Fluid Mechanics Part 1: Newton's Law of Viscosity

This video introduces fundamental concepts of fluid mechanics such as density, specific volume, specific gravity, bulk modulus, compressibility, dynamic viscosity, kinematic viscosity, and Newton's Law of Viscosity. Non Newtonian Fluids are also discussed.
Transcript
The field of Fluid mechanics is concerned with both fluid dynamics and hydrostatics. Fluid Dynamics looks at fluids in motion and studies the forces produced by the fluid on objects that are immersed within it. In contrast, Hydrostatics deals with fluids at rest in equilibrium.
Fluids can be categorized as either a gas or liquid. Gases expand to fill their containers yet are easily compressed. Liquids take the shape of their container typically leaving a free surface and require effort to compress. Some important properties of fluids are its density (ro=m/volume), specific volume (v=1/ro), specific gravity (s=ro/row), Bulk Modulus (K=dp/dV/V), compressibility (Beta=1/K), viscosity (mu), and kinematic viscosity (nu=mu/ro). These properties are functions of variables such as Temperature (T) and Pressure (P). Whether the fluid under consideration is a gas or liquid also affects the temperature and pressure dependence of its properties since the interactions occurring at the molecular level are different for a gas and liquid.
Density is defined as mass per unit volume. Here "m" is mass with units of kg, "V" is volume with units of m^3, and "rho" is density with units of kg/m^3. As the mass in a unit volume increases so does its density. A few examples of different material densities are that of air with a density of 1.29 kg/m^3, water with a density of 999.8 kg/m^3, and lead with a density of 11,340 kg/m^3. These measurements for density were taken at standard temperature and pressure or STP for short. At STP the temperature and pressure of the surrounding environment are 273.15 K or 0 degrees Celsius for temperature and 101.3 kPa or 1 atm for pressure. What the temperature and pressure are is important because density is actually a function of both.
Take water for example. Water is very unique because its density is a complex function of temperature. If we hold pressure constant at 1 atmosphere we see that it has a maximum density at 0 degrees Celsius. At very low temperatures below 0 degrees Celsius, water freezes into ice and its density decreases the lower its temperature gets. For temperatures greater than 0 degrees Celsius as the temperature increases the density of water decreases as well. In general the density of water is insensitive to changes in temperature. There is only about a 5% difference in its density from 0 degrees Celsius to 100 degrees Celsius.
The temperature dependence of density for air is less complicated. As temperature increases density decreases. However, the decrease in density is much more dramatic for air than it is for water. There is a 21% decrease in density going from -25 degrees Celsius to 45 degrees Celsius. Here the difference in the temperature dependence of density for a gas and liquid is evident. The density for gasses is much more sensitive to temperature than for liquids.
Specific volume is the reciprocal of density. Here "nu" is specific volume. It has SI units of m^3/kg. Providing a new variable for the reciprocal of density will be useful in the future because it reduces the complexity of formulas.
There are fluids however, that do not have a linear relationship between shear stress and velocity gradient and are called non-Newtonian fluids. These non-Newtonian fluids have their own constitutive relationships. The first of these is called an Inviscid Fluid. Inviscid fluids are fluids that experience no shear stresses despite having velocity gradients. They are also known as superfluids. An example of an inviscid fluid is liquid helium once it is cooled to 2.17 K at 1 atmosphere. Another non-Newtonian fluid is a Bingham Plastic. Bingham Plastics do not begin to flow until the shear stress applied to it equals the yield stress, tau not. Once the yield stress is reached the relation between shear stress and velocity gradient is linear. The last example is called a Pseudo Plastic Fluid. The shear stress to velocity gradient relationship for a Pseudo Plastic Fluid is non-linear. As the shear stress applied to the fluid increases the viscosity of the fluid decreases. This is described as shear thinning.
Now that we know what dynamic viscosity is let us define Kinematic Viscosity. Kinematic viscosity is the ratio of dynamic viscosity to density with SI units of meters squared per second. Here, "nu" is kinematic viscosity. Kinematic viscosity is useful since this ratio appears frequently in equations.
Lets see how we can use Newtons Law of Viscosity to find the shear stress throughout a fluid in a couette flow. Water, a Newtonian Fluid, at 20 degrees Celsius is placed in between two flat plates a distance h = 0.1 m apart. Since the viscosity of water has been previously..

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Is there going to be a part 2?