Thermodynamics

54 | ThermodynamicsDA c = pD 2 /4V avgSteam•m = rA c V avg• •E = meFIGURE 2–4Mass and energy flow rates associatedwith the flow of steam in a pipe ofinner diameter D with an averagevelocity of V avg .or, on a unit mass basis,(2–3)where V denotes the velocity of the system relative to some fixed reference1frame. The kinetic energy of a rotating solid body is given by 2Iv 2 where Iis the moment of inertia of the body and v is the angular velocity.The energy that a system possesses as a result of its elevation in a gravitationalfield is called potential energy (PE) and is expressed asor, on a unit mass basis,(2–4)(2–5)where g is the gravitational acceleration and z is the elevation of the centerof gravity of a system relative to some arbitrarily selected reference level.The magnetic, electric, and surface tension effects are significant in somespecialized cases only and are usually ignored. In the absence of sucheffects, the total energy of a system consists of the kinetic, potential, andinternal energies and is expressed asor, on a unit mass basis,E U KE PE U m V 2e u ke pe u V 2(2–6)(2–7)Most closed systems remain stationary during a process and thus experienceno change in their kinetic and potential energies. Closed systemswhose velocity and elevation of the center of gravity remain constant duringa process are frequently referred to as stationary systems. The change inthe total energy E of a stationary system is identical to the change in itsinternal energy U. In this text, a closed system is assumed to be stationaryunless stated otherwise.Control volumes typically involve fluid flow for long periods of time, andit is convenient to express the energy flow associated with a fluid stream inthe rate form. This is done by incorporating the mass flow rate ṁ, which isthe amount of mass flowing through a cross section per unit time. It isrelated to the volume flow rate V . , which is the volume of a fluid flowingthrough a cross section per unit time, byMass flow rate: m # rV # rA c V avg 1kg>s2(2–8)which is analogous to m rV. Here r is the fluid density, A c is the crosssectionalarea of flow, and V avg is the average flow velocity normal to A c .The dot over a symbol is used to indicate time rate throughout the book.Then the energy flow rate associated with a fluid flowing at a rate of ṁ is(Fig. 2–4)Energy flow rate: E # m # e1kJ>s or kW2(2–9)which is analogous to E me.ke V 22 1kJ>kg2PE mgz1kJ2pe gz1kJ>kg22 mgz1kJ22 gz1kJ>kg2