For $\mu = 1$, we have \begin{align*} \frac{\dd p_{xx}}{\dd x} + \frac{\dd p_{xy}}{\dd y} + \frac{\dd p_{xz}}{\dd z} &= -\left(\frac{\dd(\rho u^{2})}{\dd x} + \frac{\dd(\rho uv)}{\dd y} + \frac{\dd(\rho uw)}{\dd z} + \frac{\dd(\rho u)}{\dd t}\right) \\ &= -u \left(\frac{\dd(\rho u)}{\dd x} + \frac{\dd(\rho v)}{\dd y} + \frac{\dd(\rho w)}{\dd z} + \frac{\dd\rho}{\dd t}\right) \\ &\quad -\rho \left(u\, \frac{\dd u}{\dd x} + v\, \frac{\dd u}{\dd y} + w\, \frac{\dd u}{\dd z} + \frac{\dd u}{\dd t}\right) \\ &= -\rho\, \frac{Du}{Dt} \Tag{(53.72)} \end{align*} by~\Eq{(53.71)}. $Du/Dt$~is the acceleration of the element of the fluid. This is the well-known equation of hydrodynamics when no body-force is \index{Hydrodynamics, equations of}% acting. (By adopting Galilean coordinates any field of force acting on the mass of the fluid has been removed.) Equations \Eq{(53.71)} and \Eq{(53.72)} express directly the conservation of mass and momentum, so that for Galilean coordinates these principles are contained \index{Momentum!conservation of}% in \[ \dd T^{\mu\nu}/\dd x_{\nu} = 0. \] In fact $\dd T^{\mu\nu}/\dd x_{\nu}$ represents the rate of creation of momentum and mass in unit volume. In classical hydrodynamics momentum may be created in the volume (i.e.\ may appear in the volume without having crossed the boundary) by the action of a body-force $\rho X$, $\rho Y$, $\rho Z$; and these terms are added on the right-hand side of~\Eq{(53.72)}. The creation of mass is considered impossible. Accordingly the more general equations of \emph{classical hydrodynamics} are \[ \frac{\dd T^{\mu\nu}}{\dd x_{\nu}} = (\rho X, \rho Y, \rho Z, 0). \Tag{(53.81)} \] In the \emph{special relativity theory} mass is equivalent to energy, and the body-forces by doing work on the particles will also create mass, so that \[ \frac{\dd T^{\mu\nu}}{\dd x_{\nu}} = (\rho X, \rho Y, \rho Z, \rho S), \Tag{(53.82)} \] where $\rho S$~is the work done by the forces $\rho X$, $\rho Y$, $\rho Z$. These older formulae are likely to be only approximate; and the exact formulae must be deduced by extending the general relativity theory to the case when fields of force are present, viz.\ to non-Galilean coordinates.