A 1:80 model of an airplane is tested in 68°F air that has a velocity of 150 ft/sec, (a) At what speed should the model be towed when fully submerged in 80°F water? (b) What prototype drag in air would a model resistance of 1.25 Ib in water represent?

Question

A 1:80 model of an airplane is tested in 68°F air that has a velocity of 150 ft/sec, (a) At what speed should the model be towed when fully submerged in 80°F water? (b) What prototype drag in air would a model resistance of 1.25 Ib in water represent?

Accepted Answer

(a) Equating Reynolds numbers, [latex]\frac{150 imes L}{16.0 imes 10^{-5}}=\frac{V imes L}{0.930 imes 10^{-5}} [/latex] or V = 8.72 ft/sec in water.

(b) Since p varies with [latex] ho V^2 [/latex], equating the Euler numbers will produce

[latex]\frac{ ho _{m}V^2_{m}}{p_{m}} =\frac{ ho _{p}V^2_{p}}{p_{p}} [/latex] or [latex]\frac{p_{m}}{p_{p}} =\frac{ ho _{m}V^2_{m}}{ ho _{p}V^2_{p}} [/latex]

But forces acting are (pressure x area), or p L²; hence

[latex]\frac{F_{m}}{F_{p}}=\frac{p_{m}L^2_{m}}{p_{p}L^2_{p}} =\frac{ ho _{m}V^2_{m}L^2_{m}}{ ho _{p}V^2_{p}L^2_{p}} [/latex]

or [latex]F_{r}= ho _{r}V^2_{r}L^2_{r} [/latex] [equation (6)]

To obtain the velocity of the prototype in air, equate Reynolds numbers. We obtain

[latex]\frac{V_{m}L_{m}}{ u _{air}} =\frac{V_{p}L_{p}}{ u _{air}} [/latex] or [latex]\frac{150 imes L_{p}/80}{ u _{air}}=\frac{V_{p}L_{p}}{ u _{air}} [/latex] and [latex]V_{p} =1.875 [/latex] ft/sec

Then [latex]\frac{1.25}{F_{p}}=\left(\frac{1.94}{0.00233} ight)\left(\frac{8.72}{1.875} ight)^2 \left(\frac{1}{80} ight)^2 [/latex] and [latex]F_{p}=0.444 [/latex] lb

Question 6.25: A 1:80 model of an airplane is tested in 68°F air that has a...

This Question has been Answered.

Already have an account?

Login

Related Answered Questions