$$\require{cancel}$$

# 14: Fluid Mechanics

Picture yourself walking along a beach on the eastern shore of the United States. The air smells of sea salt and the sun warms your body. Suddenly, an alert appears on your cell phone. A tropical depression has formed into a hurricane. Atmospheric pressure has fallen to nearly 15% below average. As a result, forecasters expect torrential rainfall, winds in excess of 100 mph, and millions of dollars in damage. As you prepare to evacuate, you wonder: How can such a small drop in pressure lead to such a severe change in the weather?

Pressure is a physical phenomenon that is responsible for much more than just the weather. Changes in pressure cause ears to “pop” during takeoff in an airplane. Changes in pressure can also cause scuba divers to suffer a sometimes fatal disorder known as the “bends,” which occurs when nitrogen dissolved in the water of the body at extreme depths returns to a gaseous state in the body as the diver surfaces. Pressure lies at the heart of the phenomena called buoyancy, which causes hot air balloons to rise and ships to float. Before we can fully understand the role that pressure plays in these phenomena, we need to discuss the states of matter and the concept of density.

• 14.1: Prelude to Fluid Mechanics
Picture yourself walking along a beach on the eastern shore of the United States. The air smells of sea salt and the sun warms your body. Suddenly, an alert appears on your cell phone. A tropical depression has formed into a hurricane. Atmospheric pressure has fallen to nearly 15% below average. As a result, forecasters expect torrential rainfall, winds in excess of 100 mph, and millions of dollars in damage.
• 14.2: Fluids, Density, and Pressure (Part 1)
A fluid is a state of matter that yields to sideways or shearing forces. Liquids and gases are both fluids. Fluid statics is the physics of stationary fluids. Density is the mass per unit volume of a substance or object while pressure is the force per unit perpendicular area over which the force is applied. Pressure due to the weight of a liquid of constant density is given by the product of the liquid's depth, density, and acceleration due to gravity.
• 14.3: Fluids, Density, and Pressure (Part 2)
Pressure is defined for all states of matter, but it is particularly important when discussing fluids. An important characteristic of fluids is that there is no significant resistance to the component of a force applied parallel to the surface of a fluid. The molecules of the fluid simply flow to accommodate the horizontal force. A force applied perpendicular to the surface compresses or expands the fluid.
• 14.4: Measuring Pressure
Gauge pressure is the pressure relative to atmospheric pressure. Absolute pressure is the sum of gauge pressure and atmospheric pressure. Open-tube manometers have U-shaped tubes and one end is always open. They are used to measure pressure. A mercury barometer is a device that measures atmospheric pressure. The SI unit of pressure is the pascal (Pa), but several other units are commonly used.
• 14.5: Pascal's Principle and Hydraulics
Pressure is force per unit area. A change in pressure applied to an enclosed fluid is transmitted undiminished to all portions of the fluid and to the walls of its container. A hydraulic system is an enclosed fluid system used to exert forces.
• 14.6: Archimedes’ Principle and Buoyancy
Buoyant force is the net upward force on any object in any fluid. The buoyant force is always present and acting on any object immersed either partially or entirely in a fluid. Archimedes’ principle states that the buoyant force on an object equals the weight of the fluid it displaces.
• 14.7: Fluid Dynamics
Flow rate Q is defined as the volume V flowing past a point in time t. The SI unit of flow rate is (m^3)/s, but other rates can be used, such as L/min. Flow rate and velocity are related by the product of the cross-sectional area of the flow by its average velocity. The equation of continuity states that for an incompressible fluid, the mass flowing into a pipe must equal the mass flowing out of the pipe.
• 14.8: Bernoulli’s Equation
Bernoulli’s equation states that pressure is the same at any two points in an incompressible frictionless fluid. Bernoulli’s principle is Bernoulli’s equation applied to situations in which the height of the fluid is constant. Bernoulli’s principle has many applications, including entrainment and velocity measurement.
• 14.9: Viscosity and Turbulence
In this subsection, we introduce the forces of friction that act on fluids in motion. For example, a fluid flowing through a pipe is subject to resistance, a type of friction, between the fluid and the walls. Friction also occurs between the different layers of fluid. These resistive forces affect the way the fluid flows through the pipe.
• 14.E: Fluid Mechanics (Exercises)
• 14.S: Fluid Mechanics (Summary)

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).