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Pressure head represents the pressure exerted by a column of water.  It is represented as a unit of length in feet or in metres.

It is a component of hydraulic head along with the potential energy of the water column.


The Velocity head is a means of describing the pressure at a point due to the velocity of the moving liquid.  A moving liquid has momentum.  This momentum has a force at all points in front of the moving fluid.  This is referred to as the velocity head.

The velocity head represents the kinetic energy due to the motion of the liquid.

Another way of describing it is by imagining it as the pressure the fluid would have at a specific point if the moving fluid is suddenly stopped.


 where h is the velocity head,
           v is the velocity and
           g is acceleration due to gravity

Head in fluid dynamics refers to the level of the liquid above the datum line.  We, therefore, say a head of 5 feet of water.

The head of a static liquid gives an idea about the pressure caused by the level of liquid and the potential energy due to the height of the liquid above the datum line.

Thus the hydraulic head is caused by two factor.  The static pressure and the potential energy of the liquid above the datum line.

However, it is important to note that the head is not energy.  It is a way of describing the static pressure and the potential energy.

Head is an important parameter in the design and discussion.

A datum line is a line of reference used in many engineering disciplines such as in fluid dynamics, surveying and in construction.

The use of a datum line helps compare different heights and provides a constant reference point which helps in calculations.

Statement
An increase of speed always occurs with a decrease in the pressure or the potential energy of a fluid.

Bernoulli's theorem is generally applied to incompressible fluids although it can also be applied to compressible liquids in more sophisticated forms.

Consider a liquid flowing in a tube.  If the area of the tube decreases in a certain section of the tube, the speed of the liquid in the section increases.  This is accompanied by a drop in the pressure of the liquid.

Bernoulli's theorem is based on the law of conservation of energy which states that the amount of energy in a flow that is steady is constant.  When the speed of the liquid increases, the kinetic energy increases.  To keep the total energy constant, there is a drop in the static pressure and the pressure energy.


Where P is the pressure energy
           ρ is the density
           v is the velocity and
           h is the head.

What is Laminar Flow in liquids ?

When the flow of a liquid is smooth and regular, the flow is called laminar flow. The laminar flow is a flow in which each liquid particle has a definite path.  These paths do not cross with one another.  Laminar flow is also called streamlined flow.

There are no cross currents or eddies in laminar flow.  The different layers of the fluid slide over one another. These layers of fluid are called laminae, hence the term, laminar flow.

Laminar flow occurs at low velocity with liquids with high velocity.

Laminar flow occurs when the Reynolds number is low.

What is Turbulent Flow ?

In turbulent flow, the velocity and the direction of the fluid particles vary from time to time.  The particles do not have a specified path and move in a haphazard and irregular manner.  Turbulent flow is also called eddy flow.

Examples of turbulent flow are the flow in rivers, the wind and the blood flow in arteries.

A differential manometer is used to measure the difference in pressure between two points.

The differential manometer is a U tube manometer.  It consists of a U shaped tube.  The tube is filled with a liquid, usually water or mercury.

The two limbs of the U tube are connected to two points in a pipeline or any other hydraulic system.

The pressure of the two points act upon the liquid in the differential manometer.   The liquid in the two limbs will not be at different levels as the pressure in the two points will be different.

The difference in the levels of the liquids in the two limbs gives the difference in the pressure.  The U tube can be calibrated to give readings directly in units of pressure.

Flow


What is a Steady Flow?

A Steady flow is a condition in which the quantity of liquid flowing per unit time is constant.

In steady flow, the velocity, pressure and density at a given point are constant.

Mathematically, for steady flow



where P is any quantity such as velocity, density or pressure.

What is an Unsteady flow ?

An Unsteady flow is one in which the quantity is not constant but varying.  In unsteady flow, the characteristics of the liquid such as velocity, density or pressure are not constant.

All flows are unsteady while starting.  They may become steady later.  For instance, the flow from a tap may be unsteady when opened and it may become steady later.

A compressible flow is one in which the density is constant throughout the flow.  Liquids are generally assumed to be incompressible.  

A liquid flowing through a pipe is an example of compressible flow.

Incompressible flow is one in which the density of the fluid is not constant.

Example: The flow of gas through a pipe is an example of compressible flow.

In uniform flow, the magnitude and the direction of the flow are constant.  In non uniform flow, the magnitude and the direction can change from time to time.

The flow of liquid through a pipeline of constant cross section can be uniform as the velocity will be constant throughout the line.

On the other hand, if the pipe has different diameter at different sections, the velocity will not be constant and the flow is said to be non-uniform.

A steady flow can be uniform or non-uniform.  Similarly, an unsteady flow can also be uniform or non-uniform.

The Mach number is a value which represents the ratio of the speed of an object to the speed of sound.

The speed of sound depends on parameters such as density and temperature.  The Mach number is named after Ernst Mach, an Austrian physicist.  If the Mach number is less than 1, it implies that the speed of the object is lesser than the speed of sound.  When the speed of the object exceeds the speed of sound, the Mach number will be greater than 1.

For instances, supersonic aircraft which fly at speeds above the speed of sound have a Mach number that is greater than 1.

When the speed of the flow or of an object is equal to the speed of sound, the flow is said to be sonic flow.  If it is less than one it is subsonic and if it is greater than 1 it is supersonic.

A Streamline a line drawn tangential to the velocity vector.  There cannot be a flow normal to a streamline.

The equation for streamlines is du/u = dv/v = dw/w

A collection of stream lines is called a streamtube.

What is a Pathline in a flow

A pathline is a path traced by an individual particle in a flow.

A streakline consists of fluid particles which have passed a specific point or line.

A Timeline describes adjacent particles at a given moment in time.

The Volumetric Discharge refers to the ratio of the total volume of the flow to the time.  It is also known as the discharge.

Discharge = Volume / Time

Relation between Volumetric and Mass Discharge

Discharge = Volume / Time

Now,
Volume = Mass / Density

Therefore,
Discharge = Mass / (Density x Time )

Mass Flow rate = Mass/Time

There fore volumetric flow rate = Mass Flow rate / Density

In fluids, the velocity is not constant.  In a fluid in motion, the velocity is zero at the wall and increases symmetrically towards the center.  This is known as the velocity profile.  The velocity is maximum at the center.

The mean velocity is average value of the velocity of the individual layers.

In pipelines with constant cross section.

The velocity of the fluid can be calculated from the discharge if the cross sectional area is known.

Velocity = Discharge / Area

In fluids in motion, the velocity is not constant.  At the walls of the pipe, the velocity is zero.  The velocity progressively increases as we move to the center.

In a free vortex, as in water flowing through a drain hole, the velocity increases progressively from the periphery towards the centre where it is infinite.

This change in velocity is called the velocity profile or velocity distribution.

Pressure energy refers to the energy of the liquid due to its pressure.  As the pressure of a fluid increases, the pressure on the molecules of the fluid causes some energy to be stored.

Pressure energy is defined as the ratio of the pressure difference to the specific weight of the liquid.  The unit of pressure energy is Joules/kg

Pressure Energy along with the potential energy and the kinetic energy constitutes the Total Energy of a liquid.

A vortex is a rotation of the flow about an axis or a curved line.  Vortices are formed either naturally or can be forced.

A Free vortex requires no external torque.  It occurs when the water drains out of a tank or container.  In a free vortex, the velocity is lowest in the outer periphery and it progressively increases towards the centre.  Thus, the velocity profile is inversely proportional to the radius of the vortex.

A Forced vortex is formed when an external torque is applied.  An example would be fluid rotated by a pump impeller.  In a forced vortex all the particles are at the same velocity.

A manometer is a device in which columns of liquid are used to measure the pressure. Typical liquids used are mercury or water.

The Manometer used to measure low pressure, vacuum pressure and differential pressure.

The Manometer is easy to construct.  It gives a precise measurement with little scope for errors unlike other instruments.

It also enables the measurement of negative pressure.

There are different types of manometers.  Some of the types are

U tube manometer
Differential manometer
Piezometer tube
Inverted U tube manometer
Inclined Manometer