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

Answer:

Explanation:

Given

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

Using Reynolds number similarity

$(Re)_m=(Re)_p$

$(\frac{Vl}{\nu })_m=(\frac{Vl}{\nu })_p$

Properties of air

$\nu _{air}=1.57\times 10^{-4} ft/s$

Properties of sea water

$\nu _{sea}=1.26\times 10^{-5} ft/s$

$\left ( \frac{V_ml_M}{\nu _m}\right )=\left ( \frac{V_pl_p}{\nu _p}\right )$

$V_p=V_m\left ( \frac{l_m}{l_p}\right )\left ( \frac{\nu _p}{\nu _m}\right )$

$V_p=180\times \frac{1}{15}\times \frac{1.26\times 10^{-5}}{1.57\times 10^{-4}}$

$V_p=0.963\ ft/s$