Quiz2Soln

Quiz2Soln - ECM 005 Quiz 3 Solutions D.M. Lavenson February...

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ECM 005 Quiz 3 Solutions D.M. Lavenson February 10, 2011 1 Problem 1 1.1 Part A We are examining Brinkman’s equation in this problem, given as μ d 2 v dx 2 - μ κ v - Δ P L = 0 , (1) where v is the velocity, x is the position, or distance, along which the fluid velocity is directed (direction of fluid motion), μ is the fluid viscosity, κ is the porous membrane permeability through which the fluid flows, L is the length across which the pressure drop is measured, and Δ P is the pressure difference across the length L . Below in table 1 are the dimensions (and units) of the variables requested. Recall that dimensions are NOT units, Force and Pressure are not dimensions, and that x does indeed have dimensions (of length). The legend for the primary dimensions in the table is as follows: M = mass, L = length, t = time, Θ = temperature. 1.2 Part B Now we must determine the SI units of the permeability, κ . We can do this by realizing that in the Brinkman’s equation, all separate terms must have the same units/dimensions
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Quiz2Soln - ECM 005 Quiz 3 Solutions D.M. Lavenson February...

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