Case 3: PLvap < P < PHvap

In this case all the air/gas is free and part of the liquid is vaporized (cavitation phenomenon).

Then the fluid density is defined as:

• For the free air part, we can use our previous results with θ=1 (Equation 14) Equation 20: Case 3: free air at P and T

• For the liquid part, a fraction of the liquid is vaporized. There is no standard convention here, so we can consider a vapor mass fraction rather than a volume fraction, defined as:

For the cavitation phenomenon, the same law used for aeration is applied. The vapor mass fraction is only pressure dependent and given by the polynomial:

The mass of vapor is then given with the vapor mass fraction and the total liquid mass (see section Vapour):

And the volume of vapor is:

Equation 21: Case 3: vapor at P and T

• For the liquid part, the mass of liquid is given by the vapor mass fraction Equation 22: Case 3: liquid at P and T

For the fluid density, we obtain:

Equation 23: Case 3: fluid density at P and T

Where:

Note that we have

Equation 24: Case 3: fluid density at P and T

Where

And

The bulk modulus is computed from the density expression and Equation 2, which leads to:

Equation 25: Case 3: fluid bulk modulus at P and T

Elementary case

The fluid density is then:

Equation 26: Case 3: fluid density at P and T for elementary

and the corresponding consistent bulk modulus is then

Equation 27: Case 3: fluid bulk modulus at P and T for elementary