For the equation $\text{F}\propto {\text{A}}^{\text{a}}{\text{V}}^{\text{b}}{\text{D}}^{\text{c}}$,where F is the force, A is the area, V is the velocity D is the

            density, the dimensional formula gives the following values

$$\begin{gathered} \text{F}\alpha {\text{A}}^{\text{a}}{\text{V}}^{\text{b}}{\text{D}}^{\text{c}} \\ \text{F}-\text{Force}-\left[{\text{MLT}}^{-\text{2}}\right] \\ \text{A}-\text{Area-}\left[{\text{L}}^{\text{3}}\right] \\ \text{V}-\text{Velocity}-\left[{\text{LT}}^{-\text{1}}\right] \\ \text{D}-\text{Density-}\left[{\text{ML}}^{-\text{3}}\right] \\ \left[{\text{MLT}}^{-\text{2}}\right]={\left[{\text{L}}^{\text{2}}\right]}^{\text{a}}{\left[{\text{LT}}^{\text{-1}}\right]}^{\text{b}}{\left[{\text{ML}}^{-\text{3}}\right]}^{\text{C}} \\ \left[{\text{MLT}}^{-\text{2}}\right]=\left[{\text{M}}^{\text{c}}{\text{L}}^{{ }^{\text{2a}+\text{b}-\text{3c}}}{\text{T}}^{-\text{b}}\right] \\ \text{c}=\text{1 } \\ -\text{b}=-\text{2} \\ \text{b}=\text{2 } \\ \text{2a}+\text{b}-\text{3c}=\text{1 } \\ \text{2a}+\text{2}-\text{3}=1 \\ \text{2a}-\text{1}=\text{1} \\ \text{a}=\text{2/2}=\text{1} \\ \text{a}=\text{1} \end{gathered}$$