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If there ever was a universal formula of everything 1) this is it:
of state
$PV=nRT\,$ or $p-p_0=B\left(\left(\frac{\rho}{\rho_0}\right)^m -1\right)$ 2)
of conservation of momentum
$\rho \left(\frac{\partial u}{\partial t} + u \frac{\partial u}{\partial x} + v \frac{\partial u}{\partial y} + w \frac{\partial u}{\partial z}\right) -\frac{\partial}{\partial z}\left(\mu\left(\frac{\partial u}{\partial z} + \frac{\partial w}{\partial x}\right)\right) -
\rho g_x $
$=-\frac{\partial p}{\partial x} + \frac{\partial}{\partial x}\left(2 \mu \frac{\partial u}{\partial x} - \frac{2\mu}{3} \nabla \cdot \mathbf{v}\right) +
\frac{\partial}{\partial y}\left(\mu\left(\frac{\partial u}{\partial y} + \frac{\partial v}{\partial x}\right)\right)$
$\rho \left(\frac{\partial v}{\partial t} + u \frac{\partial v}{\partial x} + v \frac{\partial v}{\partial y}+ w \frac{\partial v}{\partial z}\right) -
\frac{\partial}{\partial z}\left(\mu\left(\frac{\partial v}{\partial z} + \frac{\partial w}{\partial y}\right)\right) -
\rho g_y $
$=-\frac{\partial p}{\partial y} +
\frac{\partial}{\partial x}\left(\mu\left(\frac{\partial v}{\partial x} + \frac{\partial u}{\partial y}\right)\right) +
\frac{\partial}{\partial y}\left(2 \mu \frac{\partial v}{\partial y} - \frac{2\mu}{3} \nabla \cdot \mathbf{v}\right) $
$\rho \left(\frac{\partial w}{\partial t} + u \frac{\partial w}{\partial x} + v \frac{\partial w}{\partial y}+ w \frac{\partial w}{\partial z}\right) - \frac{\partial}{\partial z}\left(2 \mu \frac{\partial w}{\partial z} - \frac{2\mu}{3} \nabla \cdot \mathbf{v}\right) $ $=-\frac{\partial p}{\partial z} + \frac{\partial}{\partial x}\left(\mu\left(\frac{\partial w}{\partial x} + \frac{\partial u}{\partial z}\right)\right) + \frac{\partial}{\partial y}\left(\mu\left(\frac{\partial w}{\partial y} + \frac{\partial v}{\partial z}\right)\right)+ \rho g_z $
of mass continuity
$\frac{\partial \rho}{\partial t} + \nabla \cdot (\rho \mathbf{v}) = 0$ 3)
of conservation of energy
$ -\rho \frac{D h}{D t}=\frac{D p}{D t} + \nabla \cdot (k \nabla T) + \mu \left(2\left(\left(\frac{\partial u}{\partial x}\right)^2 + \left(\frac{\partial v}{\partial y}\right)^2 + \left(\frac{\partial w}{\partial z}\right)^2\right) \\\\+ \left(\frac{\partial v}{\partial x} + \frac{\partial u}{\partial y}\right)^2 + \left(\frac{\partial w}{\partial y} + \frac{\partial v}{\partial z}\right)^2 + \left(\frac{\partial u}{\partial z} + \frac{\partial w}{\partial x}\right)^2\right) + \lambda (\nabla \cdot \mathbf{v})^2$4)
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