Industries involved in viscosity measurement [27, 36] continue to use the CGS system of units, since centimeters and grams yield convenient numbers for many fluids. The absolute viscosity (μ) unit is the poise, named after J. L. M. Poiseuille, a French physician who in 1840 performed pioneering experiments on water flow in pipes; 1 poise = 1 g/(cm-s).

Question

Industries involved in viscosity measurement [27, 36] continue to use the CGS system of
units, since centimeters and grams yield convenient numbers for many fluids. The absolute
viscosity [latex](\mu)[/latex] unit is the poise, named after J. L. M. Poiseuille, a French physician who in
1840 performed pioneering experiments on water flow in pipes; 1 poise = 1 g/(cm-s). The kinematic viscosity [latex]( u)[/latex] unit is the stokes, named after G. G. Stokes, a British physicist who in 1845 helped develop the basic partial differential equations of fluid momentum; [latex]1 stokes=1 cm^2 /s[/latex]. Water at 20°C has [latex]\mu ≈0.01[/latex] poise and also [latex] u≈0.01[/latex] stokes. Express these results in (a) SI and (b) BG units.

Accepted Answer

• Approach: Systematically change grams to kg or slugs and change centimeters to meters or feet.
• Property values: Given [latex]\mu = 0.01 g/(cm-s)[/latex] and [latex] u=0.01 cm^2[/latex]

• Solution steps: (a) For conversion to SI units
[latex]\mu = 0.01 \frac {g} {cm.s} =0.01 \frac{g(1 kg/1000g)}{cm(0.01 m/cm)s} =0.001\frac{kg}{m.s} u =0.01\frac {cm^2} {s}= 0.01 \frac{cm^2(0.01m/cm)^2}{s}[/latex]
• For conversion to BG units
[latex]\mu = 0.01 \frac {g} {cm.s} = 0.01 \frac {g(1 kg/1000 g)(1 slug/14.5939 kg)} {(0.01 m/cm)(1 ft/0.3048 m)s} = 0.0000209 \frac {slug} {ft .s}[/latex]

[latex] u=0.01\frac {cm^2}{s}= 0.01 \frac{cm^2(0.01m/cm)^2(1 ft/0.3048 m)^2}{s} = 0.0000108 \frac {ft^2}{s}[/latex] Ans. (b)
• Comments: This was a laborious conversion that could have been shortened by using
the direct viscosity conversion factors in App. C. For example, [latex]\mu_{BG}=\mu_{SI}/47.88[/latex].

Question 1.2: Industries involved in viscosity measurement [27, 36] contin...

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