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A missile, diameter 2m and length 10m is tested in a wind tunnel to determine the forces acting on the real prototype A 1/20th scale model is to be used if the maximum allowable speed of the prototype missile is 10 m/s, what should be the speed of air in the tunnel to achieve dynamic similarity?

Respuesta :

Answer:

speed of air is 200 m/s

Explanation:

given data

length dl = 10 m

diameter dp = 2 m

maximum allowable speed Vp = 10 m/s

scale  [tex]\frac{Dp}{Dm}[/tex] = 1/20th

to find out

speed of air in the tunnel to achieve dynamic similarity

solution

we know in dynamic similarity  ratio of force at corresponding point in model are equal and different dimensionless no is use for dynamic similarity

so

Rem = Rep

Re is modal law

so

[tex]( \frac{\rho VD}{\mu}) p=  (\frac{\rho VD}{\mu} ) m[/tex]

and

VpDp = VmDm

so [tex]\rho p = \rho m[/tex]

[tex]\mu p = \mu m[/tex]

so

10 × [tex]\frac{Dp}{Dm} = Vm[/tex]

Vm = 200 m/s

so speed of air is 200 m/s

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