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FORMS OF ENERGY Types or Forms of Energy
Stored Energies – energies stored within the body which goes or dependent upon the flow of mass. o Stored energies are a function of mass or dependent on the presence of mass. o (e.g.) Potential energy (PE), Kinetic energy (KE), Internal energy (U) and Flow work (PV)
Transition Energies – energies in transit (on the move) which are not dependent upon the flow of the mass. o (e.g.) Heat (Q), Mechanical Work (W), Power (P)
Stored Energies 1. Gravitational Potential Energy (PE) – stored energy due to its elevation above any arbitrary datum plane.
o
Where: o o o o
PE = gravitational potential energy (expressed in Joules [J], foot-pound force [ft-lbf] ) ΔPE = change in gravitational potential energy (expressed in Joules [J], foot-pound force [ft-lbf] ) z = elevation from the ground (expressed in meters [m], feet/foot [ft] ) Δz = change in elevation from the ground (expressed in meters [m], feet/foot [ft] )
2. Kinetic Energy (KE) – stored energy of a body by virtue of its motion or velocity.
Forms of Energy
METD-323 – Lesson 02
Prepared by: Engr. Christian Kenneth D. Garduce
o
Where: o KE = kinetic energy (expressed in Joules [J], foot-pound force [ft-lbf] ) o ΔKE = change in kinetic energy (expressed in Joules [J], foot-pound force [ft-lbf] ) o v = velocity of the moving object (expressed in meters-per-second [m/s], feet-per-second [ft/s] )
3. Internal Energy (U) – stored energy due to its motion of molecules and forces of attraction between them. An increase in internal energy results in the rise of temperature or a change in phase.
o
Where: o
cv = specific heat of gas at constant volume (expressed in
o
ΔT = change in absolute temperature (expressed in Kelvins [K], degrees Rankine [°R] )
,
)
4. Flow Work or PV-Energy (WF) – is the work done in pushing a fluid across a boundary, usually into or out of a system.
o
Where:
Forms of Energy
2
o
P = pressure (expressed in Pa, kPa, lbf/ft , psi)
o
V = volume (expressed in m or ft )
3
3
METD-323 – Lesson 02
Prepared by: Engr. Christian Kenneth D. Garduce
o
R = gas constant (expressed in
o
ΔT = change in absolute temperature (expressed in Kelvins [K], degrees Rankine [°R] )
,
)
5. Enthalpy or Useful Energy (H) – is a composite property applicable to all fluids and is defined as the sum of the internal energy and the flow work of the substance.
o
Where: o
cp = specific heat of gas at constant pressure (expressed in
o
ΔT = change in absolute temperature (expressed in Kelvins [K], degrees Rankine [°R] )
,
)
Transition Energies 1. Heat (Q) – is energy in transit (on the move) from body or system to another solely because of a temperature difference between the bodies or systems a. Q is positive (+) when heat is added to the body or system b. Q is negative (-) when heat is rejected by the body or system
Forms of Energy
METD-323 – Lesson 02
Prepared by: Engr. Christian Kenneth D. Garduce
2. Work (W) – is the product of the displacement of the body and the component of the force in the direction of the displacement. a. Work done by the system is positive (outflow of energy) b. Work done on the system is negative (inflow of energy)
Steady Flow Energy Equation
Steady Flow Energy Equation (SFEE) is an equation that describes the total energy flow of an open system. It is assumed that the mass flow through the system to be constant, this is why it is called “Steady Flow Energy.” The SFEE is used to analyze a fluid flow across a piping system with the consideration of losses. o o o
Forms of Energy
There is neither accumulation nor diminution of mass within the system. (Law of Conservation of Mass) There is neither accumulation nor diminution of energy within the system. (Law of Conservation of Energy) The state of the working substance at any point in the system remains constant.
METD-323 – Lesson 02
Prepared by: Engr. Christian Kenneth D. Garduce
Fluid Flow Continuity Equation (for Incompressible Fluid / Perfect Fluid)
where density of the incompressible fluid doesn’t change at entry and exit points, therefore ρ1 = ρ2.
o
Where: o o o o
A = area normal to the flow (expressed in square meters [m2], square feet [ft2] ) v = velocity of the fluid (expressed in meters-per-second [m/s], feet-per-second [ft/s] ) V’ = volume flow rate (expressed in cubic meters-per-second [m3/s], cubic feet-per-second [ft3/s] ) m’ = mass flow rate (expressed in kilograms-per-second [kg/s], pounds-per-second [lb/s] )
Non-Flow Energy Equation
Non-flow process is a process in which only the energy enters and leaves the system but not mass. It is also called controlled mass approach or closed system. Here the volume may vary and hence the boundary is movable.
Forms of Energy
METD-323 – Lesson 02
Prepared by: Engr. Christian Kenneth D. Garduce
Sample Problems: 1.
2. 3.
4. 5.
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7.
During a steady flow process, the pressure of the working substance drops from 200 to 20 psia, the speed increases from 200 to 1000 fps, the internal energy of the open system decreases 25 BTU/lb, and the specific volume increases from 1 to 8 ft3/lbm. No heat is transferred. Determine the work per lb. Is it done on or done by the substance? If the mass flow rate (reference #1) is 10 lbm/min, determine the work in horsepower. Steam is supplied to a fully loaded 100-hp turbine at 200 psia with u1 = 1163 BTU/lb, v1 = 2.65 ft3/lb, and v1 = 400 fps. Exhaust is at 1 psia with u2 = 925 BTU/lb, v2 = 294 ft3/lb and v2 = 1100 fps. The heat lost from the steam in the turbine is 10 BTU/lb. Neglect potential energy change and determine the work per lb of steam. Determine the steam flow rate in lb/h (reference #3). An air compressor (an open system) receives 272 kg per minute or air at 99.29 kPa, and a specific volume of 0.026 m 3/kg. The air flows steady through the compressor and is discharged at 689.5 kPa and 0.0051m3/kg. The initial internal energy of the air is 1594 J/kg, and at discharge the internal energy is 6241 J/kg. The cooling water circulated around the cylinder carries away 4383 J/kg air. The change in kinetic energy is 896 J/kg increase. Compute the work done. Is it done by or done on the system? A centrifugal pump operating under steady flow conditions delivers 2,270 kg/min of water from an initial pressure of 82740 Pa to a final pressure of 275800 Pa. The diameter of the inlet pipe to the pump is 15.24 cm and the diameter of the discharge pipe is 10.16 cm. What is the work? A turbine operates under steady flow conditions, receiving steam at the following state: pressure 1200 kPa, temperature at 188 degC, enthalpy 2785 kJ/kg, speed 33.3 m/s and elevation of 3 meters. The steam leaves the turbine at the following state: pressure 20 kPa, enthalpy 2512 kJ/kg, speed 100 m/s and elevation 0 m. Heat is lost to the surroundings at the rate of 0.29 kJ/s. If the rate of the steam flow through the turbine is 0.42 kg/s, what is the power output of the turbine in kW?
Forms of Energy
METD-323 – Lesson 02
Prepared by: Engr. Christian Kenneth D. Garduce