Editing Stiffened equation of state
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It can be shown, by linearizing the [[Euler equations]], that the [[speed of sound]] in water is given by | It can be shown, by linearizing the [[Euler equations]], that the [[speed of sound]] in water is given by | ||
:<math>c^2=\frac{\gamma p+p^* }{\rho_0}</math>, | :<math>c^2=\frac{\gamma p+p^* }{\rho_0}</math>, | ||
from which the value of | from which the value of $p^*$ may be computed given all the other variables. | ||
Thus water behaves as though it is an [[ideal gas]] that is ''already'' under about 20,000 atmospheres (2 GPa) pressure, and explains why water is commonly assumed to be incompressible: when the external pressure changes from 1 atmosphere to 2 atmospheres (100 kPa to 200 kPa), the water behaves as an ideal gas would when changing from 20,001 to 20,002 atmospheres (2000.1 MPa to 2000.2 MPa). | Thus water behaves as though it is an [[ideal gas]] that is ''already'' under about 20,000 atmospheres (2 GPa) pressure, and explains why water is commonly assumed to be incompressible: when the external pressure changes from 1 atmosphere to 2 atmospheres (100 kPa to 200 kPa), the water behaves as an ideal gas would when changing from 20,001 to 20,002 atmospheres (2000.1 MPa to 2000.2 MPa). |