Write the expression for the wind force (F).

  F = CDρV2A2                                                (I)

Here, drag coefficient is CD, density of air is ρ, velocity of air is V, cross-sectional area of the building is A.

Conclusion:

The equation (I) can be rearranged to get CD as follows:

  CD=2FρV2A                                                 (II)

The dimensions of the various terms in the equation (II) are given by:

  F=MLT−2ρ=ML−3V=LT−1A=L2

Substitute the above in equation (II) to get the dimensions of CD.

  CD=MLT-2(ML-3)(LT-1)2(L2)CD=MLT-2(ML-3)(L2T-2)(L2)CD=M0L0T0

Thus, the drag coefficient CD is dimensionless.