Modes of Work Transfer

P M V SubbaraoProfessor

Mechanical Engineering Department

I I T Delhi

ManyMore Needs/Happenings are Equivalent to Displacement Work!!!

Displacement Work

Generalized Process in A Control Mass

• p = p0 + k (V-V0)

• p2 = p02 + k (V-V0)2

• Polytropic Nature of Fluid Process:

pVn = Constant– n: Polytropic constant.

– n=0 : Constant Pressure Process.

– n=: Constant Volume Process.

The Polytropic Process by A Control Mass

• One in which the pressure-volume relation is given as pVn=constant

• “n” may have any value from minus to plus infinity.• Work transfer during a polytropic process.

• For a vapour (Real Gas) under going a process.

2v

a

bv

RTp

Evolution of Wind Turbines

• Wind is a clean, safe, renewable form of energy.• Although the use of wind power in sailing vessels appeared in

antiquity, the widespread use of wind power for grinding grain and pumping water was delayed until – the 7th century in Persia, – the 12th century in England, and – the 15th century in Holland.

• 17th century, Leibniz proposed using windmills and waterwheels together to pump water from mines in the Harz Mountains.

• Dutch settlers brought Dutch mills to America in the 18th century. • This led to the development of a multiblade wind turbine that was

used to pump water for livestock.• Wind turbines were used in Denmark in 1890 to generate electric

power. • Early in the 20th century American farms began to use wind

turbines to drive electricity generators for charging storage batteries.

SOME TYPES OF WIND TURBINES: HAWT

SOME TYPES OF WIND TURBINES: VAWT

Schematic of Modern Wind Turbines

Wind Flow Past A Locked Wind Turbine

Work Transfer in A Wind Turbine : Control Volume

Work Transfer in a Flow Device : Control Volume

• A Centrifugal Compressor

Outlet : po, To, Vo

Continuous flow system

Pressure at inlet is pi and pressure at exist is po

always.

Fluid with Vi,Ti enters and leaves with Vo and To.

The volume is subjected to a changing pressure field..

p

How to define the infinitesimal work?

Inlet : pi, Ti, Vi

V

Work Transfer in a Flow Device : Control Volume

Acquisition of Work from Constant Volume Flow Process

The Hydro Power House

Wind generation for developing countries

• Unlike the trend toward large-scale grid connected wind turbines seen in the West.

• The more immediate demand for rural energy supply in developing countries is for smaller machines in the 5 - 100 kW range.

• These can be connected to small, localized micro-grid systems and used in conjunction with diesel generating sets and/or solar photovoltaic systems.

• The main area of growth being for very small battery charging wind turbines (50 - 150 Watts).

• In Inner Mongolia there are over 30,000 such machines used by herders for providing power for lighting, televisions, radios, etc.

• Other applications for small wind machines include water pumping, telecommunications power supply and irrigation.

Polytropic work Transfer in A Flow Device

Shaft WorkEnergy transmission with a rotating shaft is very common in engineering practice.

A force F acting through a moment arm r generates a torque T of

psp rFT ,

drFdTW psp .. ,

dt

drF

dt

dTP psp

.. ,

Spring Work

Work Done on Elastic Solid Bars

For linear elastic springs, the displacement x is proportional to the force applied

Work Transfer in Nature

How can a baby snail come out of a egg shell?

Who controls the Growth Shape & Equilibrium Shape of A Crystal

Why cutting of a solid consumes power?

Who decides the beauty of Table Cloth ???

The Role of Surface Tension in Engineering

• When splitting a solid, the amount of energy required is 2A, where 2A is the area created (one A on each side).

• This energy is less than that needed just to break the bonds, since there is atomic and electronic relaxation.

• The surface energy is always positive because the atoms are less bound at the surface.

• The surface tension can be defined as the reversible work of formation of a unit area of surface at constant T, V, m.

• The surface tension is the two-dimensional analog to the pressure.

mVTA

E

,,

The tendency to minimize surface energy is a defining

factor in the morphology and composition of surfaces and

interfaces. This Is important for Solids &

Liquids.

The relative change in internal energy of a control mass w.r.t. change in surface area at constant temperature, volume.

Law of a Nature:

Thermodynamic Definition of Surface Tension

Material g J/m2

Tungsten (solid) 2.9

Iron (solid) 2.2

Iron (liquid) 1.9

MgO 1.2

Mercury (liquid) 0.5

Water 0.07

Acetic acid 0.03

Nitrogen (liquid) 0.01

Helium (liquid) 0.0003

Values of Surface Tension for Selected Materials

Work Associated with the Stretching of a Liquid Film

The Faraday’s Work : An Amazing form of Work Transfer

•Consider a conducting rod PQ moving at a steady speed V perpendicular to a field with a flux densityB.•An electron (negative charge e) in the rod will experience a force (= Bev) that will push it towards the end P.

Description of Work done by A Conductor

• The same is true for other electrons in the rod, so the end P will become negatively charged, leaving Q with a positive charge.

• As a result, an electric field E builds up until the force on electrons in the rod (unit length) due to this electric field (= Ee) balances the force due to the magnetic field

BeVEe

Force per unit charge on Rod of unit length:

BVE

For a rod of length L, define the EMF as :

BLVEMF

What happens when the EMF drives a current in an external circuit?

To do this, imagine that the rod moves along a pair of parallel conductors that are connected to an external circuit

Electrical Loading of Conductor

The EMF will now cause a current to flow in the external resistor R. This means that a similar current flows through the rod itself giving a magnetic force, BIL to the left.

Quantification of the Faraday’s Work

L is now the separation of the two conductors along which the rod PQ moves. An equal and opposite force (to the right) is needed to keep PQ moving at a steady speed.

In a time t, the rod moves a distance x = Vt

Work done on the rod

tVLIBW 21

The Pairs of Work Transfers

Energy dissipated in R = power x time = EMF I× t

Giving : B × I × L ×V × t = EMF × I × t

or, as before, EMF = B × V × L

http://tap.iop.org/fields/electromagnetism/414/page_46948.html