussion and examples: http://www.engineersedge.com/thermodynamics/steam_tables.htm

One should be able to find discussion in a textbook on introduction to thermodynamics.

 

[jim hardy]

have you had intro to thermodynamic properties of water?

Density of each phase is a straight lookup in the saturated table.
When you have a mix of liquid and vapor it's just simple algebra to figure density of the mix

i use the one at boilerroomservices dot com, go there and click on click on Boiler Steam Tables,
they give density as specific volume which is 1/density
just look it up for the temperature or pressure you are given.
That's Mother Nature's kind gift to Thermo students - at saturated condition either temp or pressure defines your point on the saturation curve.

i use English units but metric steam tables abound at sites like engineeringtoolbox
boilerroomservices has metric ones too i think, perhaps poke around their site a bit

this is very basic to thermo so master it soon .

BTW two phase flow is not at all simple so you are allowed some initial bewilderment.

old jim