Fluid Dynamics
Fluid Dynamics is the study of the motion and behavior of fluids, both liquids and gases. It is a branch of physics that focuses on understanding the fundamental principles that govern the movement of fluids and how they interact with their surroundings.
Fluid dynamics has many practical applications in engineering, including the design of aircraft, ships, and automobiles, the design of fluid delivery systems, and the development of energy efficient technologies. It is also important in a wide range of scientific fields, including meteorology, oceanography, and geology, as well as in the study of the behavior of fluids in the human body.
Fluid Classification
 Real Fluid  A fluid that possesses viscosity. All fluids are considered to be real fluids.
 Ideal Fluid  It is incompressible and has no viscosity. Ideal fluid is only an imaginary fluid, as all the fluids known have some viscosity.
 Ideal Plastic Fluid  A fluid in which the shear stress is more than the yield value and shear stress is proportional to the rate of shear strain or velocity gradient.
 Newtonian Fluid  A real fluid in which the shear stress is directly proportional to the rate of shear strain or velocity gradient.
 Non Newtonian Fluid  A real fluid in which the shear stress is not directly proportional to the rate of shear strain or velocity gradient.
 Compressible Fluid  A fluid in which the density of fluid changes with the change in external force or pressure. All gases are considered to be compressible.
 Incompressible Fluid  A fluid in which the density of a fluid does not change with the change in external force or pressure. All liquids are considered to be incompressible.
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Nomenclature & Symbols for Engineering, Mathematics, and Science
Fluid Dynamics Glossary
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 Absolute Pressure  A pressure at absolute zero can only exist in a total vacuum and any pressure above this is called absolute pressure.
 ACFM  Actual cubic feet per minute is a unit of volumetric flow. It is primarily used by manufacturers of blowers and compressors to measure how much air is being moved across the equipment.
 Acoustic Flowmeter  This type of flowmeter (ultrasonic) can give a continuous measurement of the flow rates of both open channel or pipe.
 Actual Vapor Pressure  The measurement to the amount of water vapor that is in a volume of air.
 Aeration  Aeration is the process where water is subjected to intimate air contacting for the purpose of removing contaminating gasses or to saturate it with dissolved oxygen.
 Air–fuel Ratio  The mass ratio of air to fuel mixture present in an internal combustion engines. Because it is a ratio, it is unitless.
 Amagat's Law  States that the volume of a mixture is equal to the sum of the partial volume of its components.
 Archimedes Principle  The upward bouyancy force that is extended on a body that is completely or partially immersed in a fluid and is equal to the weight of the fluid that the body displaces.
 Average Force  used when the instantaneous velocity is not measured precisely between two points.
 Average Velocity  The average of any given velocities where the acceleration is constant. The calculation for average velocity with zero accleration is shown below.
 Avogadro's Law  When temperature and pressure are held constant, the volume of a gas is proportional to the number of moles of gas present.
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Barlow's Formula  Relates to burst pressure, the point just before or at when a pipe or tubing fails under pressure.
 Bernoulli's Equation  A way of describing the conservation of energy principle in an incompressible fluid.
 BordaCarnot Equation  A empirical description of the mechanical loss energy losses of the fluid due to a sudden flow expansion.
 Boyle's Law  States that the volume occupied by a given mass of gas varies inversely with the absolute pressure if the temperature remains constant.

Brackish  A relative term used for water having a total dissolved solids concentration less than brine but more than in potable water.

Brake Horsepower  The engine's horsepower required to overcome the loss in power caused by the pump.

Bulk Modulus  The elastic relationship between an applied pressure that acts to change the volume of the substance and the ability of a substance to withstand changes in volume when under compression.
 Bulk Modulus and Compressibility Relationship 
 Bulk Modulus of Elasticity  The elastic relationship between an applied pressure that acts to change the volume of the substance and the ability of a substance to withstand changes in volume when under compression.

Buoyancy  When a liquid applies upward force on an object that is completely submerged or floating.
 Buoyancy Mass  The amount of matter an object has relative to the density of the liquid.
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 Chezy Coefficient  Dependent on surface roughness and the hydraulic mean depth.
 Chezy Formula  Applies to the steady velocity with turbulent flow in a open channel.
 Coefficient of Discharge  See Discharge Coefficient
 Coefficient of Viscosity  See Viscosity Coefficient
 Colebrook Equation  See ColebrookWhite Equation

ColebrookWhite Equation  Used toiteratively solve the DarcyWeisback friction factor.

Combined gas Law  The relationship between pressure volume and temperature for a system with a constant amount of gas.
 Compatibility  Ability of two or more waters to be blended without a chemical reaction producing insoluble compounds.
 Compression Ratio  The ratio of the maximum volume to the minimum volume in a cylinder.
 Computational Fluid Dynamics  A computerbased mathematical model of fluids in a space.
 Continuity Equation  The moving of a quantity through a pipe in a steady flow.
 Continuity Equation for Area  This formula calculates the initial crosssection area of the pipe.
 Continuity Equation for Density  This formula calculates the initial density of the fluid.
 Continuity Equation for Mass  This formula states that the mass entering a system is equal to the mass leaves the system both at the same rate.
 Continuity Equation for Velocity  This formula calculates the initial velocity in a pipe.
 Coriolis Acceleration  Always acts perpendicular to the angular velocity and linear velocity.
 Coriolis Force  Experienced by an object traversing a path in a rotating frame of reference.
 Cracking Pressure  The pressure at which the fluid starts to leak through the valve before the set pressure is reached.
 Crirical Flow  The variation of specific energy with depth at a constant discharge showing the minimum in the specific energy at a depth called critical depth at which the Froude number has a value of one.
 Cubic Inch Displacement  The size of the engine. Determine by calculating the engine number of cylinders multiplied cylinder bore area multiplied by the stroke of the crankshaft.
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 Dalton’s Law  States that the total pressure of a gas mixture is equal to the sum of the partial pressures of the individual gas components of the mixture.
 Darcy Flux  See Darcy Velocity
 Darcy Friction Factor  Brkić  The Brkić approximation is one way of estimating the Darcy friction factor for use in pressure drop calculations.
 Darcy Friction Factor  Free Surface Flow  Free surface flow describes flow that experiences zero shear forces.
 Darcy Friction Factor  Laminar Flow  The equation on this page should be used only when the flow regime is fully laminar. If the flow regime is transition flow or turbulant flow, other approximations for the Darcy Friction Factor should be made.
 Darcy Velocity  The volumetric flow per unit area of a porous mediun.
 Darcy's Law  The law states that this rate is directly proportional to the drop in vertical elevation between two places in the medium and indirectly proportional to the distance between them.
 Dew Point  The temperature at which air must be cooled to become saturated with water vapor.
 Dimensionless Numbers  See these articles, they contain a lot of fluid related information.
 Discharge Coefficient  The ratio of actual discharge to the theoretical discharge.
 Drag Force  The drag on a body as is moves through a fluid (gas or liquid).
 Dry Gas  A natural gas with very little liquid hydrocarbons or water vapor. It consists of almost 100% of methane \((CH4)\).
 Dynamic Shear Viscosity  The resistance to shearing flow of a fluid, where adjacent layers move parallel to each other in different ways.
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 Engine Horsepower  The estimate of engine horsepower after a quarter mile run using the trap speed.
 Evaporation  The condition that occurs when heat is absorbed by the surface of a liquid and it changes to vapor.
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 Fan Efficiency  The ratio of input and output power.
 Flow 
 Flow Coefficient  Described as the volume (in US gallons) of water at 60°F that will flow per minute through a valve with a pressure drop of 1 psi across the valve.
 Fluid Oxidation  A fluid degradation phenomenon that occurs when it is exposed to oxygen. This leads to an increase in viscosity and TAN (total acid number) as well as the eventual formation of insoluble solids.
 Fluid Power  Describes hydraulic and pneumatic transmit of power from one location to another.
 Fluid Pressure  Fluid at rest, exerts a force perpendicular to any surface in comes in contact with.
 Fluid Pressure at Depth  The pressure exerted on a fluid depends only on the depth of the fluid.
 Fluid Velocity  How fast the process is traveling in a pipe.
 Friction  The mechanical resistance to the relative movement of two surfaces.
 Friction Coefficient  The ratio between two contacting surfaces and the frictional force that resists the normal force of the object.
 Friction Loss  How much loss of flow through a pipe is due to the viscosity, the measure of the internal friction/resistance to the flow of a liquid near the surface of the pipe.
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Hagen–Poiseuille Equation  The pressure loss in a fluid flowing through a long cylindrical pipe.
 Hagen–Poiseuille Law  See Hagen–Poiseuille Equation
 Hard Water  Water with a total hardness of 1 gpg or more as calcium carbonate equivalent.
 HazenWilliams Coefficient  Used in the HazenWilliams Equation. The lower the coefficient, the smoother the pipe is. The higher the coefficient, the less fluid flow is restricted.
 HazenWilliams Friction Coefficient  See HazenWilliams Coefficient
 HazenWilliams Flow Rate Equation  This flow rate formula is used in HazenWilliams equations and the coefficient formula.
 HazenWilliams Flow through a Pressurized Pipe Equation  The HazenWilliams Equation can be used for flow through an open channel or through a pressurized pipe.
 HazenWilliams Flow through an Open Channel Equation  HazenWilliams method is only valid for water flowing at ambient temperatures, the DarcyWeisbach method should be used for other liquids or gases
 HazenWilliams Head Loss due to Friction Equation  This head loss due to friction formula is used in HazenWilliams equations.
 HazenWilliams Hydraulic Grade Equation  This hydraulic grade formula is used in HazenWilliams equations and the coefficient formula.
 HazenWilliams Hydraulic Radius Equation  This hydraulic radius formula is used in HazenWilliams equations and the coefficient formula.
 HazenWilliams Mean Flow Velocity Equation  This fluid velocity formula is used in HazenWilliams equations and the coefficient formula.
 HazenWilliams Pipe Inside Diameter Equation  This inside pipe diameter formula is used in HazenWilliams equations and the coefficient formula.
 Head Friction Loss in Fittings and Valves  The pressure drop caused by fittings and valves.
 Head Gasket Volume  The head gasket volume based on the cylinder bore and the gasket's compressed thickness.

Head Loss  A pressure loss due to the resistance of the fluid and obstructions along the way in a pipe.
 Head Pressure  The pressure at a specific point to the vertical distance at another specific point.
 Head Velocity  The liquid is allowed to flow from the tank while additional liquid is being added. The movement of the liquid through the pipe is converted to kinetic energy that is called head velocity.
 Horsepower  A measure of power or the rate of doing work. It is typically used to describe the work of an engine or machine and is the equivalent of moving 33,000 pounds through the distance of one foot in one minute.
 Humidity  The amount of moisture in the air.

Hydraulics  The force or motion applied on a confined liquid.
 Hydraulic Conductivity  The ease with which a fluid can move through porous spaces or fractures.
 Hydraulic Depth  The area crosssection of water in a pipe or channel divided by the wetting perimeter.
 Hydraulic Diameter  Normally used when the flow is in noncircular pipe or tubes and channels.
 Hydraulic Diameter of a Duct, Pipe or Tube  Used to calculate the Reynolds Number, friction factor or for calculating pressure drop across two points.
 Hydraulic Diameter of a Rectangular Tube  Used to calculate the Reynolds Number, friction factor or for calculating pressure drop across two points.

Hydraulic Diameter of a Right Triangle  Used to calculate the Reynolds Number, friction factor or for calculating pressure drop across two points.
 Hydraulic Diameter of a Square Tube  Used to calculate the Reynolds Number, friction factor or for calculating pressure drop across two points.
 Hydraulic Diameter of a Tube within a Tube  Used to calculate the Reynolds Number, friction factor or for calculating pressure drop across two points.
 Hydraulic Diameter of an Ellipse  Used to calculate the Reynolds Number, friction factor or for calculating pressure drop across two points.
 Hydraulic Diameter of an Isosceles Triangle  Used to calculate the Reynolds Number, friction factor or for calculating pressure drop across two points.
 Hydraulic Efficiency  The ratio of hydrodynamic energy in the form of fluid to the amount of mechanical energy delivered to the rotor.
 Hydraulic Energy  Is presurized fliud, static or in motion, used to achieve machine motion.
 Hydraulic Gradient Flow Rate  Measure the amount of fluid that flows in a given time past a specific.
 Hydraulic Head  The measurement mechanical energy due to pressure of a fluid from a higher elevation to a lower elevation.
 Hydraulic Power 

Hydraulic Radius  The area crosssection of water in a pipe or channel divided by the wetting perimeter.
 Hydraulic Radius of a Partially Full Pipe (Less than Half Full) 
 Hydraulic Radius of a Pipe  The area crosssection of water in a pipe or channel divided by the wetting perimeter.
 Hydraulic Radius of a Rectangular Channel  The area crosssection of water in a pipe or channel divided by the wetting perimeter.
 Hydraulic Radius of a Trapezoidal Channel (Equal Side Slopes)  The area crosssection of water in a pipe or channel divided by the wetting perimeter.
 Hydraulic Radius of a Rapezoidal Channel (Unequal Side Slopes)  The area crosssection of water in a pipe or channel divided by the wetting perimeter.
 Hydraulic Radius of a Triangular Channel  The area crosssection of water in a pipe or channel divided by the wetting perimeter.
 Hydrostatic Pressure  The pressure a fluid exerts on an immersed object.
 Hydrostatic Weighting  You can determine the average density of any object without nead for volume or measuring the mass per unit volume.
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 Laminar Flow  Generally happens when dealing with low Reynolds numbers in pipes. This could be due to low velocities, large diameters or high viscosities.
 Law of Partial Volumes  See Amagat's Law
 Lift Force  An body moving through a fluid (gas or liquid) or air, is the force exerted perpendicular to the direction of travel.
 Liquid  A specific volume and can hold any shape it is contained within.
 Liquid Pressure Recovery Factor  The ratio of pressure drop that occures between the vena contracta and the upstream pressure.
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 Manning's Roughness Coefficient  Measures the frictional resistance exerted by a channel, culvert or pipe on the flow.
 Mean Depth  The average water depth in a stream channel or conduit computed by dividing the crosssection area by the surface width.
 Mechanical Efficiency  The ratio of theoretical power the pump needs to operate to the actual power delivered to the pump itself.
 Mole Fraction  The number of molecules (moles) of a solution in a mixture divided by the total number of moles present in the solution.
 Momentum  An object is the amount of mass in motion.
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 Natural Gas  Has very little liquid hydrocarbons or water vapor. It consists of almost 100% of methane \((CH4)\).

Newton's Law of Viscosity  States that shear stress between adjacent fluid layers is porportional to the velocity gradients between the two layers.
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 Operating Pressure  The operating pressure of equipment occurs when the plant or process is operating at steady state conditions.
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 Pascal's Law  States that the increase in pressure is uniformly applied in all directions in a confined fluid.
 Poiseuille Equation  See Hagen–Poiseuille Equation
 Poiseuille Law  See Hagen–Poiseuille Equation
 Piston Deck Volume  Calculation with a known bore, piston deck distance, volume of piston bumps and volume of piston depressions.
 Potential Energy of a Fluid at an Elevation  A fluid at a higher elevation will have more energy than the same fluid at a lower elevation.
 Preignition Cylinder Pressure of an Engine  The compression pressure of an engine.
 Pressure  The force exerted perpendicular to the surface of an object and is expressed as force per unit area.
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 Raw Water  Untreated water or any water before it reaches a specific water treatment device or process.
 Rayleigh–Taylor Instability  The instability of an interface between two fluids of different densities which occures when the lighter fluids is pushing the heavier fluid.
 Reduced Pressure  A fluid is the actual pressure.
 Reduced Specific Volume  A fluid is ratio of the specific volume of a substance's critical pressure and temperature.
 Reduced Temperature  A fluid is the actual temperature.
 Relative Humidity  A measure of the amount of moisture in the air with respect to the temperature.
 Relative Viscosity  The ratio of the viscosity of a solution to the viscosity of a solution used.
 Rotating Horsepower  It is converting the objects horsepower into rotational motion.
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 Saturated Liquid  Absorbed as much heat energy as it can without vaporizing.
 Saturated Vapor  A vapor at a temperature of the boiling point on the verge of condensing.
 Saturated Vapor Pressure  The pressure applied by air that is mixed with water vapor, at a given temperature, at its maximum saturation point.
 Seepage Velocity  Represents the actual velocity of a fluid flowing through the void spaces in the soil.
 Slug Flow  Occurs when the speed of the vapor phase pushes the waves from the wavy flow regime onto each other.

Soft Water  Any water which contains less than 1.0 gpg (17.1 mg/l) of hardness minerals, expressed as calcium carbonate equivalent.
 Softened Water  Any water that is treated to reduce hardness minerals, expressed as calcium carbonate equivalent.

SoudersBrown Equation  Used to find the maximum allowable vapor velocity in vaporliquid seperation vessels.
 Specific Gravity of Gas  The ratio of the density of the gas to the density of air at a standard pressure and temperature.
 Specific Weight  The weight per unit volume of a substance.
 Spray Flow  Also known as mist or dispersed flow occurs when twophase flow where the liquid phase is the dispersed phase and exists in the form of many droplets, while the gas phase is the continuous phase.
 Static Discharge Head  The highest liquid surface in the discharge system above the centerline of the pump.
 Static Head  The vertical distance from a reference point of the liquid to a lower reference point of the liquid.
 Static Head Pressure  See Head Pressure
 Static Suction Head  The height of the liquid surface in the suction tank above the centerline of the pump.
 StokesEinstein Equation  Used for evaluating diffusion of spherical particles through a liquid with low Reynolds numbers.
 Stokes' Law  The force that is put on a small sphere, slowing down the movement through a viscous fluid.
 Strainer  A closed vessel that collect solid particles to be separated while passing a fluid through a removable screen.
 Subcooled Liquid  If a liquid is not saturated, meaning the liquid is not at its boiling point, it is called subcooled.
 Surge  A temporary and fairly large increase in the voltage or current in an electric circuit or cable.
 Surface Tension  The energy or force at the surface of a liquid that holds it together.
 Suspended Solids  This figure is the sum of all of the suspended material found in a water sample or process stream.
 SwameeJain Equation  Accurate to 1.0% of the ColebrookWhite Equation
 System Head  The difference between the total discharge head minus the total suction head.
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 Torricelli's Law  The fluid efflux velocity flowing through an orifice under gravity at the bottom of a tank filled to a depth. This is the same velocity from the orifice as a falling body over the same height due to gravity.
 Torricelli's Principle  See Torricelli's Law
 Torricelli's Theorem  See Torricelli's Law
 Total Acid Number (TAN)  Measures the fluid acidity and indication of fluid oxidation. It is determined by the amount of potassium hydroxide in milligrams that it needs to neutralize the acids in one gram of fluid.

Total Discharge Head  The total of the friction, pressure, and static discharge.
 Total Displacement  In engine design, the total displacement is the amount of volume displaced by engine cylinders.
 Total Dissolved Solids  The matter that remains in water which remains in solution.
 Total Head  The sum of the discharge flange and the sum of the suction flange.
 Total Pump Efficency  The conversion of one form of energy into another form of energy.
 Total Suction Head  The total of the friction, pressure, and static discharge.
 Turbidity  The cloudiness or haziness of a fluid caused by individual particles (suspended solids) that are generally invisible to the naked eye.
 Turbulence  Any deviation from parallel flow in a pipe due to rough inner walls obstructions or direction changes.
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 Underwater Pressure  The added pressure exerted underwater directly above a spot at the water level.
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 Valve Flow Coefficient Cv/Kv  The number of US gallons of water at 60°F that will flow throuhg a valve in one minute when the pressure differential across the valve is one pound per square inch (psi).
 Valve Sizing Coefficient  See Valve Flow Coefficient
 Vapor Pressure  A substance is the pressure at a certain temperature when the liquid and vapor are in equilibrium.
 Vaporization  A physical change of a substance from a liquid phase to a gas phase.
 Vena Contracta  The narrowest point in a fluid stream where the diameter of the stream and fluid velocity is at its maximum, resulting in lower pressure at that point.
 Venturi Meter Flow Rate  Measures the velocity of a fluid through a pipe.
 Viscosity Coefficient  The tangential friction force required to preserve a unit velocity gradient between two parallel layers of liquid of unit area.
 Viscosity Index  A measure of a fluid's sensitivity to change in viscosity with change in temperature.
 Viscosity of a Mixture  Calculates the effective viscosity of gasses.
 Viscosity of a Slurrty  Slurry being a mixture of liquids and solids, is comparitive to the viscosity of the liquid phase.
 Volumetric Efficiency  The calculation for an internal combustion engine. This is the calculation for the volumetric efficiency for an internal combustion engine.
 Volumetric Flow Rate  The amount of fluid that flows in a given time past a specific point.
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 Water Absorption  The increase in weight expressed as a percentage of its dry weight after immersion in water for a specified time.
 Water Flow Rate through an Orifice 
 Water Hammer  Occurs when a valve is suddenly opened or closed.
 Water Hardness  The hardness of water is a measure of the constituents in solution which tend to precipitate from the water when heated.
 Water Quality  A term used to describe chemical and/or physical characteristics of a water stream or source as they apply to its ultimate use.
 Water Resistance  Capable of withstanding limited exposure to water.
 Water Softening  Water Softening is the process that reduces the ions (cations) that cause water hardness.
 Water Vapor Diffusion  The process by which water vapor spreads or moves through permeable materials caused by a difference in water vapor pressure.
 Water Vapor Pressure  The pressure of water vapor at a given temperature, also the component of atmospheric pressure contributed by the presence of water vapor.
 Weber Number  Used in fluid mechanics is often useful in analysing fluid flows where there is an interface between two different fluids, especially for multiphase flows with strongly curved surfaces.
 Wetting Perimeter  The portion of the channel that is in contact with the fluid flowing.
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