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HomeworkSolutions_C6

# HomeworkSolutions_C6 - Problem#1 A fluid with viscosity...

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Problem #1 : A fluid with viscosity 18.3 cp and density 1.32 g/cm3 is flowing in a long horizontal tube of radius 1.05 in (2.67 cm). For what pressure gradient will the flow become turbulent? Answer: The minimum value of Re 4 /( ) wD π µ = needed to produce turbulent flow in a long, smooth tube is about 2100. Poiseuille’s law holds until this critical Re value, giving ( ) 4 0 critical Re<Re 8 L PPR w L πρ = Hence, the pressure gradient needed to initiate the laminar-turbulent transition is () 2 5 44 3 88 4 Re 2100 1.1 10 Pa/km 4 critical dp w D dz R R R µµπ ρ == = Problem #2: Water is flowing through a long, straight, level run of smooth 6.00 in inner diameter pipe, at temperature 68 0 F. The pressure gradient along the length of the pipe is 1 psi/mile. (a) Determine the wall shear stress τ 0 in Pa? (b) Assume the flow to be turbulent and determine the radial distance from the pipe wall at which , using Fig. 5.5-3 in the textbook (second edition), also available in the lecture note. Pay attention at the definition of dimensionless variables.

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HomeworkSolutions_C6 - Problem#1 A fluid with viscosity...

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