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Energy Equation

Energy Equation. Mechanical Energy?. Forms of energy that can be converted to MECHANICAL WORK completely and directly by mechanical device(s). Kinetic energy (K E ) & Potential energy (P E ) are forms of Mechanical energy (e mech ). Thermal energy is not in the form of e mech.

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Energy Equation

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  1. Energy Equation

  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

  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

  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

  5. Flow Work & Flow Energy 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;

  6. 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)

  7. Flow Work & Flow Energy (Contd.) From previous Figure also; Work generated per unit mass is same for top and bottom generation i.e.; emechtop = emechbottom

  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

  9. Mechanical Efficiency Mechanical Efficiency is defined as; Where; Emech,out = Emech,in – Emech,loss

  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

  11. Pump & Turbine Efficiency (Contd.) Pump efficiency is defined as; Where;

  12. Pump & Turbine Efficiency (Contd.) While turbine efficiency is defined as; Where;

  13. Motor & Generator Efficiency Should not be confused with ηmech Motor Efficiency; Generator Efficiency;

  14. Motor & Generator Efficiency (Contd.) ηpump ηmotor Motor (Pump) Flowing Fluid Electrical Power ηturbine ηgenerator Flowing Fluid Electrical Power Generator (Turbine)

  15. 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

  16. Combined Efficiency (Contd.) Mathematically; For pump-motor For turbine-generator

  17. Energy Simplification Simplification in term of emech can be written as; emechin – emechout = ∆emechsystem + emechloss For steady operation, energy balance turns to be; emechin = emechout + emechloss That’s steady flow analysis!

  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

  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

  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

  21. Next Lecture? Bernoulli’s Equation

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