When a paper cake case falls right way up through air, it quickly reaches terminal velocity. The drag force, D acting on the case is given by D=f§¤Av©÷ where §¤ is the density of air (1.2kg/m©ø), v is the terminal velocity, A is the cross-sectional area of the base of the case, f is known as he shape factor. Can you plz help me to devise an experiment to determine the shape factor for empty cases?

Sure:
You will have to know the velocity of the box in the airstream. Two ways: drop it from a height, and measure the fall of the box with a video camera, then determining its velocity. You can measure the crossectional area. Let it hit a scale, and record f.

another way: Use a auto to generate motion attach a box to a string which is attached to spring scale. At a constant veloctity, let the box into the airstream behind the car. Measure the force on the spring.