Dynamic viscosity (u) relates the deformation rate of a fluid in response to a shear stress. Common approximations of the viscosity of gases as a function of temperature are: (i) power law μ/Ho (T/TO)" and (ii) Sutherland law: μ/o (T/T₁) ³/² (To+S)/(T+S), where n and S are constants, and μ is the reference viscosity at a reference temperature To; for air, n≈ 0.7, S≈ 110 K, and μ 1.71 10-5N s/m² at To = 273.16 K. For liquids, a common approximation is given by In(μ/μ)~ a + b(To/T) + c(To/T)2, with a, b and c constants; for water at To 273.16 K, Ho 0.001792 kg/(m-s), a≈ -1.94, b-4.80 and c = 6.74. a. ) Using the different approximations provided above, produce one plot (by means of the computational tool of your choice, such as gnuplot, Matlab, Microsoft Excel, LibreOffice Calc, etc.) that shows /Ho as a function of T [K] for air and water in the temperature range T€ [250, 500] K. Use the same reference temperature To = 273.16 K for both fluids, and annotate the plot clearly (with axis labels, legend). b. Which of the two approximations for air provides a better estimate for μ at T = 375 K? Note: Use the following experimental data points for your assessment: i. Hep (T = 75 °C) = 2.076-10-5 N-s/m² ii. Hep (T = 200°C) = 2.573-10-5 N s/m² C. Comparing air and water, what is the primary physical difference between these two fluids in terms of the dynamic viscosity as a function of temperature?

Structural Analysis

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ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

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Dynamic viscosity (u) relates the deformation rate of a fluid in response to a shear stress. Common
approximations of the viscosity of gases as a function of temperature are: (i) power law μ/μ₁~
(T/To)" and (ii) Sutherland law: μ/μ (T/T₁)³/² (To+S)/(T+S), where n and S are constants,
and μ is the reference viscosity at a reference temperature To; for air, n≈ 0.7, S≈ 110 K, and μ₁ ≈
1.71-10-5N s/m² at To = 273.16 K. For liquids, a common approximation is given by In(μ/μo)~
a + b(To/T) + c(To/T)², with a, b and c constants; for water at To 273.16 K, Ho
0.001792 kg/(ms), a ≈ -1.94, b≈ -4.80 and c≈ 6.74.
a.
) Using the different approximations provided above, produce one plot (by means
of the computational tool of your choice, such as gnuplot, Matlab, Microsoft Excel,
LibreOffice Calc, etc.) that shows μ/μo as a function of T [K] for air and water in the
temperature range T€ [250, 500] K. Use the same reference temperature To = 273.16 K
for both fluids, and annotate the plot clearly (with axis labels, legend).
b.
Which of the two approximations for air provides a better estimate for μ at T =
375 K? Note: Use the following experimental data points for your assessment:
C.
d.
e.
air
i. Hep (T = 75 °C) = 2.076-10-5 N-s/m²
,air
ii. Hep (T = 200°C) = 2.573-10-5 N-s/m²
Comparing air and water, what is the primary physical difference between these
two fluids in terms of the dynamic viscosity as a function of temperature?
For the entire temperature range plotted, which fluid has higher viscosity?
Compare the values of viscosity at T = 300 K.
Regarding the μ/μo vs. T curves you produced, comment on the validity of this
chart. Are there any physical limitations not accounted for here with these
approximations?

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a) Consider a power law for the viscosity of the gases given:

$\frac{μ}{μ_{o}} = {(\frac{T}{T_{o}})}^{n} \frac{μ}{μ_{o}} = {(\frac{T}{273.16})}^{0.7} \frac{μ}{μ_{o}} = 0.01970 {(T)}^{0.7}$

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