A long, round wire with radius a is pulled at a constant speed Uo through a...
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A long, round wire with radius a is pulled at a constant speed Uo through a long, round tube of radius b along its centerline. The tube is filled with a viscous fluid with constant density p and viscosity μ. Assume that the flow is laminar and fully developed with d = 0 (where z is the coordinate along the tube axis), and that uz = uz (r) only. (a) (b) (c) Find the velocity profile u₂ (r). What is the force per unit length required to maintain the motion of the wire? Consider now the situation where b→ ∞ and the fluid and wire are initially at rest. At time t = 0, the wire is impulsively moved to the right at a constant velocity Uo. Write out the appropriate equation of motion for this case, as well as the necessary boundary and initial conditions. Can you apply a similarity solution to solve this problem? Why or why not? 26 ρ, μ 2a Uo A long, round wire with radius a is pulled at a constant speed Uo through a long, round tube of radius b along its centerline. The tube is filled with a viscous fluid with constant density p and viscosity μ. Assume that the flow is laminar and fully developed with d = 0 (where z is the coordinate along the tube axis), and that uz = uz (r) only. (a) (b) (c) Find the velocity profile u₂ (r). What is the force per unit length required to maintain the motion of the wire? Consider now the situation where b→ ∞ and the fluid and wire are initially at rest. At time t = 0, the wire is impulsively moved to the right at a constant velocity Uo. Write out the appropriate equation of motion for this case, as well as the necessary boundary and initial conditions. Can you apply a similarity solution to solve this problem? Why or why not? 26 ρ, μ 2a Uo
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Related Book For
Numerical Methods For Engineers
ISBN: 9780071244299
5th Edition
Authors: Steven C. Chapra, Raymond P. Canale
Posted Date:
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