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Gases and liquids

Divergence of a vector field as a measure for the strength of a source

Derivation of the continuity equation (conservation of mass)

In fluid mechanics, the equation for balancing mass flows and the associated change in density (conservation of mass) is called the continuity equation. Continuity equation for one-dimensional flows Experience shows that mass can...
Momentum transfer as the cause of viscosity in ideal gases

Viscosity of an ideal gas

The viscosity of ideal gases is mainly based on the momentum transfer due to diffusion between the fluid layers. Definition of viscosity In the article Viscosity, the cause of viscosity was mainly attributed...
Centrifugal pump

How does a centrifugal pump work?

Centrifugal pumps have a wide range of applications where the pressure increase is caused by centrifugal forces. Radial, axial and mixed flow pumps Centrifugal pumps are turbomachines that pump liquids by means of...
Elevation head (geodetic suction head and discharge head)

Pressure head and head loss

Learn more about the difference between elevation head, pressure head, friction head (head loss) and total static head of a piping system in this article. Static head of a pump Pumps are used...
Moody chart for determining the Darcy friction factor as a function of the Reynolds number

Moody chart (diagram)

The Moody diagram is a chart showing the Darcy friction factor of a pipe as a function of the Reynolds number for selected roughnesses of the pipe wall. Pressure loss In the article...
Valve and pipe elbow in a pipeline system

Pressure loss in pipe systems (Darcy friction factor)

Pressure losses in pipes are caused by internal friction of the fluid (viscosity) and friction between fluid and wall. Pressure losses also occur in components. Introduction When fluids flow through pipes, energy losses...
Flettner rotors on a ship

What ist the Magnus effect?

The Magnus effect refers to the lateral force acting on rotating round bodies in a flow! Introduction Anyone who has ever played football has most likely already had to deal with the Magnus...
Filling of a higher located pool

Exercises with solutions based on the Bernoulli equation

In this article exercises with solutions based on the Bernoulli equation are given. Bernoulli equation The Bernoulli equation is based on the conservation of energy of flowing fluids. The derivation of this equation...
Venturi tube (Venturi nozzle)

Venturi effect

The Venturi effect describes the decrease of (static) pressure in flowing fluids with increasing flow velocity due to a constricted section. Pressure as volume specific energy Pressure is usually measured in the unit...
Prandtl tube (dynamic pressure probe)

What is a Prandtl tube and how does it work?

A Prandtl tube is used to measure the dynamic pressure. From this, the flow speed relative to the tube can be determined. Stagnation pressure and stagnation point If a flow hits a plate...
Blowing off a roof on the lee side by a storm

Examples and applications of the Venturi effect

Learn more about examples and technical applications of the Venturi effect in this article. Venturi effect The Venturi effect (Bernoulli effect) refers to the decrease in pressure in flowing gases or liquids with...
Drag coefficients of different bodies

Drag coefficient (friction and pressure drag)

Drag coefficients are dimensionless similarity parameters for describing the drag of flowed around bodies. Parasitic drag (skin friction drag und pressure drag) When a body moves through a fluid or a fluid flows...
Completely laminar flow around a sphere

Flow around spherical bodies (Stokes’ law of friction)

Stokes' law of friction describes the drag force acting on a spherical body around which a laminar flow passes. Flow resistance and drag coefficient When a fluid (liquid or gas) flows around a...
Turbulators (vertex generators) on the wing of an airplane to generate a turbulent flow around it

Flow separation (boundary layer separation)

In the case of a boundary layer separation (flow separation), the flow can no longer follow the profile of the body around which it flows and separates turbulently from it. Introduction When a...
Hydrodynamische Grenzschicht, thermische Grenzschicht und Konzentrationsgrenzschicht

Dimensionless numbers of the boundary layers (Prandtl, Schmidt and Lewis number)

To describe the heat and mass transport, dimensionless numbers are introduced to describe the processes within the boundary layers. Learn more about this in this article. This article provides answers to the...
Definition of the thermal boundary layer (temperature boundary layer)

Thermal and concentration boundary layer

In addition to the hydrodynamic boundary layer, the thermal boundary layer and the concentration boundary layer also have a decisive influence on the entire heat and mass transport in a flow....
Acceleration of the air when flowing around a wing and the resulting decrease in pressure

Parasitic drag (skin friction drag & form/pressure drag)

Drag is the force of resistance that a moving body experiences in a fluid due to frictional and pressure forces. Introduction In the article on boundary layers, it was explained, using the example...
Convective heat transfer between a heated pipe and a fluid flowing through it

Prandtl number

The Prandtl number is a dimensionless similarity parameter to describe the transport of heat and momentum. Definition In the article on the different boundary layers, the importance of these boundary layers with respect...
Lewis number as a measure for the ratio of the thickness of the thermal boundary layer and the concentration boundary layer

Lewis number

The Lewis number is a dimensionless similarity parameter to describe heat and mass transport. The Lewis number always comes into play when a flowing fluid is transferring both heat by conduction and...
Schmidt number as a measure for the ratio of the thickness of the hydrodynamic boundary layer and the concentration boundary layer

Schmidt number

The Schmidt-number is a dimensionless similarity parameter to describe transport of mass and momentum. Not only the transport of momentum and the heat transfer influence each other as already explained in detail...
Convective heat transfer at a flat plate with laminar-turbulent flow

Calculation of the Nusselt numbers for forced flows over plates and in pipes

In this article you will find formulas for calculating the local and average Nusselt numbers for forced flows over plates and in pipes with circular cross sections. Nusselt number The definition and importance...
Definition of the heat transfer coefficient for convective heat transport

Heat transfer coefficient for thermal convection

The heat transfer coefficient describes the convective heat transfer from a solid to a flowing fluid and vice versa! Introduction The heat transfer coefficient describes the convective heat transfer from a solid to...
Definition of the hydrodynamic boundary layer (velocity boundary layer)

Hydrodynamic boundary layer

The hydrodynamic boundary layer of a flow has a decisive influence on heat and mass transport. Introduction In this article we take a closer look at the boundary layers between a solid surface...
Influence of the hydrodynamic and thermal boundary layer on convective heat transfer

Nusselt number to describe convective heat transfer

The Nusselt number is a dimensionless similarity parameter to describe convective heat transfer, independent of the size of the system. Introduction Convective heat transfer describes the heat transport between a solid surface and...
Pathline (trajectory) of a paper ship in a steady stream

Difference between streamlines, pathlines, streaklines and timelines

In order to make the flow of fluids "visible", one often uses the model of streamlines, pathlines (trajectories), streaklines or timelines. Pathlines (trajectories) Pathlines are flow paths that the fluid particles take while...
Fluid element on a curved streamline

Equation of motion of a fluid on a streamline

In this article we derive the equation of motion of a fluid element on a streamline and one perpendicular to it. Introduction In the following we want to derive the equation of motion...
Derivation of the Bernoulli equation using a flow in a pipe

Derivation of the Bernoulli equation

The Bernoulli equation describes the relationship between static, dynamic and hydrostatic pressure for inviscid and incompressible fluids. Static, dynamic and hydrostatic pressure Due to the pressure acting in resting fluids, a force is...
Pressure difference as drive for flows

Derivation of Hagen-Poiseuille equation for pipe flows with friction

The Hagen-Poiseuille equation describes the parabolic velocity profile of frictional, laminar pipe flows of incompressible, Newtonian fluids. Drive and resistance for flows The flow of fluids through pipes is of great importance in...
Setup of a rotational viscometer

Experimental determination of viscosity (viscometer)

Viscometry is the experimental determination of the viscosity of liquids and gases with so-called viscometers. Definition of viscosity (Newton's law of fluid friction) Viscosity describes the internal resistance to flow of a fluid...
Division of the pressure drop to different causes

Energetic analysis of the Hagen-Poiseuille law

The Hagen-Poiseuille equation for describing the parabolic velocity profile of fluids in pipes applies only to long pipes for energy reasons! Summary As derived in detail in the article on the Hagen-Poiseuille equation,...
Aircraft model in a wind tunnel to study the flow around the aircraft

Reynolds number (laminar and turbulent flow)

The Reynolds number is a dimensionless similarity parameter for describing a forced flow, e.g. whether it is an alminar or turbulent flow. Laminar and turbulent flow The definition of viscosity implies that the...
Toothpaste as a typical example of a non-Newtonian fluid (Bingham Fluid)

Viscosity of liquids and gases

The viscosity of a fluid is a measure of the internal resistance to flow! It is caused by intermolecular forces and transport of momentum within the fluid. Introduction If one looks at the...
Dry adiabatic and wet adiabatic lapse rate (temperature gradient)

Derivation of the barometric formula (adiabatic atmosphere)

The barometric formula for an adiabatic atmosphere takes into account the decrease in temperature with increasing altitude and the associated effects on air pressure. Barometric formula for an isothermal atmosphere In the article...
Influence of the rate of decrease on the outflow velocity

Discharge of liquids (Torricelli’s law)

Torricelli's law (Torricelli's theorem) states that the discharge velocity of a liquid equals a free fall of the liquid from the liquid surface to the opening of the tank. Outflow speed (discharge...
Hot air balloon

How does a hot air balloon work: Buoyancy in gases

Buoyant forces act not only in liquids but also in gases. This will be illustrated in the following by the example of a hot air balloon. Buoyancy In the article Buoyancy, the physical...
Hydraulic bottle jack

How does a hydraulic jack work: Pascals law

A hydraulic jack is based on Pascal's law, which states that the pressure in liquids acts equally in all directions. Pascal's law In the article Pressure it has already been explained that pressure...
Demonstration of the siphon-spillway-principle

Siphon

In this article, learn more about what a siphon is and how it works in practice. Introduction If, for example, you want to empty a pool by a garden hose, you only have...

Pressure in liquids (hydrostatic pressure)

The pressure at a certain depth of a liquid, which is caused by the weight of the liquid column above it, is referred to as hydrostatic pressure! Introduction In the same way as...
Container ship

How do boats float: Buoyancy in liquids

Buoyancy is the force directed against gravity that an object experiences when submerged in a fluid (liquid or gas). Indroduction Everyone may have tried to lift another person and found that this requires...
Water tower

Applications and examples of hydrostatic pressure

Learn more about applications and examples related to hydrostatic pressure in this article. Hydrostatic pressure In the article Pressure in liquids, the formation of hydrostatic pressure and its calculation was explained in detail....
Drinking straw in a glass with water

How does a drinking straw work?

Sucking creates a vacuum in the drinking straw, so that the greater ambient pressure pushes the beverage through the drinking straw. Indroduction Drinking out of a straw sounds quite simple at first. One...
Decrease in air density with increasing height

Derivation of the barometric formula (isothermal atmosphere)

The barometric formula describes the decrease of air pressure with increasing altitude. Introduction At sea level the atmospheric pressure is about 1 bar. However, practice shows that the air pressure decreases more and...
Pressure on a flat surface

Pressure in gases

The pressure of gases is caused on a microscopic level by collisions of the gas molecules with its container walls! Introduction Pressure p in the physcal sense is determined as the quotient of...
Pressing a drawing pin together between two fingers

Pressure

The pressure describes the force distribution on a surface and is therefore a measure of the magnitude with which a surface is loaded! Definition In everyday life one often encounters the concept of...