A prototype boat is 30 meters long and is designed to cruise at 9 m/s. Its drag is to be simulated by a 0.5-meter-long model pulled in a tow tank. For Froude scaling find a)-The tow speed b)-The ratio of model to prototype drag c)-The ratio of model to prototype power.

a) 1.16 m/s

b)  1/216000

c)  (√15)/6480000

Explanation:

The parameters given are;

Length of boat prototype, lp = 30 m

Speed of boat prototype = 9 m/s

Length of boat model, lm= 0.5 m

a) lm/lp = 0.5/30 = 1/60 = ∝

(vm/vp) = ∝^(1/2) = √∝ = (1/60)^(1/2)

vm = 9 × (1/60)^(1/2) = 1.16 m/s

b) The ratio of the model to prototype drag, Fm/Fp, is given as follows;

Fm/Fp = (vm/vp)²×(lm/lp)² = ∝³

Fm/Fp = (1/60)³ = 1/216000

c) The ratio of the model to prototype power  pm/p = (Fm/Fp) × (vm/vp) = ∝³×√∝

The ratio of the model to prototype power  pm/p = √(1/60) × (1/60)³

pm/p = √(1/60) × (1/60)³ = (√15)/6480000