Show that Froude number of a propeller with diameter D and rotational speed n(1/sec) can be given as Fn=n*sqrt(D/g)

Answer 1

I knew it was coming ! William Froude :)

Fr = v/sqrt(Lg)

v = n R or (1/2) n D

(1/2) n D / sqrt (D g)

= (1/2) n sqrt D/sqrt g

= (1/2) n sqrt (D/g)

the 1/2 does not matter, arbitrary constant

Answer 2

Fr = v/sqrt(Lg)

v = n R or (1/2) n D

(1/2) n D / sqrt (D g) <-----

= (1/2) n sqrt D/sqrt g

= (1/2) n sqrt (D/g)

What's the explanation of replacing L with D there?

Answer 3

L is any old length on your model or ship or dam or whatever
It just has to be the same length on the ship and the model and the speed measured at the bow or at the propeller tip as long as you are consistent from ship to model. The point is that you will get the same wave shapes at the same Froude number.

Answer 4

Got it. I also am studying Naval Architecture by the way. And thanks for answering my other question about sloshing water frequency :)

Answer 5

if you multiply any lengths by 4, you must multiply the speeds by 2 to be at the same Fr.

Answer 6

Great !