Question

The drag characteristics for a newly designed automobile having a maximum characteristic length of 20 ft are to be determined through a model study. The characteristics at both low speed (approximately 20 mph) and high speed (90 mph) are of interest. For a series of projected model tests, an unpressurized wind tunnel that will accommodate a model with a maximum characteristic length of 4 ft is to be used. Determine the range of air velocities that would be required for the wind tunnel if Reynolds number similarity is desired. Are the velocities suitable

Answer 1

The speed range is between 100 and 450 mph (not possible)

Step-by-step explanation:

Given data:

Maximum characteristic length = 20 ft

Low speed = 20 mph

High speed = 90 mph

Maximum characteristic length of the model = 4 ft

Question: Determine the range of air velocities that would be required for the wind, VMT = ?

Are the velocities suitable?

It is desired that Reynolds's number be equal

Re = (Re)MT

Here MT is model test

`(\rho VL)/(\mu ) =((\rho _(MT) V_(MT) L_(MT) )/(\mu _(MT) ) )_(MT)`

`v=(\mu )/(\rho )`

`\mu =v*\rho`

Substituting

`(VL)/(v ) =(V_(MT) L_(MT) )/(v _(MT) )`

`(V_(MT) )/(V ) =(L )/(L_(MT) )`

`(V_(MT) )/(V ) =(20)/(4) =5`

`V_(MT) =5V`

Velocity at slow speed:

`V_(MT) =5*20=100mph`

Velocity at high speed

`V_(MT) =5*90=450mph`

The speed range is between 100 and 450 mph (not possible)