Download Solve three (any) of the following problems: Problem 1

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 (M L−1 T −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 F d depends on the fluid
density ρ, the fluid viscosity µ ([µ] = M L −1 T −1 ), the radius of the sphere r, and the speed of the
sphere v. Use dimensional analysis to find a general form for F d .
Problem 3
Find the volume flow rate W (L3 T −1 ) of blood flowing in an artery as a function of the pressure
drop per unit length u (M L−2 T −2 ), the radius r (L) of artery, the blood density ρ (M L −3 ), the
blood viscosity µ (M L−1 T −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 (M L2 T −3 ) of the windmill. Assume that P is a function of the density of the air ρ
(M L−3 ), viscosity of the air µ (M L−1 T −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 ), diameter δ (L), initial angle θ with horizon (dimensionless), density of the air ρ (M L −3 ), viscosity µ
(M L−1 T −1 ), gravity g (LT −2 ), and speed of sound s of the air s (LT −1 ). Use dimensional analysis
to find F .
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