A mixing basin in a sewage filtration plant is stirred by mechanical agitation (paddlewheel) with a power input \(\dot{W}(\mathrm{ft} \cdot \mathrm{lb} / \mathrm{s})\). The degree of mixing of fluid particles is measured by a "velocity gradient" \(G\) given by

\[ G=\sqrt{\frac{\dot{W}}{\mu V}} \]

where \(\mu\) is the fluid viscosity in \(\mathrm{lb} \cdot \mathrm{s} / \mathrm{ft}^{2}\) and \(\forall\) is the basin volume in \(\mathrm{ft}^{3}\). Find the units of the velocity gradient.