Evan

A ship with propeller 20 ft in diameter is designed to move in water at speed of 25ft/s when the propeller turns at 2 revolutions/s. Before making the ship the thrust force must be determined.To do this, we build a 1/10 scale model of ship to be tested in a model ship basin, in which we can measure the thrust force of the propeller on the model ship, and we can vary the speed of the model ship. We assume that we may neglect viscosity. There is a certain speed V' and rotational speed n', at which the model ship and its propeller should be run, so that when we measure the thrust of the propeller on the model ship, we can calculate the thrust force of the large propeller. Find V' and n' and describe a method for calculating the thrust force, F, of the large propeller.HINT: Since we know D,V, and n for the large ship, we could compute F from F=rho(D^2)(V^2)theta[(nD/V),(gD/V^2)] if we knew theta(nD/V,gD/V^2) for some unknown function theta. But F', the measured thrust force of the model, also satisfies F, with D', V', and n' replacing D, V, and n. Thus, what is needed is a means of finding theta(nD/V,gD/V^2) by using this info.Note: D= is diameter of propeller; V is the speed of the ship; rho is the density of the water;F is the thrust force of propeller; n is the rotational speed (in revs/second);g is the accel. due to gravity; and mu is the viscosity of the water.

AronZ

That is not easy. propeller design is really part of hydrodynamics and physics. I don't think that by just knowing the scale model is 1/10 of the original ship, it is possible to find out the information you want, because it is probably not a linear relationship between propeller size, propeller speed and thrust (there are few linear relationships in hydro and aero-dynamics).