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Chapter 13

Fluid Mechanics

Characteristics of Fluids
When a force is applied parallel to the top surface of a solid, it resists the applied force due to the internal frictional forces between the layers…
Density
Density is an important characteristic of substances, crucial in determining whether an object sinks or floats in a fluid. Its SI unit is kg/m3, and…
Pressure of Fluids
There are many examples of pressure in fluids in everyday life, such as in relation to blood (high or low blood pressure) and in relation to weather…
Variation of Atmospheric Pressure
Change in atmospheric pressure with height is particularly interesting. The decrease in atmospheric pressure with increasing altitude is due to the…
Pascal's Law
In 1653, the French philosopher and scientist Blaise Pascal published "Treatise on the Equilibrium of Liquids," which discussed the…
Application of Pascal's Law
Pascal's experimentally proven observations—that a change in pressure applied to an enclosed fluid is transmitted undiminished throughout…
Pressure Gauges
Most pressure gauges, like those on scuba tanks, are calibrated to read zero at atmospheric pressure. Readings from such gauges are called the gauge…
Buoyancy
When an object is placed in a fluid, it either floats or sinks. All objects in a fluid experience a buoyant force. For example, a metal ball sinks,…
Archimedes' Principle
Archimedes' principle states that an upward buoyant force exerted on a body that is immersed partially or entirely in a fluid is equal to…
Density and Archimedes' Principle
When a lump of clay is dropped into water, it sinks. But if the same lump of clay is molded into the shape of a boat, it starts to float. Because of…
Accelerating Fluids
When a fluid is in constant acceleration, the pressure and buoyant force equations are modified. Suppose a beaker is placed in an elevator…
Surface Tension and Surface Energy
When a paint brush is immersed in water, the bristles wave freely inside the water. When it is taken out, the bristles stick together. The reason…
Excess Pressure Inside a Drop and a Bubble
The shape of a small drop of liquid can be considered spherical, neglecting the effect of gravity. This drop can further be considered as two equal…
Contact Angle
When a solid is dipped inside a liquid, the liquid surface becomes curved near the contact. For some solid–liquid interfaces, the liquid is…
Rise of Liquid in a Capillary Tube
When very thin cylindrical tubes, called capillaries, are dipped in a liquid, the liquid rises or falls in the tube compared to the surrounding…
Laminar and Turbulent Flow
Fluid dynamics is the study of fluids in motion. Velocity vectors are often used to illustrate fluid motion in applications like meteorology. For…
Equation of Continuity
Fluid motion is represented by either velocity vectors or streamlines. The volume of a fluid flowing past a given location through an area during a…
Bernoulli's Equation
In the middle of the nineteenth century, it was observed that two trains passing each other at a high relative speed get pulled towards each other.…
Bernoulli's Principle
Bernoulli's equation incorporates how fluid pressure changes across a static, incompressible fluid by equating the kinetic energy contribution to…
Bernoulli's Principle: Applications
There are many devices and situations in which fluid flows at a constant height and so can be analyzed using Bernoulli's principle. These devices…
Energy Conservation and Bernoulli's Equation
Applying the conservation of energy principle or the work-energy theorem to an incompressible, inviscid fluid in laminar, steady, irrotational flow…
Viscosity
When water is poured into a glass, it falls freely and quickly, whereas if honey or maple syrup is poured over a pancake, it flows slowly and sticks…
Poiseuille's Law and Reynolds Number
Any fluid in a horizontal tube can flow due to pressure differences—fluid flows from high to low pressure. The flow rate (Q) is the ratio of…
Stokes' Law
Viscous forces, like friction, are intermolecular forces that resist the relative motion of molecules over each other. When a solid body moves…

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