A Term Report on;

“The Equation of Mechanical Energy“

Submitted to : Sir Kamran Sibtain & Sir Ifkar Ahsan Naqvi “Transport Phenomena”

Group Members

S. M. Sibtain Jafri (2k8-ChE-108)Badar Rasheed (2k8-ChE-113)Waqas Siddique (2k8-ChE-120)Zafar Afzal (2k8-ChE-127)

Section ‘B’ , 8th Semester

September 7 , 2012

ACKNOWLEDGEMENT

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First of all, I would like to say Alhamdulillah, for giving me the strength and health to do this work until it done.

Not forgotten to my Family for providing everything.

Internet, books, computers and all that as my source to complete this report. They also supported me and encouraged me to complete this task.

Then I would like to thank my teacher, Sir Kamran Sibtain & Sir Ifkar Ahsan Naqvi for guiding me. We had some difficulties in doing this task, but he taught us patiently until we knew what to do. They tried and tried to teach us until we understand what we supposed to do in completing this report.

And Thanks to my Friends who encouraged throughout this project. Last but not least, my friends who were my Group Members and doing this job with me and sharing our ideas. They were helpful that when we combined and discussed together, we had this task done.

Content

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Topic Page No.

Acknowledgement 2

The Equation of Mechanical Energy 4

Mechanical Energy 4

Derivation 4,5,6

Applications of The Equation of Mechanical Energy 7

Other Applications 9

References 12

THE EQUATION OF MECHANICAL ENERGY

Introduction

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Many fluid systems are designed to transport a fluid from one

location to another at a specified flow rate, velocity, and elevation difference,

and the system may generate mechanical work in a turbine or it may consume

mechanical work in a pump or fan during this process. These systems do not

involve the conversion of nuclear, chemical, or thermal energy to mechanical

energy. Also, they do not involve heat transfer in any significant amount, and

they operate essentially at constant temperature. Such systems can be

analyzed conveniently by considering only the mechanical forms of energy

and the frictional effects that cause the mechanical energy to be lost (i.e., to

be converted to thermal energy that usually cannot be used for any useful

purpose).

Mechanical Energy

The mechanical energy can be defined as the form of energy that

can be converted to mechanical work completely and directly by an ideal

mechanical device such as an ideal turbine. Kinetic and potential energies are

the familiar forms of mechanical energy. Thermal energy is not mechanical

energy, however, since it cannot be converted to work directly and completely

(the second law of thermodynamics).

Derivation

Mechanical energy is not conserved in a flow system, but that

does not prevent us from developing an equation of change for this quantity.

We can obtain equations of change for a number of non conserved quantities,

such as internal energy, enthalpy, and entropy. The equation of change for

mechanical energy, which involves only mechanical terms, may be derived

from the equation of motion

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We take the dot product of the velocity vector v with the equation

of motion and then do some rather lengthy rearranging, making use of the

equation of continuity

We also split up each of the terms containing into two

parts. The final result is the equation of change for kinetic energy:

At this point it is not clear why we have attributed the indicated physical

significance to the terms and

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We now introduce the potential energy (per unit mass) defined by

Then the last term may be rewritten as:

T he equation of continuity may now be used to replace

The latter may be written as if the potential energy is

independent of the time. This is true for the gravitational field for systems that

are located on the surface of the earth; then where g is the

(constant) gravitational acceleration and h is the elevation coordinate in the

gravitational field.

With the introduction of the potential energy, assumes the following form:

This is an equation of change for kinetic-plus-potential energy.

Since above equations contain only mechanical terms, they are both referred

to as the equation of change for mechanical energy.

The term may be either positive or negative depending on

whether the fluid is undergoing expansion or compression. The resulting

temperature changes can be rather large for gases in compressors, turbines,

and shock tubes.

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The term is always positive for Newtonian fluids because

it may be written as a sum of squared terms:

which serves to define the two quantities hence the

index i takes on the values 1, 2, 3, the velocity components

and the Cartesian coordinates

The symbol is the Kronecker delta, which is 0 if

The quantity describes the degradation of mechanical energy into

thermal energy that occurs in all flow systems (sometimes called the viscous

dissipation heating) This heating can produce considerable temperature rises

in systems with large viscosity and large velocity gradients, as in lubrication,

rapid extrusion, and high-speed flight.

(Another example of conversion of mechanical energy into heat is the rubbing

of two sticks together to start a fire, which scouts are presumably able to do.)

When we speak of "isothermal systems," we mean systems in which there are

no externally imposed temperature gradients and no appreciable temperature

change resulting from expansion, contraction, or viscous dissipation.

Applications of The Equation of Mechanical Energy

The most important use of Eq. is for the development of the

macroscopic mechanical energy balance (or engineering Bernoulli equation)

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Other Applications

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References

“Transport Phenomena, Second Edition R. Byron Bird, Warren E.

Stewart, Edwin N. Lightfoot”

SlideShare.com

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