energy equation. chapter 2 lecture 3 2 mechanical energy? forms of energy that can be converted to...
TRANSCRIPT
Energy Equation
Energy EquationChapter 2 Lecture 3 2
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
Energy EquationChapter 2 Lecture 3 3
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
Energy EquationChapter 2 Lecture 3 4
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
Energy EquationChapter 2 Lecture 3 5
For a flowing fluid, emech can be written;
emech= eflow + KE + PE
= (P/ρ) + (V2/2) + (gz)
Changes of emech for a flowing fluid turns to;
Flow Work & Flow Energy
2 2
2 1 2 12 12mech
P P V Ve g z z
Energy EquationChapter 2 Lecture 3 6
Flow Work & Flow Energy (Contd.)
If emech > 0 = work is supplied to the fluidIf emech < 0 = work is extracted from the fluidIf emech = 0 = flow properties constant
Consider;
(Cengel & Cimbala, 2006)
Energy EquationChapter 2 Lecture 3 7
Flow Work & Flow Energy (Contd.)
Work generated per unit mass is same for top and bottom generation i.e.;
emech top = emech bottom
From previous Figure also;
Energy EquationChapter 2 Lecture 3 8
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
Energy EquationChapter 2 Lecture 3 9
Mechanical Efficiency
Mechanical Efficiency is defined as;
, ,
, ,
1mech out mech lossmech
mech in mech in
E E
E E
Where;
Emech, out = Emech, in – Emech, loss
Energy EquationChapter 2 Lecture 3 10
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
Energy EquationChapter 2 Lecture 3 11
Pump & Turbine Efficiency (Contd.)
Pump efficiency is defined as;
Where;
Energy EquationChapter 2 Lecture 3 12
While turbine efficiency is defined as;
Where;
Pump & Turbine Efficiency (Contd.)
Energy EquationChapter 2 Lecture 3 13
Motor & Generator Efficiency
Should not be confused with ηmech
Motor Efficiency;
Generator Efficiency;
Energy EquationChapter 2 Lecture 3 14
Motor & Generator Efficiency (Contd.)
ElectricalPower
Flowing Fluid
Motor(Pump)
Generator(Turbine)
FlowingFluid
ElectricalPower
ηmotor
ηturbine
ηpump
ηgenerator
Energy EquationChapter 2 Lecture 3 15
Combined Efficiency
Ratio of the increase in the mechanical energy of the fluid to the electrical power consumption of the motor
Pump-Motor System
Turbine-Generator SystemRatio of the decrease in the mechanical energy of the fluid to the electrical power generation of the generator
Energy EquationChapter 2 Lecture 3 16
Combined Efficiency (Contd.)
Mathematically;
|| fluidmech,
outelect,
outmech,inmech,
outelect,generaorturbinegen-turbine E
W
EE
W
inelect,
pump
inelect,
fluidmech,
inelect,
inmech,outmech,motorpumpmotor-pump W
W
W
E
W
EE
For turbine-generator
For pump-motor
Energy EquationChapter 2 Lecture 3 17
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!
Energy EquationChapter 2 Lecture 3 18
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
Energy EquationChapter 2 Lecture 3 19
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
Energy EquationChapter 2 Lecture 3 20
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
Energy EquationChapter 2 Lecture 3 21
Next Lecture?
Bernoulli’s Equation