Question

In the SI system of units, dynamic viscosity of water μ at temperature T (K) can be computed from μ=A10B/(T-C), where A=2.4×10-5, B=250 K and C=140 K. (6 points) (a) Determine the dimensions of A. (b) Determine the kinematic viscosity of water at 20°C. Express your results in both SI and BG units.

Answer 1

Answer:

0.00000103149529075 m²/s

0.0103149529075 stokes

Explanation:

A = $2.4\times 10^-5$

B = 250 K

C = 140 K

T = 20°C

$\rho$ = Density of water = 998 kg/m³

Viscosity is given by

$\mu=A\times 10^{\dfrac{B}{T-C}}\\\Rightarrow \mu=2.4\times 10^{-5}\times 10^{\dfrac{250}{273.15+20-140}}\\\Rightarrow \mu=0.00102943230017\ Pas$

Kinematic viscosity is given by

$\nu=\dfrac{\mu}{\rho}\\\Rightarrow \nu=\dfrac{0.00102943230017}{998}\\\Rightarrow \nu=0.00000103149529075\ m^2/s$

The kinematic viscosity is 0.00000103149529075 m²/s

In BG units $0.00000103149529075\times 10^4=0.0103149529075\ stokes$