A long wire of length L to be coated moves at a velocity V0 through a long cylindrical die filled with an incompressible fluid (density ρ and kinematic viscosity μ). Using cylindrical co-ordinates (r-z) and assuming that pressure is uniform (i.e. dp/dz = 0 and dp/dr = 0). Assume that the flow is steady, laminar and fully developed (neglect any end effects). Clearly 4 show all steps, starting from the Navier-Stokes equations, simplifying them, specify proper boundary conditions. (a) Find velocity vz as a function of radius inside the die. Use continuity, and momentum equations and clearly show which terms vanish (and why). (b) Also find the force F required to pull the wire in terms of the given known parameters such as V0, L, μ, R1, R2 etc.
A long wire of length L to be coated moves at a velocity V0 through a long cylindrical die filled with an incompressible fluid (density ρ and kinematic viscosity μ). Using cylindrical co-ordinates (r-z) and assuming that pressure is uniform (i.e. dp/dz = 0 and dp/dr = 0). Assume that the flow is steady, laminar and fully developed (neglect any end effects). Clearly 4 show all steps, starting from the Navier-Stokes equations, simplifying them, specify proper boundary conditions. (a) Find velocity vz as a function of radius inside the die. Use continuity, and momentum equations and clearly show which terms vanish (and why). (b) Also find the force F required to pull the wire in terms of the given known parameters such as V0, L, μ, R1, R2 etc.
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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A long wire of length L to be coated moves at a velocity V0 through a long cylindrical die
filled with an incompressible fluid (density ρ and kinematic viscosity μ). Using cylindrical
co-ordinates (r-z) and assuming that pressure is uniform (i.e. dp/dz = 0 and dp/dr = 0).
Assume that the flow is steady, laminar and fully developed (neglect any end effects). Clearly
4
filled with an incompressible fluid (density ρ and kinematic viscosity μ). Using cylindrical
co-ordinates (r-z) and assuming that pressure is uniform (i.e. dp/dz = 0 and dp/dr = 0).
Assume that the flow is steady, laminar and fully developed (neglect any end effects). Clearly
4
show all steps, starting from the Navier-Stokes equations, simplifying them, specify proper
boundary conditions.
(a) Find velocity vz as a function of radius inside the die. Use continuity, and momentum
equations and clearly show which terms vanish (and why).
(b) Also find the force F required to pull the wire in terms of the given known parameters
such as V0, L, μ, R1, R2 etc.
boundary conditions.
(a) Find velocity vz as a function of radius inside the die. Use continuity, and momentum
equations and clearly show which terms vanish (and why).
(b) Also find the force F required to pull the wire in terms of the given known parameters
such as V0, L, μ, R1, R2 etc.
Transcribed Image Text:Z
R₂
R₁
Incompressible fluid
Vo
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