We are interested in predicting the aerodynamic drag of a pick-up truck. We have

Question

We are interested in predicting the aerodynamic drag of a pick-up truck. We have available a small wind tunnel which can only accommodate a model truck. The model truck is a one-third scale model. That is, it is geometrically similar to the full-sized truck, but each linear dimension is smaller by a factor of three. Assuming that the design speed of the full scale truck is 100 km/hr and the wind tunnel uses sea-level air, what should the wind speed be in the wind tunnel Explain. The measured drag of the model in the wind tunnel is 200 Newtons. What is the predicted drag of the full-scale truck at the design speed Explain. For the full-scale truck traveling at the design speed, what engine power, in kilowatts, is required to overcome aerodynamic drag

Explanation / Answer

Solution:

Given : Dimension ratio ie La/Lm = Lr is 3 units

a)

For velocity ie Va/Vm = sqrt (Lr)

where Va is velocity of actual truck & Vm is Velocity of model

Vm = Va/sqrt(Lr)

       = 100/sqrt(3)

Vm =57.73 km/hr

b)

Fm= 200N

Fa/Fm = Lr^3

            =Fm x Lr^3

            = 200 x 3^3

            = 5400 N

c)

Power is given by Force x Velocity

so Fa=5400 N

& Va=100 km/hr = 27.77 m/s

So power Pa = 5400 x 27.77

                      = 150000 W

                      = 150 kW.

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