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

## Pressure Head

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

## 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

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.

## Datum Line

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

## Bernoulli's theorem

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.

## Differential Manometer

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.

Labels:
differential,
manometer

## Laminar and Turbulent Flow

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.

## Flow - Steady and Unsteady Flows

# 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.

## Uniform and Non-Uniform Flows

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.

Labels:
flow,
non-uniform,
uniform

## Compressibile and Incompressible flows

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.

Labels:
compressible,
flow,
incompressible

## Mach number

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.

## Streamline in a flow

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.

Labels:
flow,
pathline,
streamline

## Volumetric 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

Labels:
discharge,
volumetric

## Mean Velocity in Fluid

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

## Velocity Profile

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

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.

## Forced Vortex and a Free Vortex

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.

## Manometers - An Overview

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

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