Problem $2(20$ points$)$ A turbine is located in a dam. The shaft torque, $T_s$ delivered to the turbine's blades is a function of the mass flow rate of fluid through the system $m^{},$ the fluid depth upstream of the dam $H,$ the fluid density $,$ and the angular velocity of the blades, $.$ Find the dimensionless groups $($pi groups$)$ for this relationship. Use $m^{},H,$ and $$ as your repeating variables.

Hint: the dimensions for torque are $\{M\}\{L{\}}^2\{T{\}}^{-2}$