</font><font color="blue" class="small">( Does anyone know, while you cannot compress a fluid, does it still expand and contract with temperature?)</font>
MR,
Your query got me to wondering about the effects of temperature on the pressure in a resting hydraulic cylinder. I hope this contribution doesn’t insult anyone's intelligence on the Forum. As I scratched around, this is what I came up with.
For sure, in all the courses, manuals, books, etc. on the subject of hydraulics, we are constantly bombarded with the “fact” that liquids are incompressible, and that this is basis of hydraulic systems. Well, actually all liquids ARE indeed compressible, although to a much lesser extent than gases are. The compressibility of a liquid can be measured in the lab, as can a liquid’s ability to expand when it is heated (dilatometry). Both compressibility and “expansibility” are unique properties of a substance that are determined by its chemical composition/structure.
The compressibility of hydraulic fluid is quite small, but it is not zero. Because it is so small, the reciprocal of the compressibility coefficient, a large number, is seen more frequently. This reciprocal is called the bulk modulus, <font color="green"> beta, </font> which is a measure of a fluid’s
resistance to compression. The unit of measurement for the coefficient of bulk modulus is <font color="green"> pressure </font>. For hydraulic fluid, the average coefficient of bulk modulus is 250,000 psi. More on that number in a minute…
All “normal” substances expand when heated and contract when cooled (water is an exception at freezing, and that’s why ice floats). The coefficient of thermal expansion, designated <font color="red"> alpha,</font> for mineral-based hydraulic oil is on the order of 0.00064. The unit of measurement for the expansion coefficient is 1/T, the <font color="red"> reciprocal of temperature </font>.
Expansion of Oil
In the problem being discussed in this thread, we are considering changes in PRESSURE as a function of changes in TEMPERATURE, keeping the volume constant. That is, the hydraulic fluid is trapped in a constant volume hydraulic cylinder, and heat is being applied to it from outside. In reality, however, we have to also consider the hoses, which of course can distend somewhat as the pressure rises. Not surprisingly, it turns out that the
effective bulk modulus for hydraulic fluid in a system with rigid steel cylinders coupled with somewhat distensible hoses is LESS than its absolute bulk modulus. The combined bulk modulus for hydraulic oil plus high pressure hose is on the order of 47,500 psi.
Fluidpower Journal
Where the heck is all this going, you ask?
The formula which brings all this together is quite straightforward:
<font color="blue">dP/dT</font> = <font color="red"> alpha </font> x <font color="green"> beta </font>
That is, the change in Pressure per degree change in Temperature is given by the product of multiplying the coefficients of bulk modulus and thermal expansion. The result is a number whose units of measurement are psi/degree.
Using the average numbers above for hydraulic fluid,
dP/dT = 0.00064 x 47,500 = 30.4 psi/degree C rise in the actual oil temperature.
As we all recognize, there are a myriad of additional contributing factors, such as state of well being of seals (leak down), heat sink value of the mass of metal in the hydraulic cylinder, etc. that will affect the actual rise in Pressure in a given situation. Notwithstanding, these coefficients do explain how and why pressure build-up can occur in hydraulic cylinders which are exposed to heat, and they help us to quantify the magnitude of the change. If changes are too great, installation of relief valve, etc. may be in order
Hydraulic Decompression
