$1.$ DIMENSIONAL ANALYSIS

Derive an expression for the discharge Q over a spillway in the form of a function including dimensionless parameters. The discharge Q is dependent on height of the spillway P $,$ head H on the spillway $($height of water above the crest of spillway$),$ viscosity of water $\backslash (\backslash$mu $\backslash ),$ density of water $\backslash (\backslash$rho $\backslash ),$ surface tension $\backslash (\backslash$sigma $\backslash ),$ and acceleration due to gravity g $.$ Use $\backslash (\backslash$mathrm$\{$Q$\},\backslash$rho $\backslash ),$ and H as the repeating variables.