Energy Equation
Mechanical Energy?
Forms of energy that can be converted to
MECHANICAL WORK completely and
directly by mechanical device(s)
Kinetic energy (KE) & Potential energy (PE)
are forms of Mechanical energy (emech)
Thermal energy is not in the form of emech
Chapter 2 Lecture 3
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Energy Equation
Mechanical Energy? (Contd.)
Pressure can be associated with emech
P = P/A = N/m2 = (N.m)/m3 = J/m3
It’s energy per unit volume!
Systems used to transport fluid may
exerted or extracted energy
Chapter 2 Lecture 3
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Energy Equation
Flow Work
It’s the work effect produced due to
pressure acting over the distance
Stated in the amount of per unit mass (P/ρ)
Convenient to be expressed in fluid
properties terms as part of the fluid energy
It’s called as FLOW ENERGY
Chapter 2 Lecture 3
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Energy Equation
Flow Work & Flow Energy
For a flowing fluid, emech can be written;
emech
=
=
eflow
(P/ρ)
+ KE
+ PE
+ (V2/2) + (gz)
Changes of emech for a flowing fluid turns to;
emech 
Chapter 2 Lecture 3
P2  P1

V22  V12

 g  z2  z1 
2
5
Energy Equation
Flow Work & Flow Energy (Contd.)
If emech > 0 = work is supplied to the fluid
If emech < 0 = work is extracted from the fluid
If emech = 0 = flow properties constant
Consider;
(Cengel & Cimbala, 2006)
Chapter 2 Lecture 3
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Energy Equation
Flow Work & Flow Energy (Contd.)
From previous Figure also;
Work generated per unit mass is same for
top and bottom generation i.e.;
emech top = emech bottom
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Energy Equation
Energy Transfer and Efficiency
emech is transferred by rotating devices such
as pump and turbine
Pump = Transfer emech from shaft to fluid
Turbine = Transfer emech from fluid to shaft
Efficiency of emech conversion is ηmech
Chapter 2 Lecture 3
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Energy Equation
Mechanical Efficiency
Mechanical Efficiency is defined as;
mech 
Emech ,out
Emech ,in
 1
Emech ,loss
Emech ,in
Where;
Emech, out = Emech, in – Emech, loss
Chapter 2 Lecture 3
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Energy Equation
Pump & Turbine Efficiency
In fluid system, attention is given to increase
the pressure, velocity and elevation
This is done by supplying mechanical energy
to the fluid by pump of fan
Also, by reversing the process to reduce the
pressure, velocity, and elevation of the fluid
This is done by extracting mechanical energy
from the fluid by turbine
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Energy Equation
Pump & Turbine Efficiency (Contd.)
Pump efficiency is defined as;
Where;
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Energy Equation
Pump & Turbine Efficiency (Contd.)
While turbine efficiency is defined as;
Where;
Chapter 2 Lecture 3
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Energy Equation
Motor & Generator Efficiency
Should not be confused with ηmech
Motor Efficiency;
Generator Efficiency;
Chapter 2 Lecture 3
13
Energy Equation
Motor & Generator Efficiency
(Contd.)
Electrical
Power
Flowing
Fluid
Chapter 2 Lecture 3
ηmotor
ηturbine
Motor
(Pump)
ηpump
Generator ηgenerator
(Turbine)
14
Flowing
Fluid
Electrical
Power
Energy Equation
Combined Efficiency
Pump-Motor System
Ratio of the increase in the mechanical energy
of the fluid to the electrical power consumption
of the motor
Turbine-Generator System
Ratio of the decrease in the mechanical energy
of the fluid to the electrical power generation of
the generator
Chapter 2 Lecture 3
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Energy Equation
Combined Efficiency (Contd.)
Mathematically;
For pump-motor
pump -motor  pumpmotor
E mech, out  E mech, in E mech, fluid Wpump





Welect,in
Welect,in
Welect,in
For turbine-generator
Welect,out
 E
 turbine-gen   turbinegeneraor  
Emech, in
Chapter 2 Lecture 3
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mech, out
Welect,out

| E mech, fluid |
Energy Equation
Energy Simplification
Simplification in term of emech can be written as;
emech in – emech out = ∆emech system + emech loss
For steady operation, energy balance turns to be;
emech in = emech out + emech loss
That’s steady flow analysis!
Chapter 2 Lecture 3
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Energy Equation
Examples & Tutorials
Consider a river flowing toward a lake at
an average velocity of 3 m/s at a rate of
500 m3/s at a location 90 m above the
lake surface. Determine the total
mechanical energy of the river water per
unit mass and the power generation
potential of the entire river at that
location
Chapter 2 Lecture 3
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Energy Equation
Examples & Tutorials (Contd.)
Electric power is to be generated by installing
a hydraulic turbine-generator at a site 70 m
below the free surface of a large water
reservoir that can supply water at a rate of
1500 kg/s steadily. If the mechanical power
output of the turbine is 800 kW and the
electric power generation is 750 kW,
determine the turbine efficiency and the
combine turbine-generator efficiency of this
plant. Neglect losses in the pipes
Chapter 2 Lecture 3
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Energy Equation
Examples & Tutorials (Contd.)
At a certain location, wind is blowing steadily
at 12 m/s. Determine the mechanical energy
of air per unit mass and the power generation
potential of a wind turbine with a 50 m
diameter blades at that location. Also
determine
the
actual
electric
power
generation assuming an overall efficiency of
30 percent. Take air density to be 1.25 kg/m3
Chapter 2 Lecture 3
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Energy Equation
Next Lecture?
Bernoulli’s
Equation
Chapter 2 Lecture 3
21
Energy Equation