Thermodynamics

gz b E # mech m # e mech m # a P r V 22(2–11)Chapter 2 | 59where P/r is the flow energy, V 2 /2 is the kinetic energy, and gz is the potentialenergy of the fluid, all per unit mass. It can also be expressed in rateform aswhere ṁ is the mass flow rate of the fluid. Then the mechanical energychange of a fluid during incompressible (r constant) flow becomesand¢e mech P 2 P 1r V 2 2 V 2 12 g 1z 2 z 1 21kJ>kg2(2–12)¢E # mech m # ¢e mech m # a P 2 P 1r V 2 2 V 2 12 g 1z 2 z 1 2b1kW2(2–13)Therefore, the mechanical energy of a fluid does not change during flow if itspressure, density, velocity, and elevation remain constant. In the absence of anylosses, the mechanical energy change represents the mechanical work suppliedto the fluid (if e mech 0) or extracted from the fluid (if e mech 0).EXAMPLE 2–2Wind EnergyA site evaluated for a wind farm is observed to have steady winds at a speedof 8.5 m/s (Fig. 2–10). Determine the wind energy (a) per unit mass, (b) fora mass of 10 kg, and (c) for a flow rate of 1154 kg/s for air.Solution A site with a specified wind speed is considered. Wind energy perunit mass, for a specified mass, and for a given mass flow rate of air are tobe determined.Assumptions Wind flows steadily at the specified speed.Analysis The only harvestable form of energy of atmospheric air is thekinetic energy, which is captured by a wind turbine.(a) Wind energy per unit mass of air ise ke V 2(b) Wind energy for an air mass of 10 kg is218.5 m>s222a 1 J>kgb 36.1 J>kg1 m 2 2>sE me 110 kg2136.1 J>kg2 361 J(c) Wind energy for a mass flow rate of 1154 kg/s isE # m # e 11154 kg>s2136.1 J>kg2 a1 kW b 41.7 kW1000 J>sDiscussion It can be shown that the specified mass flow rate corresponds toa 12-m diameter flow section when the air density is 1.2 kg/m 3 . Therefore, awind turbine with a wind span diameter of 12 m has a power generationpotential of 41.7 kW. Real wind turbines convert about one-third of thispotential to electric power.FIGURE 2–10Potential site for a wind farm asdiscussed in Example 2–2.© Vol. 36/PhotoDisc8.5 m/s—