Answer to Question #130090 in Mechanics | Relativity for Ariyo Emmanuel

Question

1. What is a Newtonian fluid? Is water a Newtonian fluid?
2. How does viscousities of (a) liquids and (b) gases vary with
temperature?

Answer 1

1. Newtonian liquid is a liquid that is characterized by a linear connection between shear stress and velocity gradient. This makes velocity to be distributed as following:

Aspect ratio between shear stress and velocity gradient is viscosity. Newtonian liquid is a ideal model. In real life it is hard to find truly Newtonian liquids. In most cases, water with a good accuracy can be considered as a Newtonian liquid.

2. (a) liquids: $\mu = A e^{\frac{B}{T}}$ , A,B = const.

(b) gases: from elementary calculations using kinetic theory of gases $\mu \propto T^{1/2}$

from more precise theory (Chapman–Enskog theory): $\mu = \mu_0 (\frac{T}{T_0})^{3/2} \frac{T_0+C}{T+C}$