1.7 Newtons law of viscosity.

It states that the shear stress of  a fluid element in a fluid layer which is flowing with some velocity is directly proportional to the rate of shear strain. The equation we have already seen in viscosity concept is the one proposed by newton. It is given as

And if the constant of proportionality is introduced then the equation becomes

Where, μ is the constant of proportionality and is called as the coefficient of dynamic viscosity or viscosity.
τ is the shear stress and
du/dy is the rate of shear strain 

Types of fluids based on newtons law

1. Newtonian Fluids
2. Non-Newtonian Fluids

1.Newtonian Fluids

Fluids which behave according to the equation of Newtons law of viscosity are called as Newtonian Fluids. 

2. Non Newtonian Fluids

Fluids which do not satisfy the newtons law of viscosity or the newtons equation on viscosity are called as non-newtonian fluids.

Note:

1. All real fluids are Non Newtonian Fluids.
2. All ideal fluids accept the Newtons law of viscosity and are called as Newtonian fluids.
3. Water, thin motor oil are considered to be partially Newtonain Fluids.

Example Problem:
This is an example problem and remember that the values in the real life will be in the order of exponential. All the values given here are for the sake of beginners.
Consider a fluid flowing in a river. If the shear stress is  equal to 10N/m² distance between the fluid layers is 2m. Fluid is flowing with a velocity of 5m/s. 

1. Find whether the fluid is Newtoinain Fluid or non Newtonian fluid if the coefficient of dynamic viscosity is 40N.s/m².
2. Find the viscosity of the fluid if it were a Newtonian fluid.

Sol: 

1.We know from the equation that   

Therefore we can observe that

 10 ≠ 40x5/2

Therefore the given fluid is not a Newtonian Fluid.

2.If it was a Newtonian Fluid then from the above equation it can be found that 

μ = 4N.s/m².

References:

http://en.wikipedia.org/wiki/Non-Newtonian_fluid

http://en.wikipedia.org/wiki/Newtonian_fluid

http://www.enchantedlearning.com/math/symbols/