3. The velocity, u (m/s), of air flowing across a flat surface is measured at several distances y (m) away from the surface. (Think about a fan blowing air over a table and measuring the air velocity at several heights above the table.) Use Newton's viscosity law du dy τιμ· and the second order centered first finite difference method to determine the shear stress, T (N/m²), at distances y = 0.006, 0.012, and 0.018 m. Assume a constant value for the dynamic viscosity μ = 1.8 x 10-5Ns/m². How do you think your answers would change if you use higher order finite differences? y (m) 0.000 0.00200 0.00600 0.0120 0.0180 0.0240 u (m/s) 0.000 0.067 2.291 5.047 9.041 0.572
3. The velocity, u (m/s), of air flowing across a flat surface is measured at several distances y (m) away from the surface. (Think about a fan blowing air over a table and measuring the air velocity at several heights above the table.) Use Newton's viscosity law du dy τιμ· and the second order centered first finite difference method to determine the shear stress, T (N/m²), at distances y = 0.006, 0.012, and 0.018 m. Assume a constant value for the dynamic viscosity μ = 1.8 x 10-5Ns/m². How do you think your answers would change if you use higher order finite differences? y (m) 0.000 0.00200 0.00600 0.0120 0.0180 0.0240 u (m/s) 0.000 0.067 2.291 5.047 9.041 0.572
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
Show your work for one distance and for the others just fill in the table
Transcribed Image Text:3. The velocity, u (m/s), of air flowing across a flat surface is measured at several distances y (m) away
from the surface. (Think about a fan blowing air over a table and measuring the air velocity at several
heights above the table.) Use Newton's viscosity law
du
dy
τ= μ·
and the second order centered first finite difference method to determine the shear stress, T (N/m²),
at distances y = 0.006, 0.012, and 0.018 m. Assume a constant value for the dynamic viscosity
μ = 1.8 x 10-5Ns/m². How do you think your answers would change if you use higher order finite
differences?
y (m) 0.000 0.00200 0.00600 0.0120 0.0180 0.0240
u (m/s) 0.000 0.067 0.572 2.291 5.047 9.041
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