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Viscous media

The drag coefficient

For fluids, like air, where regime II applies, one defines the dimensionless quantity of drag coefficient C_d by

F_res = C_d ρ_fluidv²S/2

• ρ_fluid represents the density of the fluid.
  
• S is the reference area.

For a sphere S=πr², hence

C₂ = πC_d ρ_fluid/2

Furthermore, for a sphere C_d=0.47, whereas, moreover the density of air under normal conditions equals about 1.2 kg/m³.
From all that we may determine the pressure coefficient C₂ for a spherical ball which is moving in air, namely

C₂ = πC_d ρ_fluid/2 = 0.89 kg/m³

which is the value we have used at the previous page.

We could also be interested in a relation between the quadratic coefficient B and the pressure coefficient C₂. For that we must recall the definition of C₂ given a few pages before. We find

mB = C₂r²

The plastic ball has a mass of 0.35 kg and a radius of 10 cm. Furthermore, for B we obtained a value of about 0.025 m^-1. Hence, for C₂ we find then C₂ = mBr^-2 = 0.88 kg/m³. This is also an excellent agreement within the errors of our method and measurements.

More on drag can be found here.

solid spheres