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# Fluids

• • Contributed by Michael Fowler
• Beams Professor (Physics) at University of Virginia

• 1.1: Hydrostatics
• 1.2: Boyle's Law and the Law of Atmospheres
We’ve discussed the concept of pressure in the previous lecture, introduced units of pressure (Newtons per square meter, or Pascals, and the more familiar pounds per square inch) and noted that a fluid in a container exerts pressure on all the walls, vertical as well as horizontal—if a bit of wall is removed, the fluid will squirt out.
• 1.3: The Bernoulli Effect
Suppose air is being pumped down a smooth round tube, which has a constant diameter except for a section in the middle where the tube narrows down to half the diameter, then widens out again. Assume all the changes in diameter take place smoothly, and the air flows steadily down the tube, with no eddies or turbulence.
• 1.4: Viscosity
Viscosity is, essentially, fluid friction. Like friction between moving solids, viscosity transforms kinetic energy of (macroscopic) motion into heat energy. Heat is energy of random motion at the molecular level, so to have any understanding of how this energy transfer takes place, it is essential to have some picture, however crude, of solids and/or liquids sliding past each other as seen on the molecular scale.
• 1.5: Calculating Viscous Flow
In this lecture, we’ll derive the velocity distribution for two examples of laminar flow. First we’ll consider a wide river, by which we mean wide compared with its depth (which we take to be uniform) and we ignore the more complicated flow pattern near the banks. Our second example is smooth flow down a circular pipe. For the wide river, the water flow can be thought of as being in horizontal “sheets”, so all the water at the same depth is moving at the same velocity.
• 1.6: Using Dimensions
Some of the most interesting results of hydrodynamics, such as the sixteen-fold increase in flow down a pipe on doubling the radius, can actually be found without doing any calculations, just from dimensional considerations.
• 1.7: Stokes’ Law
We’ve seen how viscosity acts as a frictional brake on the rate at which water flows through a pipe, let us now examine its frictional effect on an object falling through a viscous medium.
• 1.8: Inertial Drag Force and the Reynold's Number

Thumbnail: Fog (water particle) wind tunnel visualization of a NACA 4412 airfoil at a low-speed flow (Re=20.000) (CC SA-BY 3.0; Georgepehli).