HomeworkSolutions_C3

# HomeworkSolutions_C3 - Problem#1 The results from the flow...

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Problem #1: The results from the flow problem of a falling film are only valid for a laminar flow. For the falling film, this flow regime can only obtained if the Reynolds number, defined by 4 Re z u ρ δ μ = is smaller or equal 20. 1. If the film liquid is water at 20 0 C (kinematic viscosity = 0.010037 cm 2 /s), what is the maximum volume flow rate per unit wall width W. 2. For Re = 10, and the wall is vertical, calculate the film thickness. 3. If one wants to choose a different coordinate system as follows: the y and z coordinates are the same, but the x coordinate is: x = 0 at the solid wall, and δ at the gas liquid interface. Show that the velocity is then given by 2 2 cos 1 2 z gx u ρδ β μδ x ⎛⎞ ⎛⎞ =− ⎜⎟ ⎜⎟ ⎝⎠ ⎝⎠ What is your comment on this choice of coordinate? Answer: 1. Maximum volume flow rate per unit wall width The volume flow rate w/ ρ per unit wall width W is related to Reynolds number as follows Re 4 w Q W ν == To obtain the laminar flow: Re =≤ 4 20 Q Thus the maximum volume flow rate for the laminar flow of the falling film Qc max ./ 20 4 0 050185 2 m s 2. Film thickness The film thickness can be calculated from equation of mass flow rate: where βρ = ⎟ = = 33 4 1 9 80665 0 009167 13 2 g w Wg gm s cm cos cos Re cos , . / .

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HomeworkSolutions_C3 - Problem#1 The results from the flow...

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