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Fluid Mechanics

A fluid is any substance having the ability to flow: to freely change shape and move under the influence of a motivating force. Fluid motion may be analyzed on a microscopic level, treating each fluid molecule as an individual projectile body. This approach is extraordinarily tedious on a practical level, but still useful as a simple model of fluid motion.

Some fluid properties are accurately predicted by this model, especially predictions dealing with potential and kinetic energies. However, the ability of a fluid’s molecules to independently move give it unique properties that solids do not possess. One of these properties is the ability to effortlessly transfer pressure, defined as force applied over area.

 

Pressure

The common phases of matter are solid, liquid, and gas. Liquids and gases are fundamentally distinct from solids in their intrinsic inability to maintain a fixed shape. In other words, liquids and gases tend to fill whatever solid containers they are held in. Similarly, both liquids and gases both have the ability to flow, which is why they are collectively called fluids... click here to read more...

 

Pascal’s Principle and Hydrostatic Pressure

We learned earlier that fluids tend to evenly distribute the force applied to them. This tendency is known as Pascal’s principle, and it is the fundamental principle upon which fluid power and fluid signaling systems function. In the example of a hydraulic lift given earlier, we assume that the pressure throughout the fluid pathway is equal... click here to read more...

 

Fluid Density Expressions

Fluid density is commonly expressed as a ratio in comparison to pure water at standard temperature. This ratio is known as specific gravity. For example, the specific gravity of glycerin may be determined by dividing the density of glycerin by the density of water... click here to read more...

 

Manometers

Expressing fluid pressure in terms of a vertical liquid column makes perfect sense when we use a very simple kind of motion-balance pressure instrument called a manometer. A manometer is nothing more than a piece of clear (glass or plastic) tubing filled with a liquid of known density, situated next to a scale for measuring distance. The most basic form of manometer is the U-tube manometer, shown here... click here to read more...

 

Systems of Pressure Measurement

Pressure measurement is often a relative thing. What we mean when we say there is 35 PSI of air pressure in an inflated car tire is that the pressure inside the tire is 35 pounds per square inch greater than the surrounding, ambient air pressure. It is a fact that we live and breathe in a pressurized environment. Just as a vertical column of liquid generates a hydrostatic pressure, so does a vertical column of gas. If the column of gas is very tall, the pressure generated by it will be substantial enough to measure. Such is the case with Earth’s atmosphere, the pressure at sea level caused by the weight of the atmosphere is approximately 14.7 PSI... click here to read more...

 

Buoyancy

When a solid body is immersed in a fluid, it displaces an equal volume of that fluid. This displacement of fluid generates an upward force on the object called the buoyant force. The magnitude of this force is equal to the weight of the fluid displaced by the solid body, and it is always directed exactly opposite the line of gravitational attraction. This is known as Archimedes’ Principle. Buoyant force is what makes ships float. A ship sinks into the water just enough so the weight of the water displaced is equal to the total weight of the ship and all it holds (cargo, crew, food, fuel, etc.)... click here to read more...

 

Gas Laws

The Ideal Gas Law relates pressure, volume, molecular quantity, and temperature of an ideal gas together in one neat mathematical expression... click here to read more...

 

Fluid Viscosity

Viscosity is a measure of a fluid’s internal friction. The more “viscous” a fluid is, the “thicker” it is when stirred. Clean water is an example of a low-viscosity liquid, while honey at room temperature is an example of a high-viscosity liquid... click here to read more...

 

Reynolds Number

Viscous flow is when friction forces dominate the behavior of a moving fluid, typically in cases where viscosity (internal fluid friction) is great. Inviscid flow, by contrast, is where friction within a moving fluid is negligible. The Reynolds number of a fluid is a dimensionless quantity expressing the ratio between a moving fluid’s momentum and its viscosity... click here to read more...

 

Law of Continuity

Any fluid moving through a pipe obeys the Law of Continuity, which states that the product of average velocity (v), pipe cross-sectional area (A), and fluid density (ρ) for a given flow stream must remain constant... click here to read more...

 

Viscous Flow

The pressure dropped by a slow-moving, viscous fluid through a pipe is described by the Hagen-Poiseuille equation. This equation applies only for conditions of low Reynolds number; i.e. when viscous forces are the dominant restraint to fluid motion through the pipe, and turbulence is nonexistent... click here to read more...

 

Bernoulli’s Equation

Bernoulli’s equation is an expression of the Law of Energy Conservation for an in viscid fluid stream, named after Daniel Bernoulli. It states that the sum total energy at any point in a passive fluid stream (i.e. no pumps or other energy-imparting machines in the flow path) must be constant. Two versions of the equation are shown here... click here to read more...

 

Torricelli’s Equation

The velocity of a liquid stream exiting from a nozzle, pressured solely by a vertical column of that same liquid, is equal to the free-fall velocity of a solid mass dropped from the same height as the top of the liquid column. In both cases, potential energy (in the form of vertical height) converts to kinetic energy (motion)... click here to read more...

 

Flow Through a Venturi Tube

If an incompressible fluid moves through a venturi tube (a tube purposefully built to be narrow in the middle), the continuity principle tells us the fluid velocity must increase through the narrow portion. This increase in velocity causes kinetic energy to increase at that point. If the tube is level, there will be negligible difference in elevation (z) between different points of the tube’s centerline, which means elevation head remains constant. According to the Law of Energy Conservation, some other form of energy must decrease to account for the increase in kinetic energy. This other form is the pressure head, which decreases at the throat of the venturi... click here to read more...

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