3.2.1. Newton's Laws of Viscosities

Now let us go to the very interesting concept, the Newton's laws of viscosities, okay, which is very simplified, simple common laws of viscosity which we use for solving many of the problems in laminar and also approximate for other flow conditions.

This chunk introduces Newton's laws of viscosity, which are fundamental principles used to understand how fluids behave when they move. In fluid mechanics, viscosity describes a fluid's resistance to flow. These laws help us analyze various fluid flow scenarios, particularly in laminar flow conditions, which are smooth and orderly.

Think of viscosity like the thickness of honey versus water. Honey flows more slowly due to its higher viscosity, illustrating the concept that different fluids exhibit different resistance to flow.

As we know it that whenever we have the fluid flow conditions, we will have the no-slip conditions. That means, at these locations I will have the velocity zero. At these locations the contact of the fluid particles on the solid surface will give a velocity equal to the velocity of the plate.

No-slip conditions refer to the scenario where a fluid in contact with a solid surface does not slip. At the interface, the fluid's velocity matches that of the surface. This means that the fluid right at the boundary has a velocity of zero, while fluid just above it may be flowing at a different velocity. This gradient is crucial for understanding how forces are transmitted in fluids.

Imagine rubbing your hands on a smooth ice surface. The ice doesn't move, and neither do your hands at the point of contact. The point where your hands touch the ice is like the fluid at the solid boundary, illustrating the no-slip condition.

And shear stress will develop at this interfaces level and many of the studies the experimentally establish that this shear stress will have a directly proportional to the velocity gradient okay.

Shear stress refers to the force per unit area exerted by the fluid as it flows and interacts with other fluid layers or surfaces. The speed difference between layers (velocity gradient) leads to the development of shear stress, which is proportional to how quickly one layer of fluid moves relative to another.

Imagine spreading butter on bread. The harder you push the knife (shear stress), the easier it is to spread the butter. If the butter was frozen (high viscosity), it would be more difficult to spread, just as fluids can resist flow differently based on their viscosity.

But it has a directly proportionality quantity. And the proportionality is known as the coefficient of viscosity or dynamic of viscosity.

The coefficient of viscosity quantifies a fluid's resistance to flow and shear. It indicates how much shear stress is generated for a given velocity gradient. Different fluids have different coefficients of viscosity based on their molecular structure and interactions.

Imagine a packed jar of marbles versus a jar of jelly beans. The marbles can move easily past each other with little resistance (low viscosity), while the jelly beans stick together and resist motion more (high viscosity). The coefficient of viscosity helps in quantifying this difference.

That means one poise is 1g/cm.s. That is what we consider it the poise is in a CGS systems unit of the coefficient of viscosity or dynamic of viscosity.

Units of viscosity, such as poise, help quantify how a fluid flows. In the CGS system, one poise is defined as the viscosity of a fluid that can exert a shear stress of one dyne per square centimeter with a velocity gradient of one centimeter per second.

Using different units of viscosity is like measuring temperature in Celsius versus Fahrenheit. While both serve the same purpose of measuring temperature, knowing the units helps us understand how viscous a fluid is in different contexts.

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