An equivalent statement that implies "'incompressibility "'is that the divergence of the flow velocity is zero ( see the derivation below, which illustrates why these conditions are equivalent ).
22.
The same relationship can be shown in a different way from the fact that the incompressibility of the product of the modulus and the thermal expansion coefficient is not dependent on the pressure for a given material.
23.
Regardless of this theoretical argument, experience clearly shows that " K "'decreases with pressure, or in other words that the second derivative of the incompressibility modulus " K " " is strictly negative.
24.
For gravity, an assumption is made of the density of the fluids being constant ( i . e ., incompressibility ), and likewise " g " ( waves are not high for gravitation to change appreciably ).
25.
BSc ( Hons ) ( Adel ), PhD ( Camb ), FAA, FTSE, FACS, FAustMS was an Australian applied mathematician, notable for his sustained work in ship hydrodynamics, and for Tuck's incompressibility function.
26.
Since this notion of incompressibility for a sphere is quite different from the above definition for surfaces, often an incompressible sphere is instead referred to as an "'essential sphere "'or "'reducing sphere " '.
27.
Thus, the equivalent Young's modulus of a neo-Hookean solid in uniaxial extension is 3 \ mu, which is in concordance with linear elasticity ( E = 2 \ mu ( 1 + \ nu ) with \ nu = 0.5 for incompressibility ).
28.
One of the first uses of the incompressibility method with Kolmogorov complexity its theory of computation was to prove that the running time of a one-tape Turing machine is quadratic for accepting a palindromic language and sorting algorithms require at least n \ log n time to sort n items.
29.
There's no need for the phrase'non-compressible hydraulic fluid', because incompressibility is not vital for this device's operation . if a fluid is suitable to be used in the system that the accumulator stores power for, that's that . nothing about the accumulator requires the fluid be incompressible
30.
The incompressibility of a material is quantified by the bulk modulus B, which measures the resistance of a solid to volume compression under hydrostatic stress as B = " Vdp / dV . Here V is the volume, p is pressure, and dp / dV is the partial derivative of pressure with respect to the volume.
