07-05-2020, 12:14 PM

An extract from An Investigation Into the Required Equipment and Procedures for the Accurate Measurement of Pressure in Hydraulic Fluid Power Systems, The Fluid Power Institute (Milwaukee School of Engineering), AD-A244 165 (U.S.AR. M&E-R&R), May 1976, 139 pgs.

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1.2.1.3.1 Snubber Equation Derivation

Using the laboratory data obtained in Section 1.2.1.1, characteristic equations for various degrees of snubbing (i.e., 20°, 25°, and 10°), were obtained.

The P-Q characteristic, in general, for the orifice can be shown to be the following:

…

The above equation closely resembles the equation of a straight line:

…

A simple least-squares curvefit can now be employed to determine n and log₁₀ K. Actual calculations for these values were performed using HP-55 programmable calculator and the program given below … page 22

1.2.1.3.2 Hydlraulic Gauge Capacitance Equation

It can be shown that the pressure-volume relationship for the bourdon tube pressure gauge is:

…

The hydraulic capacitance is defined as the rate of change of volume with respect to pressure. That is,

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Applying the derivative to the original equation gives

…

Rearrangement of the above equation results in:

…

which resembles the equation of a straight line

…

The calculations necessary to obtain the least-square's fit were again performed on a programable HP-55 calculator using the program below … page 22

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1.2.1.3.1 Snubber Equation Derivation

Using the laboratory data obtained in Section 1.2.1.1, characteristic equations for various degrees of snubbing (i.e., 20°, 25°, and 10°), were obtained.

The P-Q characteristic, in general, for the orifice can be shown to be the following:

…

The above equation closely resembles the equation of a straight line:

…

A simple least-squares curvefit can now be employed to determine n and log₁₀ K. Actual calculations for these values were performed using HP-55 programmable calculator and the program given below … page 22

1.2.1.3.2 Hydlraulic Gauge Capacitance Equation

It can be shown that the pressure-volume relationship for the bourdon tube pressure gauge is:

…

The hydraulic capacitance is defined as the rate of change of volume with respect to pressure. That is,

…

Applying the derivative to the original equation gives

…

Rearrangement of the above equation results in:

…

which resembles the equation of a straight line

…

The calculations necessary to obtain the least-square's fit were again performed on a programable HP-55 calculator using the program below … page 22

"

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