hw2_001

# hw2_001 - from a pipe in the space lled with the same...

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ME220A 1 Homework 2 (due at 12:30 pm on October 31, 2011) Problem 1. Using the ideas from kinetic theory of gases, estimate dynamic viscosity of the ideal gas in terms of (1) mean free path, number of molecules per unit volume, mass of a molecule, mean velocity of molecules, and (2) eﬀective collision area, mass of a molecule, Boltzmann constant, and temperature. Problem 2. Derive Bernoulli’s equation and its analogue for potential unsteady ﬂow. Discuss the limits of applicability. Use §§ 5 and 9 of ref. 3. Problem 3. Under the inﬂuence of surface tension σ , a liquid rises to a height H in a glass tube of diameter D . How does H depend on the parameters of the problem? Use dimensional analysis to reveal this dependence. Problem 4. Construct the solution for inviscid and viscous plane stagnation-point ﬂow, cf. ﬁgure 1. Figure 1: 2D ﬂow near a stagnation point. Problem 5. Using aﬃne transforms, ﬁnd the solution for a submerged jet (liquid ejected

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Unformatted text preview: from a pipe in the space lled with the same liquid, cf. gure 2) in a half-plane x > 0,- < y < + : uu x + v u y = u yy , u x + v y = 0 , | u | , y . Here ( u,v ) is the velocity eld with ( x,y )-components, respectively. ME220A 2 u v Figure 2: Submerged jet. Problem 6. Using ane transforms, nd the solution for an axisymmetric drop spreading on a at surface, cf. gure 3, described by the following equation h t = 2 3 r r rh 3 h r , with the boundary condition h = 0 at r = and a mass conservation condition, i.e. mass of the drop should be constant. Make use of a physically relevant conservation law. Determine short and long-time behavior of the solution. h(r,t) r h(r,t) Figure 3: Spreading drop....
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## This note was uploaded on 12/29/2011 for the course ME 152 taught by Professor Krechet during the Fall '10 term at UCSB.

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hw2_001 - from a pipe in the space lled with the same...

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