The Froude number (Fr) of the flow around an object such as a sailboat is define

Question

The Froude number (Fr) of the flow around an object such as a sailboat is defined by Fr= gL/U2

g= acceleration of gravity, L = characteristic length of the object, and U = Fluid velocity far from the flow.

It is desired to simulate the flow around a sailboat in a laboratory experiment with mercury as the fluid. What model length L (in feet) and fliud speed (U) (in feet per second would be required to have the same Froude and Reynolds numbers determined when L =40ft and sailboat crusing at 25 miles per hour.

Explanation / Answer

Fr = 0.958

Re = 135.265 * 106

Numbers from last two questions

Fr = g L / U2

Re = U L /

g= 32.2 ft/sec2 ; ( for Mercury from internet) =1.2744*10-6 ft2/sec

Using all these values , we have the length and velocity relations for a model in Mercury, i.e.

L/U2 = 0.0297

U L = 172.382

Solving these relations , we get:

Umodel = 17.97 ft/sec = 12.25 mph

Lmodel = 9.59 ft

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