Question

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 theprototype will be operated in seawater. Determine the speed ofthe prototype to ensure Reynolds number similarity‘

Answer 1

Step-by-step explanation:

Given

scale i.e.
`L_r=1:15`

Using Reynolds number similarity

`(Re)_m=(Re)_p`

`((Vl)/(\\u ))_m=((Vl)/(\\u ))_p`

Properties of air

`\\u _(air)=1.57* 10^(-4) ft/s`

Properties of sea water

`\\u _(sea)=1.26* 10^(-5) ft/s`

`\left ( (V_ml_M)/(\\u _m)\right )=\left ( (V_pl_p)/(\\u _p)\right )`

`V_p=V_m\left ( (l_m)/(l_p)\right )\left ( (\\u _p)/(\\u _m)\right )`

`V_p=180* (1)/(15)* (1.26* 10^(-5))/(1.57* 10^(-4))`

`V_p=0.963\ ft/s`