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‘

Respuesta :

Answer:

Explanation:

Given

scale i.e. [tex]L_r=1:15[/tex]

Using Reynolds number similarity

[tex](Re)_m=(Re)_p[/tex]

[tex](\frac{Vl}{\nu })_m=(\frac{Vl}{\nu })_p[/tex]

Properties of air

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

Properties of sea water

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

[tex]\left ( \frac{V_ml_M}{\nu _m}\right )=\left ( \frac{V_pl_p}{\nu _p}\right )[/tex]

[tex]V_p=V_m\left ( \frac{l_m}{l_p}\right )\left ( \frac{\nu _p}{\nu _m}\right )[/tex]

[tex]V_p=180\times \frac{1}{15}\times \frac{1.26\times 10^{-5}}{1.57\times 10^{-4}}[/tex]

[tex]V_p=0.963\ ft/s[/tex]