Bulk Modulus is a measure of the resistance of a fluid to compression. It is defined as the ratio of pressure stress to volumetric strain. The value of bulk modulus equals the pressure change x 100 required to cause a one percent change in volume.
MIL-H-83282 oil has a bulk modulus of 3.0 x 105 psi. Thus, a pressure increase of 3000 psi will reduce its volume by 1.0%.
When the value of B is known (see reference table on next page), it is easy to calculate the effect of any pressure change on volume, or of any volume change on pressure.
The Coefficient of Cubical Thermal Expansion is the change in volume per unit volume caused by a change in temperature of 1°F.
MIL-H-83282 oil has a coefficient of cubical thermal expansion of 0.00046/°F. Thus a temperature rise of 100°F will increase its volume by 4.6%.
The bulk modulus and the coefficient of cubical thermal expansion can be used together to compute the pressure rise in a closed system subjected to an increasing temperature.
MIL-H-83282 oil at 0 psi is heated from 70°F to 120°F in a closed, constant volume system containing 100 cu. in.
ΔP = 3.0 x 105 x 0.00046 x 50 = 6900 psi
This is the same ΔP which would be caused by adding 2.3 cubic inches of oil with no temperature change. It is also apparent that a constant system pressure could be maintained by bleeding off 2.3 cubic inches of oil while increasing the temperature by 50°F.
|Units||psi||ΔV/V/°F||°F, min.||°F, max.|
|Bref.||=||Tangent adiabatic bulk modulus psi stated at 100°F, 2500 psi and no entrained air. A reference point.|
|??||=||Coefficient of cubical thermal expansion/°F at 100°F|
|ΔP||=||Pressure rise, psi|
|ΔT||=||Temperature rise, °F|
|P1, P2||=||Initial and final pressures, psi|
*Flash point is the lowest temperature at which sufficient combustible vapor is driven off a fuel to flash when ignited in the presence of air.
The previous examples used a constant bulk modulus for simplicity. In actual use, the bulk modulus is affected by the working pressure, temperature and percent of entrained air. Use the next 3 graphs to find the effect of these variables, and you will get a close approximation of actual conditions. The actual bulk modulus, B, of a fluid is the value in the table here as Bref. modified for the effect of pressure, temperature and percent of entrained air.
The actual bulk modulus B = EP x ET x EA x Bref.
500 psi, 60°F, 2% entrained air, MIL-H-83282.
Actual B = 0.91 x 1.10 x 0.8 x 300,000 = 240,000 psi
2000 psi, 160°F, 2% entrained air, MIL-H-83282.
Actual B = 0.98 x 0.86 x 0.98 x 300,000 = 248,000 psi
With the corrected bulk moduli for the two end points of a thermal problem, an average bulk modulus can be selected for calculation purposes. We would use 244,000 psi for B.
The effect of working pressure on bulk modulus for hydrocarbon fluids.
The effect of temperature on bulk modulus for hydrocarbon fluids.
The effect of entrained air on bulk modulus in hydrocarbon and other fluids for different working pressures.
To simplify the calculations of thermal problems with entrained air, these curves show the average effect on a 230,000 psi bulk modulus for pressure points fairly close together. If a wide change in pressure is encountered in a problem, it would be more accurate to break the changes down into two or more steps, depending on the accuracy desired.
An accurate one step formula for this relationship follows:
(Note that pressure is in units of psia.)