Thermodynamics

converted entirely from one mechanical form to another, and the mechanicalefficiency of a device or process can be defined as (Fig. 2–58)Mechanical energy outputh mech Mechanical energy input(2–44)A conversion efficiency of less than 100 percent indicates that conversion isless than perfect and some losses have occurred during conversion. Amechanical efficiency of 97 percent indicates that 3 percent of the mechanicalenergy input is converted to thermal energy as a result of frictional heating,and this will manifest itself as a slight rise in the temperature of the fluid.In fluid systems, we are usually interested in increasing the pressure,velocity, and/or elevation of a fluid. This is done by supplying mechanicalenergy to the fluid by a pump, a fan, or a compressor (we will refer to all ofthem as pumps). Or we are interested in the reverse process of extractingmechanical energy from a fluid by a turbine and producing mechanicalpower in the form of a rotating shaft that can drive a generator or any otherrotary device. The degree of perfection of the conversion process betweenthe mechanical work supplied or extracted and the mechanical energy of thefluid is expressed by the pump efficiency and turbine efficiency, defined asMechanical energy increase of the fluidh pump Mechanical energy input E mech,outE mech,in ¢E# mech,fluidW # shaft,in 1 E mech,lossE mech,in W# pump,uW # pump(2–45)Chapter 2 | 83Fan50 W m · = 0.50 kg/s1 2V 1 = 0, V 2 = 12 m/sz 1 = z 2P 1 = P2·∆Eh = mech,fluid mV · 2 2mech, fan –––––––––– · = ––––––– ·/2W shaft,in W shaft,in(0.50 kg/s)(12 m/s)=2 /2–––––––––––––––––50 W= 0.72FIGURE 2–58The mechanical efficiency of a fan isthe ratio of the kinetic energy of air atthe fan exit to the mechanical powerinput.where ¢E # mech,fluid E # mech,out E # mech,in is the rate of increase in the mechanicalenergy of the fluid, which is equivalent to the useful pumping powerW # pump,u supplied to the fluid, andh turbine Mechanical energy outputMechanical energy decrease of the fluid W# shaft,out0 ¢E # mech,fluid 0 W# turbineW # turbine,e(2–46)where 0 ¢E # mech,fluid 0 E # mech,in E # mech,out is the rate of decrease in themechanical energy of the fluid, which is equivalent to the mechanical powerextracted from the fluid by the turbine W # turbine,e, and we use the absolutevalue sign to avoid negative values for efficiencies. A pump or turbine efficiencyof 100 percent indicates perfect conversion between the shaft workand the mechanical energy of the fluid, and this value can be approached(but never attained) as the frictional effects are minimized.Electrical energy is commonly converted to rotating mechanical energyby electric motors to drive fans, compressors, robot arms, car starters, andso forth. The effectiveness of this conversion process is characterized by themotor efficiency h motor , which is the ratio of the mechanical energy output ofthe motor to the electrical energy input. The full-load motor efficienciesrange from about 35 percent for small motors to over 97 percent for largehigh-efficiency motors. The difference between the electrical energy consumedand the mechanical energy delivered is dissipated as waste heat.The mechanical efficiency should not be confused with the motor efficiencyand the generator efficiency, which are defined asMechanical power outputMotor: h motor W# shaft,out(2–47)Electric power input W # elect,in