FLUID STATICS - Fluid statics is the field of physics that involves the study of fluids at rest. Because these fluids are not in motion, that means they have achieved a stable equilibrium state, so fluid statics is largely about understanding these fluid equilibrium conditions. When focusing on incompressible fluids (such as liquids) as opposed to compressible fluids (such as most gases), it is sometimes referred to as hydrostatics. A fluid at rest does not undergo any sheer stress, and only experiences the influence of the normal force of the surrounding fluid (and walls, if in a container), which is the pressure. (More on this below.) This form of equilibrium condition of a fluid is said to be a hydrostatic condition. Fluids that are not in a hydrostatic condition or at rest, and are therefore in some sort of motion, fall under the other field of fluid mechanics, fluid dynamics. Consider a cross-sectional slice of a fluid. It is said to experience a sheer stress if it is experiencing a stress that is coplanar, or a stress that points in a direction within the plane. Such a sheer stress, in a liquid, will cause motion within the liquid. Normal stress, on the other hand, is a push into that cross-sectional area. If the area is against a wall, such as the side of a beaker, then the cross-sectional area of the liquid will exert a force against the wall (perpendicular to the cross section - therefore, not coplanar to it).

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Fluid Statics

By Andrew Zimmerman Jones

Fluid statics is the field of physics that involves the study of fluids at rest.

Because these fluids are not in motion, that means they have achieved a stable equilibrium state, so fluid statics is largely about understanding these fluid equilibrium conditions.

When focusing on incompressible fluids (such as liquids) as opposed to compressible fluids (such as most gases), it is sometimes referred to as hydrostatics.

A fluid at rest does not undergo any sheer stress, and only experiences the influence of the normal force of the surrounding fluid (and walls, if in a container), which is the pressure. (More on this below.) This form of equilibrium condition of a fluid is said to be a hydrostatic condition.

Fluids that are not in a hydrostatic condition or at rest, and are therefore in some sort of motion, fall under the other field of fluid mechanics, fluid dynamics.

Major Concepts of Fluid Statics

Sheer stress vs. Normal stress

Consider a cross-sectional slice of a fluid. It is said to experience a sheer stress if it is experiencing a stress that is coplanar, or a stress that points in a direction within the plane.

Such a sheer stress, in a liquid, will cause motion within the liquid. Normal stress, on the other hand, is a push into that cross-sectional area.

If the area is against a wall, such as the side of a beaker, then the cross-sectional area of the liquid will exert a force against the wall (perpendicular to the cross section - therefore, not coplanar to it).

The liquid exerts a force against the wall and the wall exerts a force back, so there is net force and therefore no change in motion.

The concept of a normal force may be familiar from early in studying physics, because it shows up a lot in working with and analyzing free-body diagrams.

When something is sitting still on the ground, it pushes down toward the ground with a force equal to its weight.

The ground, in turn, exerts a normal force back on the bottom of the object. It experiences the normal force, but the normal force doesn't result in any motion.

A sheer force would be if someone shoved on the object from the side, which would cause the object to move so long that it can overcome the resistance of friction.

A force coplanar within a liquid, though, isn't going to be subject to friction, because there isn't friction between molecules of a fluid. That's part of what makes it a fluid rather than two solids.

But, you say, wouldn't that mean that the cross section is being shoved back into the rest of the fluid? And wouldn't that mean that it moves?

This is an excellent point. That cross-sectional sliver of fluid is being pushed back into the rest of the liquid, but when it does so the rest of the fluid pushes back.

If the fluid is incompressible, then this pushing isn't going to move anything anywhere. The fluid is going to push back and everything will stay still.

(If compressible, there are other considerations, but let's keep it simple for now.)

Pressure

All of these tiny cross sections of liquid pushing against each other, and against the walls of the container, represent tiny bits of force, and all of this force results in another important physical property of the fluid: the pressure.

Instead of cross-sectional areas, consider the fluid divided up into tiny cubes.

Each side of the cube is being pushed on by the surrounding liquid (or the surface of the container, if along the edge) and all of these are normal stresses against those sides.

The incompressible fluid within the tiny cube cannot compress (that's what "incompressible" means, after all), so there is no change of pressure within these tiny cubes.

The force pressing on one of these tiny cubes will be normal forces that precisely cancel out the forces from the adjacent cube surfaces.

This cancellation of forces in various directions is of the key discoveries in relation to hydrostatic pressure, known as Pascal's Law after the brilliant French physicist and mathematician Blaise Pascal (1623-1662).

This means that the pressure at any point is the same in all horizontal directions, and therefore that the change in pressure between two points will be proportional to the difference in height.

Density

Another key concept in understanding fluid statics is the density of the fluid.

It figures into the Pascal's Law equation, and each fluid (as well as solids and gases) have densities that can be determined experimentally. Here are a handful of common densities.

Density is the mass per unit volume. Now think about various liquids, all split up into those tiny cubes I mentioned earlier.

If each tiny cube is the same size, then differences in density means that tiny cubes with different densities will have different amount of mass in them.

A higher-density tiny cube will have more "stuff" in it than a lower-density tiny cube.

The higher-density cube will be heavier than the lower-density tiny cube, and will therefore sink in comparison to the lower-density tiny cube.

So if you mix two fluids (or even non-fluids) together, the denser parts will sink that the less dense parts will rise.

This is also evident in the principle of buoyancy, that explains how displacement of liquid results in an upward force, if you remember your Archimedes.

If you pay attention to the mixing of two fluids while it's happening, such as when you mix oil and water, there'll be a lot of fluid motion, and that would covered by fluid dynamics.

But once the fluid reaches equilibrium, you'll have fluids of different densities that have settled into layers, with the highest density fluid forming the bottom layer, up until you reach the lowest density fluid on the top layer.

An example of this is shown on the graphic on this page, where fluids of different types have differentiated themselves into stratified layers based on their relative densities.

Andrew Zimmerman Jones

Math and Physics Expert

Education

M.S., Mathematics Education, Indiana University

B.A., Physics, Wabash College

Introduction

Academic researcher, educator, and writer with 23 years of experience in physical sciences

Works at Indiana Department of Education as senior assessment specialist in mathematics

Co-author of String Theory For Dummies

Member of the National Association of Science Writers

Experience

Andrew Zimmerman Jones is a former writer for ThoughtCo who contributed nearly 200 articles for more than 10 years. His topics ranged from the definition of energy to vector mathematics. Andrew is a dedicated educator; and he uses his background in the physical sciences, educational assessment, writing, and communications to advance that mission.

Andrew is co-author of String Theory For Dummies, which discusses the basic concepts of this controversial approach. String theory tries to explain certain phenomena that are not currently explainable under the standard quantum physics model.

Since 2018, Andrew has worked at the Indiana Department of Education as a senior assessment specialist in mathematics; prior to which he served as a senior assessment editor at CTB/McGraw Hill for 10 years. In addition, Andrew was a researcher at Indiana University's Cyclotron Facility. He is a member of the National Association of Science Writers.

Education

Andrew Zimmerman Jones received an M.S. in Mathematics Education from Indiana University–Purdue and a B.A. in Physics from Wabash College.

Awards and Publications

String Theory For Dummies (Wiley–For Dummies Series, 2009)

Harold Q. Fuller Prize in Physics (Wabash College, 1998)

ThoughtCo and Dotdash

ThoughtCo is a premier reference site focusing on expert-created education content. We are one of the top-10 information sites in the world as rated by comScore, a leading Internet measurement company. Every month, more than 13 million readers seek answers to their questions on ThoughtCo.

For more than 20 years, Dotdash brands have been helping people find answers, solve problems, and get inspired. We are one of the top-20 largest content publishers on the Internet according to comScore, and reach more than 30% of the U.S. population monthly. Our brands collectively have won more than 20 industry awards in the last year alone, and recently Dotdash was named Publisher of the Year by Digiday, a leading industry publication.

https://www.thoughtco.com/fluid-statics-4039368

FLUID DYNAMICS – Fluid dynamics is one of the two main branches of fluid mechanics, with the other branch being fluid statics, the study of fluids at rest. Since fluid dynamics involves the study of the motion of fluid, one of the first concepts that must be understood is how physicists quantify that movement. The term that physicists use to describe the physical properties of the movement of liquid is flow. Flow describes a wide range of fluid movement, such blowing through the air, flowing through a pipe, or running along a surface. The flow of a fluid is classified in a variety of different ways, based upon the various properties of the flow.

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Fluid Dynamics

Understanding What Fluid Dynamics is

by Andrew Zimmerman Jones 

Fluid dynamics is the study of the movement of fluids, including their interactions as two fluids come into contact with each other.

In this context, the term "fluid" refers to either liquid or gases.

It is a macroscopic, statistical approach to analyzing these interactions at a large scale, viewing the fluids as a continuum of matter and generally ignoring the fact that the liquid or gas is composed of individual atoms.

Fluid dynamics is one of the two main branches of fluid mechanics, with the other branch being fluid statics, the study of fluids at rest.

(Perhaps not surprisingly, fluid statics may be thought of as a bit less exciting most of the time than fluid dynamics.)

Key Concepts of Fluid Dynamics

Every discipline involves concepts that are crucial to understanding how it operates.

Here are some of the main ones that you'll come across when trying to understand fluid dynamics.

Basic Fluid Principles

The fluid concepts that apply in fluid statics also come into play when studying fluid that is in motion.

Pretty much the earliest concept in fluid mechanics is that of buoyancy, discovered in ancient Greece by Archimedes.

As fluids flow, the density and pressure of the fluids are also crucial to understanding how they will interact.

The viscosity determines how resistant the liquid is to change, so is also essential in studying the movement of the liquid. Here are some of the variables that come up in these analyses:

·               Bulk viscosity: μ

·               Density: ρ

·               Kinematic viscosity: ν = μ / ρ

Flow

Since fluid dynamics involves the study of the motion of fluid, one of the first concepts that must be understood is how physicists quantify that movement.

The term that physicists use to describe the physical properties of the movement of liquid is flow.

Flow describes a wide range of fluid movement, such blowing through the air, flowing through a pipe, or running along a surface.

The flow of a fluid is classified in a variety of different ways, based upon the various properties of the flow.

Steady vs. Unsteady Flow

If the movement of fluid does not change over time, it is considered a steady flow.

This is determined by a situation where all properties of the flow remain constant with respect to time or alternately can be talked about by saying that the time-derivatives of the flow field vanish. (Check out calculus for more about understanding derivatives.)

A steady-state flow is even less time-dependent because all of the fluid properties (not just the flow properties) remain constant at every point within the fluid.

So if you had a steady flow, but the properties of the fluid itself changed at some point (possibly because of a barrier causing time-dependent ripples in some parts of the fluid), then you would have a steady flow that is not a steady-state flow.

All steady-state flows are examples of steady flows, though. A current flowing at a constant rate through a straight pipe would be an example of a steady-state flow (and also a steady flow). 

If the flow itself has properties that change over time, then it is called an unsteady flow or a transient flow. Rain flowing into a gutter during a storm is an example of unsteady flow.

As a general rule, steady flows make for easier problems to deal with than unsteady flows, which is what one would expect given that the time-dependent changes to the flow don't have to be taken into account, and things that change over time are typically going to make things more complicated.

Laminar Flow vs. Turbulent Flow

A smooth flow of liquid is said to have laminar flow. Flow that contains seemingly chaotic, non-linear motion is said to have turbulent flow.

By definition, a turbulent flow is a type of unsteady flow. 

Both types of flows may contain eddies, vortices, and various types of recirculation, though the more of such behaviors that exist the more likely the flow is to be classified as turbulent. 

The distinction between whether a flow is laminar or turbulent is usually related to the Reynolds number (Re).

The Reynolds number was first calculated in 1951 by physicist George Gabriel Stokes, but it is named after the 19th-century scientist Osborne Reynolds.

The Reynolds number is dependent not only on the specifics of the fluid itself but also on the conditions of its flow, derived as the ratio of inertial forces to viscous forces in the following way: 

Re = Inertial force / Viscous forces

Re = (ρ V dV/dx) / (μ d²V/dx²)

The term dV/dx is the gradient of the velocity (or first derivative of the velocity), which is proportional to the velocity (V) divided by L, representing a scale of length, resulting in dV/dx = V/L.

The second derivative is such that d²V/dx² = V/L².

Substituting these in for the first and second derivatives results in:

Re = (ρ V V/L) / (μ V/L²)

Re = (ρ V L) / μ

You can also divide through by the length scale L, resulting in a Reynolds number per foot, designated as Re f = V / ν.

A low Reynolds number indicates smooth, laminar flow. A high Reynolds number indicates a flow that is going to demonstrate eddies and vortices and will generally be more turbulent.

Pipe Flow vs. Open-Channel Flow

Pipe flow represents a flow that is in contact with rigid boundaries on all sides, such as water moving through a pipe (hence the name "pipe flow") or air moving through an air duct.

Open-channel flow describes flow in other situations where there is at least one free surface that is not in contact with a rigid boundary. (In technical terms, the free surface has 0 parallel sheer stress.)

Cases of open-channel flow include water moving through a river, floods, water flowing during rain, tidal currents, and irrigation canals.

In these cases, the surface of the flowing water, where the water is in contact with the air, represents the "free surface" of the flow.

Flows in a pipe are driven by either pressure or gravity, but flows in open-channel situations are driven solely by gravity.

City water systems often use water towers to take advantage of this, so that the elevation difference of the water in the tower (the hydrodynamic head) creates a pressure differential, which is then adjusted with mechanical pumps to get water to the locations in the system where they are needed. 

Compressible vs. Incompressible

Gases are generally treated as compressible fluids because the volume that contains them can be reduced.

air duct can be reduced by half the size and still carry the same amount of gas at the same rate. Even as the gas flows through the air duct, some regions will have higher densities than other regions.

As a general rule, being incompressible means that the density of any region of the fluid does not change as a function of time as it moves through the flow.

Liquids can also be compressed, of course, but there's more of a limitation on the amount of compression that can be made. For this reason, liquids are typically modeled as if they were incompressible.

Bernoulli's Principle

Bernoulli's principle is another key element of fluid dynamics, published in Daniel Bernoulli's 1738 book Hydrodynamica.

Simply put, it relates the increase of speed in a liquid to a decrease in pressure or potential energy. 

For incompressible fluids, this can be described using what is known as Bernoulli's equation:

(v²/2) + gz + p/ρ = constant

Where g is the acceleration due to gravity, ρ is the pressure throughout the liquid, v is the fluid flow speed at a given point, z is the elevation at that point, and p is the pressure at that point.

Because this is constant within a fluid, this means that these equations can relate any two points, 1 and 2, with the following equation:

(v₁²/2) + gz₁ + p₁/ρ = (v₂²/2) + gz₂ + p₂/ρ

The relationship between pressure and potential energy of a liquid based on elevation is also related through Pascal's Law.

Applications of Fluid Dynamics

Two-thirds of the Earth's surface is water and the planet is surrounded by layers of atmosphere, so we are literally surrounded at all times by fluids ... almost always in motion.

Thinking about it for a bit, this makes it pretty obvious that there would be a lot of interactions of moving fluids for us to study and understand scientifically.

That's where fluid dynamics comes in, of course, so there's no shortage of fields that apply concepts from fluid dynamics.

This list is not at all exhaustive, but provides a good overview of ways in which fluid dynamics show up in the study of physics across a range of specializations:

·          Oceanography, Meteorology, & Climate Science - Since the atmosphere is modeled as fluids, the study of atmospheric science and ocean currents, crucial for understanding and predicting weather patterns and climate trends, relies heavily on fluid dynamics.

·           Aeronautics - The physics of fluid dynamics involves studying the flow of air to create drag and lift, which in turn generate the forces that allow heavier-than-air flight.

·           Geology & Geophysics - Plate tectonics involves studying the motion of the heated matter within the liquid core of the Earth.

·           Hematology & Hemodynamics - The biological study of blood includes the study of its circulation through blood vessels, and the blood circulation can be modeled using the methods of fluid dynamics.

·           Plasma Physics - Though neither a liquid nor a gas, plasma often behaves in ways that are similar to fluids, so can also be modeled using fluid dynamics.

·           Astrophysics & Cosmology - The process of stellar evolution involves the change of stars over time, which can be understood by studying how the plasma that composes the stars flows and interacts within the star over time.

·          Traffic Analysis - Perhaps one of the most surprising applications of fluid dynamics is in understanding the movement of traffic, both vehicular and pedestrian traffic. In areas where the traffic is sufficiently dense, the whole body of traffic can be treated as a single entity that behaves in ways that are roughly similar enough to the flow of a fluid.

Alternative Names of Fluid Dynamics

Fluid dynamics is also sometimes referred at as hydrodynamics, although this is more of a historical term.

Throughout the twentieth century, the phrase "fluid dynamics" became much more commonly used.

Technically, it would be more appropriate to say that hydrodynamics is when fluid dynamics is applied to liquids in motion and aerodynamics is when fluid dynamics is applied to gases in motion.

However, in practice, specialized topics such as hydrodynamic stability and magnetohydrodynamics use the "hydro-" prefix even when they are applying those concepts to the motion of gases.

Andrew Zimmerman Jones

Academic researcher, educator, and writer with 23 years of experience in physical sciences

Works at Indiana Department of Education as senior assessment specialist in mathematics

Co-author of String Theory For Dummies

Member of the National Association of Science Writers

Experience

Andrew Zimmerman Jones is a former writer for ThoughtCo who contributed nearly 200 articles for more than 10 years. His topics ranged from the definition of energy to vector mathematics. Andrew is a dedicated educator; and he uses his background in the physical sciences, educational assessment, writing, and communications to advance that mission. 

Andrew is co-author of String Theory For Dummies, which discusses the basic concepts of this controversial approach. String theory tries to explain certain phenomena that are not currently explainable under the standard quantum physics model. 

Since 2018, Andrew has worked at the Indiana Department of Education as a senior assessment specialist in mathematics; prior to which he served as a senior assessment editor at CTB/McGraw Hill for 10 years. In addition, Andrew was a researcher at Indiana University's Cyclotron Facility. He is a member of the National Association of Science Writers. 

Education

Andrew Zimmerman Jones has a Master of Science (M.S.) in Mathematics Education from Indiana University–Purdue, Indianapolis, Ind.; and a Bachelor of Arts (B.A.) in Physics from Wabash College, Crawfordsville, Ind. 

Awards and Publications

String Theory For Dummies (Wiley–For Dummies Series, 2009)

Graduated magna cum laude (Wabash College, 1999)

Harold Q. Fuller Prize in Physics (Wabash College, 1998)

ThoughtCo and Dotdash

ThoughtCo is a premier reference site focusing on expert-created education content. We are one of the top-10 information sites in the world as rated by comScore, a leading Internet measurement company. Every month, more than 13 million readers seek answers to their questions on ThoughtCo.

For more than 20 years, Dotdash brands have been helping people find answers, solve problems, and get inspired. We are one of the top-20 largest content publishers on the Internet according to comScore, and reach more than 30% of the U.S. population monthly. Our brands collectively have won more than 20 industry awards in the last year alone, and recently Dotdash was named Publisher of the Year by Digiday, a leading industry publication.

https://www.thoughtco.com/andrew-zimmerman-jones-2698607