Chapter 1, Problem 1.16P

Algebraic equations such as Bernoulli's relation, Bq. (1) of Example 1.3, are dimensionally consistent, but what about differential equations? Consider, for example, the boundary-layer x-momentum equation, first derived by Ludwig Prandtl in 1904:

$\rho u\frac{\partial u}{\partial x}+\rho v\frac{\partial u}{\partial y}=-\frac{\partial p}{\partial x}+\rho g_x+\frac{\partial \tau }{\partial y}$

where t is the boundary-layer shear stress and g_x is the component of gravity in the x direction. Is this equation dimen-sionally consistent? Can you draw a general conclusion?