Formulas for Viscosity

A widely used formula for the calculation of viscosity of gases is the Sutherland Equation given by

$$\mu = {{b T^{3/2}} \over {T+S}}$$ (1.8)

where b and S are constants and T is temperature expressed in Eq. 1.8 . For air $b = 1.458\times 10^{-6}{{kg} \over {m\cdot s\cdot K^{1/2}}}$ and $S = 110.4 K$.

Power Law is another approximation to calculate viscosity and is given by

$${\mu \over \mu_0} = { {\left({T \over T_0}\right)}^{0.7}}$$ (1.9)

where $\mu_0$ is the value of viscosity at a reference temperature $T_0$ ,which could be 273K.

An empirical fit for the viscosity of liquids is

$$\ln {\mu \over \mu_0} = a + b \left(T_0 \over T \right) +c \left(T_0 \over T \right)^2$$ (1.10)

For water, $T_0$ = 273.16K, $\mu_0$ = 0.001792 kg/(m.s), a=-1.94, b = -4.80 and c = 6.74.

Another empirical formula for liquids is the Andrade equation namely,

$$\mu = D \exp{B/T}$$ (1.11)

where $B$ and $D$ are constants and $T$ is the temperature in K

(c) Aerospace, Mechanical & Mechatronic Engg. 2005
University of Sydney