##### Reference no: EM13630872

A model (1/10 of scale) of a tractor-trailer rig is tested in a wind tunnel. The cross section area of the model is 0.1 m^2, the flow velocity in the wind tunnel is 75 m/s and the measured drag force is 334 N. (Note: the model length scale is 1/10 of the prototype)

1. Assuming that the drag force is a function of the cross-sectional area of the vehicle (which is the square of a length), the flow velocity, the fluid density, the fluid viscosity and the speed of sound, identify and name all the non-dimensional parameters that govern the problem.

2. Calculate the coefficient of drag assuming that the density of air is 1.25 kg/m^3.

3. Assuming that the coefficient of drag is constant, calculate the drag of the prototype for 90 km/h.

4. In order to achieve incomplete similarity, at least two non-dimensional parameters (including the coefficient of drag) need to be equal for the prototype and the model. Assuming a speed of 90 km/h for the prototype and assuming that the Reynolds numbers (prototype and model) are equal, what is the flow speed required for the model? If a flow is considered incompressible for Mach number lower than 0.2, do you think that the proposed incomplete similarity work? Why?