A model of a submarine, 1 : 15 scale, is to be tested at 180 ft/s in a wind tunnel with standard sea-level air, while the prototype will be operated in seawater. Determine the speed of the prototype to ensure Reynolds number similarity

0.96 feet / s

Explanation:

Recalling the Reynolds number for the prototype and the model,

We have, Re Model = Re prototype

Therefore: PVD / ω (model) = PVD/ω (prototype)

Recalling the value of air density and viscosity at sea level,

we have, (2.38*10-³) (180) (1/15 D prototype) : (3.74 * 10 ∧ - 7)

= (1.99) Vprototype Dprototype / (2.51 * 10 ∧ - 5)

V prototype = 76363.63 feet / 79282 s

V prototype = 0.96 feet / s

NOTE : During the calculation, both sides of the equations were dimensionless so D prototype was cancelled out on both sides and the velocity was isolated in the part of the prototype. And thus, we obtained the value 0.96 feet / s