Energy Equation

Chapter 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 (K E ) & Potential energy (P E ) are forms of Mechanical energy (e mech ) Thermal energy is not in the form of e mech

Energy Equation Chapter 2 Lecture 3 3 Mechanical Energy? (Contd.) Pressure can be associated with e mech P = P/A = N/m 2 = (N.m)/m 3 = J/m 3 It’s energy per unit volume! Systems used to transport fluid may exerted or extracted energy

Energy Equation Chapter 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 Equation Chapter 2 Lecture 3 5 For a flowing fluid, e mech can be written; e mech = e flow + K E + P E =(P/ρ) + (V 2 /2) + (gz) Changes of e mech for a flowing fluid turns to; Flow Work & Flow Energy

Energy Equation Chapter 2 Lecture 3 6 Flow Work & Flow Energy (Contd.) If e mech > 0 = work is supplied to the fluid If e mech < 0 = work is extracted from the fluid If e mech = 0 = flow properties constant Consider; (Cengel & Cimbala, 2006)

Energy Equation Chapter 2 Lecture 3 7 Flow Work & Flow Energy (Contd.) Work generated per unit mass is same for top and bottom generation i.e.; e mech top = e mech bottom From previous Figure also;

Energy Equation Chapter 2 Lecture 3 8 Energy Transfer and Efficiency e mech is transferred by rotating devices such as pump and turbine Pump = Transfer e mech from shaft to fluid Turbine = Transfer e mech from fluid to shaft Efficiency of e mech conversion is η mech

Energy Equation Chapter 2 Lecture 3 9 Mechanical Efficiency Mechanical Efficiency is defined as; Where; E mech, out = E mech, in – E mech, loss

Energy Equation Chapter 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 Equation Chapter 2 Lecture 3 11 Pump & Turbine Efficiency (Contd.) Pump efficiency is defined as; Where;

Energy Equation Chapter 2 Lecture 3 12 While turbine efficiency is defined as; Where; Pump & Turbine Efficiency (Contd.)

Energy Equation Chapter 2 Lecture 3 13 Motor & Generator Efficiency Should not be confused with η mech Motor Efficiency; Generator Efficiency;

Energy Equation Chapter 2 Lecture 3 14 Motor & Generator Efficiency (Contd.) Electrical Power Flowing Fluid Motor (Pump) Generator (Turbine) Flowing Fluid Electrical Power η motor η turbine η pump η generator

Energy Equation Chapter 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 System Ratio of the decrease in the mechanical energy of the fluid to the electrical power generation of the generator

Energy Equation Chapter 2 Lecture 3 16 Combined Efficiency (Contd.) Mathematically; For turbine-generator For pump-motor

Energy Equation Chapter 2 Lecture 3 17 Energy Simplification Simplification in term of e mech can be written as; e mech in – e mech out = ∆e mech system + e mech loss For steady operation, energy balance turns to be; e mech in = e mech out + e mech loss That’s steady flow analysis!

Energy Equation Chapter 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 m 3 /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 Equation Chapter 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 Equation Chapter 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/m 3

Energy Equation Chapter 2 Lecture 3 21 Next Lecture? Bernoulli’s Equation