Thermodynamics

230 | ThermodynamicsFIGURE 5–17Many engineering systems such aspower plants operate under steadyconditions.© Vol. 57/PhotoDiscMassinm˙1h 1INTERACTIVETUTORIALSEE TUTORIAL CH. 5, SEC. 3 ON THE DVD.Controlvolumem CV = constantE CV = constantControlvolumeMassoutFIGURE 5–18Under steady-flow conditions, themass and energy contents of a controlvolume remain constant.m˙ 2h 2m˙ 3h 3FIGURE 5–19Under steady-flow conditions, thefluid properties at an inlet or exitremain constant (do not change withtime).5–3 ■ ENERGY ANALYSIS OF STEADY-FLOWSYSTEMSA large number of engineering devices such as turbines, compressors, andnozzles operate for long periods of time under the same conditions once thetransient start-up period is completed and steady operation is established, andthey are classified as steady-flow devices (Fig. 5–17). Processes involvingsuch devices can be represented reasonably well by a somewhat idealizedprocess, called the steady-flow process, which was defined in Chap. 1 as aprocess during which a fluid flows through a control volume steadily. That is,the fluid properties can change from point to point within the control volume,but at any point, they remain constant during the entire process.(Remember, steady means no change with time.)During a steady-flow process, no intensive or extensive properties withinthe control volume change with time. Thus, the volume V, the mass m, andthe total energy content E of the control volume remain constant (Fig. 5–18).As a result, the boundary work is zero for steady-flow systems (since V CV constant), and the total mass or energy entering the control volume must beequal to the total mass or energy leaving it (since m CV constant and E CV constant). These observations greatly simplify the analysis.The fluid properties at an inlet or exit remain constant during a steadyflowprocess. The properties may, however, be different at different inletsand exits. They may even vary over the cross section of an inlet or an exit.However, all properties, including the velocity and elevation, must remainconstant with time at a fixed point at an inlet or exit. It follows that the massflow rate of the fluid at an opening must remain constant during a steadyflowprocess (Fig. 5–19). As an added simplification, the fluid properties atan opening are usually considered to be uniform (at some average value)over the cross section. Thus, the fluid properties at an inlet or exit may bespecified by the average single values. Also, the heat and work interactionsbetween a steady-flow system and its surroundings do not change with time.Thus, the power delivered by a system and the rate of heat transfer to orfrom a system remain constant during a steady-flow process.The mass balance for a general steady-flow system was given in Sec. 5–1 asainm # aoutm # 1kg>s2(5–31)The mass balance for a single-stream (one-inlet and one-outlet) steady-flowsystem was given asm # 1 m # 2Sr 1 V 1 A 1 r 2 V 2 A 2(5–32)where the subscripts 1 and 2 denote the inlet and the exit states, respectively,r is density, V is the average flow velocity in the flow direction, andA is the cross-sectional area normal to flow direction.During a steady-flow process, the total energy content of a control volumeremains constant (E CV constant), and thus the change in the total energyof the control volume is zero (E CV 0). Therefore, the amount of energyentering a control volume in all forms (by heat, work, and mass) must beequal to the amount of energy leaving it. Then the rate form of the generalenergy balance reduces for a steady-flow process to