Problem 1.16
Algebraic equations such as Bernoulli’s relation, Eq. (1) of Example 1.3 (see below), are
dimensionally consistent, but what about differential equations? Consider, for example, the
boundary-layer x -momentum equation, first derived by Ludwig Prandtl in 1904:
x
u u p
u v g
x y x y
+ = − + +
where τ is the boundary-layer shear stress and g x is the component of gravity in the x direction.
Is this equation dimensionally consistent? Can you draw a general conclusion?