A mixing basin in a sewage filtration plant is stirred by a mechanical agitator with a power input \(\dot{W} \doteq F \cdot L / T\). Other parameters describing the performance of the mixing process are the fluid absolute viscosity \(\mu \doteq F \cdot T / L^{2}\), the basin volume \(\forall \doteq L^{3}\), and the velocity gradient \(G \doteq 1 / T\). Determine the form of the dimensionless relationship.