Chapter 7, Problem 69P

Consider Problem 7.38. Experience shows that for ship-size propellers, viscous effects on scaling are small. Also, when cavitation is not present, the nondimensional parameter containing pressure can be ignored. Assume that torque, T, and power, $P$, depend on the same parameters as thrust. For conditions under which effects of μ and p can be neglected, derive scaling “laws” for propellers, similar to the pump “laws” of Section 7.5, that relate thrust, torque, and power to the angular speed and diameter of the propeller.

7.38 The thrust of a marine propeller is to be measured during “open-water” tests at a variety of angular speeds and forward speeds (“speeds of advance”). The thrust, F_T, is thought to depend on water density, ρ, propeller diameter, D, speed of advance, V, acceleration of gravity, g, angular speed, ω, pressure in the liquid, p, and liquid viscosity, μ. Develop a set of dimensionless parameters to characterize the performance of the propeller. (One of the resulting parameters, gD/V², is known as the Froude speed of advance.)