Four base dimensions for flow problems (in the absence of electromagnetic forces and chemical reactions) $$ \text{Mass } M, \quad \text{length } L, \quad \text{time } T, \quad \text{temperature } \Theta $$ We denote the dimension of a variable $q$ by $[q]$ $$ [U] = \frac{L}{T}, \qquad [P] = \frac{[\text{force}]}{[\text{area}]} = \frac{MLT^{-2}}{L^2} = ML^{-1}T^{-2} $$

\[ \begin{array}{c|ccccccc} & \qquad \Delta p \qquad & \qquad \Delta x \qquad & \qquad d \qquad & \qquad \varepsilon \qquad & \qquad U \qquad & \qquad \rho \qquad & \qquad \mu \qquad \\ \hline M & \qquad 1 \qquad & \qquad 0 \qquad & \qquad 0 \qquad & \qquad 0 \qquad & \qquad 0 \qquad & \qquad 1 \qquad & \qquad 1 \qquad \\ L & \qquad -1 \qquad & \qquad 1 \qquad & \qquad 1 \qquad & \qquad 1 \qquad & \qquad 1 \qquad & \qquad -3 \qquad & \qquad -1 \qquad \\ T & \qquad -2 \qquad & \qquad 0 \qquad & \qquad 0 \qquad & \qquad 0 \qquad & \qquad -1 \qquad & \qquad 0 \qquad & \qquad -1 \qquad \\ \end{array} \] ◀ ▶