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150A+Section+Handout+Week+10

150A+Section+Handout+Week+10 - R1 y x

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z U θ α y x air liquid g < = > R 1 R 2 U Ω ChemE 150A Section – Week 10 Problem 1:
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Quiz – ungraded (answers will be on bSpace) (1) For creeping flow past a sphere shown below, write down the r and θ components of v = - Uez In spherical coordinates, ____ ≤ θ ≤ ____ and ____ ≤ φ ≤ ____ (2) Given the following differential equation for h : ∂ ∂ + ∂∂ + ∂ ∂ = h t ση xh3 3h x3 U h x 0 where σ , η , and U are constants, we would need ____ boundary conditions in the ____-direction and ____ ________ condition for ________ in order to solve. Assuming R and H to be the characteristic length scales for x and h , respectively, and that the second and third terms in the above differential equation are of the same order of magnitude, show that H must scale as RCa 1/3 , where Ca = ηU / σ is the capillary number. (3) Fill in the blanks or circle the correct items regarding the falling-film geometry shown below. ∂ ∂ p x = _____ , ∂ ∂ p y 0 ∂℘∂ x = ∂∂ - x ρ ____ g x = _______ , g y = _______ Write the simplified form of the x-component of the Navier-Stokes equations for this geometry.
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