Solve three (any) of the following problems:
Problem 1
Find the force F(M LT −2) opposing the fall of a raindrop through air in terms of viscosity
µ(ML−1T−1), velocity v(LT −1), and the diameter r(L) of the drop. Assume that density is
neglected.
Problem 2
Assume that for a sphere traveling through a liquid, the drag force Fddepends on the fluid
density ρ, the fluid viscosity µ([µ] = M L−1T−1), the radius of the sphere r, and the speed of the
sphere v. Use dimensional analysis to find a general form for Fd.
Problem 3
Find the volume flow rate W(L3T−1) of blood flowing in an artery as a function of the pressure
drop per unit length u(M L−2T−2), the radius r(L) of artery, the blood density ρ(ML−3), the
blood viscosity µ(M L−1T−1). Use dimensional analysis.
Problem 4
A windmill is rotated by air flow to produce power to pump water. It is desired to find the
power output P(ML2T−3) of the windmill. Assume that Pis a function of the density of the air ρ
(ML−3), viscosity of the air µ(M L−1T−1), diameter of the windmill d(L), wind speed v(LT −1),
and the rotational speed of the windmill ω(T−1). Using dimensional analysis find a relationship
for P.
Problem 5
The lift force F(M LT −2) on a missile depends on its length r(L), velocity v(LT −1), diam-
eter δ(L), initial angle θwith horizon (dimensionless), density of the air ρ(M L−3), viscosity µ
(ML−1T−1), gravity g(LT −2), and speed of sound sof the air s(LT −1). Use dimensional analysis
to find F.
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