Problem The distribution of the x-component of the velocity u of a fluid near a flat surface is measured as a function of the distance y from the surface: Y(m) U (m/s) 0.002 0.00618 0.004 0.006 0.011756 0.01618 The shear stress in the fluid is described by Newton's equation: ди нах 0.008 0.019021 Txy = μ- where μ is the coefficient of dynamic viscosity. The viscosity can be thought of as a measure of the internal friction within the fluid. Fluids that obey Newton's constitutive equation are called Newtonian fluids. Calculate the shear stress at y=0 using: (i) The two-point forward (ii) (ii) the three point forward approximations for the derivative. Take μ=0.002 N-s/m² u(y) Txy
Problem The distribution of the x-component of the velocity u of a fluid near a flat surface is measured as a function of the distance y from the surface: Y(m) U (m/s) 0.002 0.00618 0.004 0.006 0.011756 0.01618 The shear stress in the fluid is described by Newton's equation: ди нах 0.008 0.019021 Txy = μ- where μ is the coefficient of dynamic viscosity. The viscosity can be thought of as a measure of the internal friction within the fluid. Fluids that obey Newton's constitutive equation are called Newtonian fluids. Calculate the shear stress at y=0 using: (i) The two-point forward (ii) (ii) the three point forward approximations for the derivative. Take μ=0.002 N-s/m² u(y) Txy
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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Transcribed Image Text:Problem
The distribution of the x-component of the velocity u of a fluid near a flat
surface is measured as a function of the distance y from the surface:
Y(m)
U (m/s)
0
0
0.002
0.00618
0.004
0.006
0.011756 0.01618
0.008
0.019021
The shear stress in the fluid is described by Newton's equation:
ди
Txy = μax
y
where u is the coefficient of dynamic viscosity. The viscosity can be
thought of as a measure of the internal friction within the fluid. Fluids that
obey Newton's constitutive equation are called Newtonian fluids. Calculate
the shear stress at y=0 using:
(i) The two-point forward
(ii) (ii) the three point forward approximations for the derivative. Take
μ=0.002 N-s/m²
u(y)
Txy
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