1. a) What is the speed at which a sphere descends through water if it has a den

Question

1. a) What is the speed at which a sphere descends through water if it has a density of 1000 kg/m^3? b) Calculate the speed at which a ball bearing with a density of 5000 kg/m^3 and a diameter of 1.0 cm falls through a medium of olive oil with a viscosity of mu= 0.030 Pa-s. The density of olive oil is 1300 kg/m^3. c) An airplane wing has a dimension of about 10m. At take off speed, an airplane will have a speed of about 65 m/s. Assuming that air has the viscosity of water (a gross overestimate), what is the Reynolds number of flow over its wing?

Explanation / Answer

terminal speed of an object of density rho in medium of density rho' is given by

Vt = sqroot(4gd(rho - rho')/3Cd(rho))

where for s spherical opbject

Cd = 24*mu/rho*d*V

a. given rho = 1000 kg/m^3 = rho'

hence

Vt = 0 m/s

b. rho = 5000 kg/m^3

d = 0.01 m

mu = 0.03 Pa-s

rho' = 1300 kg/m^3

so, Cd = 24*0.03/1300*0.01*Vt = 0.0553846/Vt

hence

sqroot(Vt) = sqroot(4*9.81*0.01*(5000 - 1300)/3*0.0553846*1300)

Vt = 6.7216 m/s

c. for an airplane wing, d = 10 m

v = 65 m/s

mu = viscosity of air = viscosity of water = 8.9*10^-4 Pa s

hence

R = rho*d*V/mu = 1000*10*65/8.9*10^-4 = 730337078.6516

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