Fluid Dynamics

fluid mechanics banner 4 Fluid Dynamics, a branch of physics that deals with the effects of force and energy on fluid properties of liquids and gases.

Fluid Dynamics deals with the ability of fluid movement and the interactions when coming in contact with two or more fluids.

Fluid Statics deals fluid at rest.

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Dimensionless numbers - See these articles, they contain a lot of fluid related information.

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Engineering, Mathematics, Science
- A - B - C - D - E - F - G - H
- H - I - J - K - L - M - N - O
- O - P - Q - R - S - T - U - V
- V - W - X - Y - Z
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$p_a$ - absolute pressure
$e$ - actual vapor pressure
$Q_a$ - air flow rate
$p_l$ - air Pressure Loss
$AFR$ - air–fuel ratio
$ \bar F$ - average force
$\bar v$ - average velocity
$Ba$ - Barlow's formula
$BHP$ - brake horsepower
$K$ - bulk modulus
$B$ - buoyancy
$m_b$ - buoyancy mass
$C$ - chezy Coefficient
$Ch$ - Chezy formula
$CR$ - compression ratio
$CFD$ - computational fluid dynamic
$v$ - Darcy velocity
$Da$ - Darcy"s law
$ \rho_p $ (Greek symbol rho) - Density
$T_d$ - dewpoint temperature
$C_d$ - discharge coefficient
$F_d$ - drag force
$\mu$ (Greek symbol mu) - dynamic shear viscosity
$EHP$ - engine horsepower
$n_f$ - fan efficiency
$C_v$ - flow coefficient
$Q$ - flow rate
$F$ - force
$f$ - friction
$\mu$ - friction coefficient
$$F L$$ - friction loss
$p_l$ - gas pressure loss through piping
$C$ - Hazen-Williams coefficient
$h_f$ - head loss frictional resistance
$HGV$ - head gasket volume
$h_l$ - head loss
$HP$ - horsepower
$k$ - hydraulic conductivity
$d_h$ - hydraulic depth
$d_h$ - hydraulic diameter
$LIQ$ - liquid
$p$ - momentum
$p$ - pressure

Fluid Dynamics Glossary

A - B - C - D - E - F - G - H - I - J - K - L - M - N - O - P - Q - R - S - T - U - V - W - X - Y - Z

A

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 flow rate -

Air flow rate through piping -

Air pipe sizing -

Air pressure loss through piping -

Air velocity through piping -

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.

B

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.

Borda-Carnot 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 of elasticity - See bulk modulus
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.

C

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 Colebrook-White equation
Colebrook-White equation - Used toiteratively solve the Darcy-Weisback 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 computer-based mathematical model of fluids in a space.

Condensate load from heating air -

Condensate load from heating liquid batch -

Condensate load from heating liquid continuous -

Condensate pipe sizing -

Continuity equation - The moving of a quantity through a pipe in a steady flow.

Continuity equation for area - This formula calculates the initial cross-section 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.

Cracking pressure - The pressure at which the fluid starts to leak through the valve before the set pressure is reached.

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.

Curb gutter flow rate -

D

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.

Density - The ratio of the amount of matter in an object compared to its volume

Dew point - The temperature at which air must be cooled to become saturated with water vapor.

Dew point temperature - The temperature the air needs to be cooled to (at constant pressure) in order to achive a relative humidity of 100%.

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.

E

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.

F

Fan efficiency - The ratio of input and output power.

Flow - See types of 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.

Flow rate - The amount of fluid that flows in a given time past a specific point.

Fluid - A substance that deforms and changes position when put under stress.

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 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.

Force - The push or pull of an object resulting in a change from rest or motion.

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.

G

Gas pressure loss through piping -

H

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.

Hazen-Williams coefficient - Used in the Hazen-Williams Equation. The lower the coefficient, the smoother the pipe is. The higher the coefficient, the less fluid flow is restricted.

Hazen-Williams friction coefficient - See Hazen-Williams coefficient

Hazen-Williams flow rate equation - This flow rate formula is used in Hazen-Williams equations and the coefficient formula.

Hazen-Williams flow through a pressurized pipe equation - The Hazen-Williams Equation can be used for flow through an open channel or through a pressurized pipe.

Hazen-Williams flow through an open channel equation - Hazen-Williams method is only valid for water flowing at ambient temperatures, the Darcy-Weisbach method should be used for other liquids or gases

Hazen-Williams head loss due to friction equation - This head loss due to friction formula is used in Hazen-Williams equations.

Hazen-Williams hydraulic grade equation - This hydraulic grade formula is used in Hazen-Williams equations and the coefficient formula.

Hazen-Williams hydraulic radius equation - This hydraulic radius formula is used in Hazen-Williams equations and the coefficient formula.

Hazen-Williams mean flow velocity equation - This fluid velocity formula is used in Hazen-Williams equations and the coefficient formula.

Hazen-Williams mean flow velocity equation - This fluid velocity formula is used in Hazen-Williams equations and the coefficient formula.

Hazen-Williams pipe inside diameter equation - This inside pipe diameter formula is used in Hazen-Williams equations and the coefficient formula.

Head - Used to express pressure or pressure energy.

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 cross-section of water in a pipe or channel divided by the wetting perimeter.

Hydraulic diameter - Normally used when the flow is in non-circular 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 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 radius - The area cross-section 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 partially full pipe (more than half full) -

Hydraulic radius of a pipe - The area cross-section of water in a pipe or channel divided by the wetting perimeter.

Hydraulic radius of a rectangular channel - The area cross-section of water in a pipe or channel divided by the wetting perimeter.

Hydraulic radius of a trapezoidal channel (equal side slopes) - The area cross-section of water in a pipe or channel divided by the wetting perimeter.

Hydraulic radius of a rapezoidal channel (unequal side slopes) - The area cross-section of water in a pipe or channel divided by the wetting perimeter.

Hydraulic radius of a triangular channel - The area cross-section 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.

L

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.

M

Manning equation - Expressed in numerous ways, a commonly used equation for the uniform flow in open channels.

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 cross-section 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.

N

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.

O

Operating pressure - The operating pressure of equipment occurs when the plant or process is operating at steady state conditions.

P

Pascal's law - States that the increase in pressure is uniformly applied in all directions in a confined fluid.

Pipe sizing for condensate recovery -

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.

Poiseuille's equation for compressible fluids -

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.

Pre-ignition 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.

Q

R

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.

Reduced viscosity -

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.

Reynolds number for gas -

Reynolds number for liquid -

Rotating horsepower -

Roughness coefficient - The roughness of the flow against the ground surface in an open channel.

S

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.
Souders-Brown equation - Used to find the maximum allowable vapor velocity in vapor-liquid 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 two-phase 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.

Steam flow rate through piping -

Steam pipe sizing -

Steam pressure loss through piping -

Steam velocity through piping -

Stokes-Einstein 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.

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.

Swamee-Jain equation - Accurate to 1.0% of the Colebrook-White Equation

System head - The difference between the total discharge head minus the total suction head.

T

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.

U

Underwater pressure - The added pressure exerted underwater directly above a spot at the water level.

Unrestrained pipe expansion -

V

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 flow coefficient for liquid -

Valve flow rate for liquid -

Valve pressure differential for liquid -

Valve sizing coefficient - See valve flow coefficient

Vapor - The gas state of a liquid or solid. Both vapor and gas are basically the same thing.

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.

Vehical engine horsepower -

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.

Venturi tube flow rate -

Viscosity - The measure of the internal friction/resistance to the flow of a liquid.

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.

W

Water absorption - The increase in weight expressed as a percentage of its dry weight after immersion in water for a specified time.

Water density by temperature -

Water flow rate through a valve -

Water flow rate through an orifice -
Water flow rate through piping -
Water hammer - Occurs when a valve is suddenly opened or closed.

Water hammer maximum surge pressure for a fluid -

Water hammer maximum surge pressure for water -

Water hammer maximum surge pressure head -

Water hammer pressure increase -

Water hardness - The hardness of water is a measure of the constituents in solution which tend to precipitate from the water when heated.

Water horsepower -

Water pipe sizing -

Water pressure loss throught piping -

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.