The power output of a hydraulic turbine depends on the diameter
d of the turbine, the density p of water, the height h of water
surface above the turbine, the gravitational acceleration g, the
angular velocity w of the turbine wheel, the discharge q of water
through the turbine, and the efficiency n of the turbine. by
dimensional analysis, generate a set of appropriate dimensionless
groups using q, p, and d as core variables. show all work.