Case 1: P > Psat

For P > Psat it is assumed that all air/gas is dissolved in the hydraulic liquid.

The mass of the liquid remains constant but the liquid volume changes:

we have a unit volume of liquid at Patm and T0, then we can write for the liquid volume at P and T:

Since: Vfluid(P, T) =Vliq(P, T) = 1 (unit volume assumptions), we obtain for the fluid:

This gives the following fluid density

Equation 11: Case 1: fluid density at P and T

Note that

gC is constant and so Equation 11 is of the form

From Equation 2 and Equation 6, we obtain for the fluid bulk modulus:

Then for P > Psat, the fluid bulk modulus is equal to the liquid bulk modulus, i.e. the fluid bulk modulus is not influenced by the air/gas content.

Elementary case:

Using Equation 11 and Equation 6, then

Note that in this case, the density can be written:

Equation 12: Case 1: fluid density at P and T for elementary

Where K is a constant:

The fluid bulk modulus is then:

Note that the Equation 12 is only applied when P > Psat and with elementary properties.