Let f, g: [0, 1] → R3 be nonintersecting closed curves. Define the linking number l (f, g) of and g by (cf. Problem 4-34
Answer to relevant QuestionsGeneralize the divergence theorem to the case of an -manifold with boundary in Rn.For the triangular element in Fig P1.3, show that a tilted free liquid surface, in contact with an atmosphere at pressure pa, must undergo shear stress and hence begin to flow. The Stokes-Oseen formula  for drag on a sphere at low velocity V is: F = 3πμ DV + 9π/16pV2D2 Where D = sphere diameter, μ = viscosity, and ρ = density. Is the formula homogeneous?(“*” means “difficult”—not just a plug-and-chug, that is) For small particles at low velocities, the first (linear) term in Stokes’ drag law, Prob. 1.10, is dominant, hence F = KV, where K is a constant. Suppose ...Wet air, at 100% relative humidity, is at 40°C and 1 atm. Using Dalton’s law of partial pressures, compute the density of this wet air and compare with dry air.
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