MECH 237 Midterm: Exam II Review

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Colorado State University
Mechanical Engineering
MECH 237
Daniel B.Olsen

MECH 237 Exam II Review CHAPTER 5: MASS AND ENERGY ANALYSIS OF CONTROL VOLUMES • The conservation of mass principle states that the net mass transfer to or from a system during a process is equal to the net change (increase or decrease) in the total mass of the system during that process, and is expressed as: m in m outm systemand 𝑚 -in =out systemdt • Where Δm system = mfinal– minitial the change in the mass of the system during the process, 𝑚 iinand 𝑚 outoute the total rates of mass flow into and out of the system, and dm system/dt is the rate of change of mass within the system boundaries. The relations above are also referred to as the mass balance and are applicable to any system undergoing any kind of process. • The amount of mass flowing through a cross section per unit time is called the mass flow rate, and is expressed as: 𝑚 = ρ 𝑉A • Where ρ = the fluid density, V = average fluid velocity normal to A, and A = cross- sectional area normal to flow direction. The volume of the fluid flowing through a cross section per unit time is called the volume flow rate and is expressed as: 𝑉 = VA = 𝑚/ ρ • The work required to push a unit mass of fluid into or out of a control volume is called flow work or flow energy, and is expressed as w = Pv. In the analysis of flow control volumes, it is convenient to combine the flow energy and internal energy into enthalpy. Then the total energy of a flowing fluid is expressed as: ▯ ▯ θ = h + ke + pe = h + + gz ▯ • The total energy transported by a flowing fluid of mass m with uniform properties is mθ. The rate of energy transport by a fluid with a mass flow rate of 𝑚 is 𝑚θ. When the kinetic and potential energies of a fluid stream are negligible, the amount and rate of energy transport become E mass = mh and 𝐸 mass = 𝑚h, respectively. • The first law of thermodynamics is essentially an expres-sion of the conservation of energy principle, also called the energy balance. The general mass and energy balances for any system undergoing any process can be expressed as: Ein– Eout = ΔE system • Where the net energy transfer by heat, work and mass = the change in internal, kinetic, potential, etc. energy. • Thermodynamic processes involving control volumes can be considered in two groups: steady-flow processes and unsteady-flow processes. During a steady- flow process, the fluid flows through the control volume steadily, experiencing no change with time at a fixed position. The mass and energy content of the control volume remain constant during a steady-flow process. Taking heat transfer to the system and work done by the system to be positive quantities, the conservation of mass and energy equations for steady-flow processes are expressed as: Σ in = Σ out𝑚 ▯ ▯ ▯ ▯ 𝑄 - 𝑊 = Σ out (h + + gz) - Σ 𝑚in + + gz) ▯ ▯ • These are the most general forms of the equations for steady-flow processes. For single-stream (one-inlet–one-exit) systems such as nozzles, diffusers, turbines, compressors, and pumps, they simplify to ▯ ▯ 𝑚 1= 𝑚 2 à ▯ A 1 1V A▯ 2 2 ▯ ▯ ▯ ▯ 𝑄 - 𝑊 = 𝑚[(h – 2 ) +1 ▯▯▯ ▯ ▯ + g(z2 – z1)] ▯ • In these relations, subscripts 1 and 2 denote the inlet and exit states, respectively. • Most unsteady-flow processes can be modeled as a uniform-flow process, which requires that the fluid flow at any inlet or exit is uniform and steady, and thus the fluid properties do not change with time or position over the cross section of an inlet or exit. If they do, they are averaged and treated as constants for the entire process. When kinetic and potential energy changes associated with the control volume and the fluid streams are negligible, the mass and energy balance relations for a uniform-flow system are expressed as m in m outm system Q – W = Σ out- Σ mhin (m u – m2 2) 1 1 system • Where Q = Q net, in Qin– Q out is the net heat input and W= W net, out W outW in is the net work output. • When solving thermodynamic problems, it is recommended that the general form of the energy balance E – E in out = ΔE system e used for all problems, and simplify it for the particular problem instead of using the specific relations given here for different processes. CHAPTER 6: THE SECOND LAW OF THERMODYNAMICS • The second law of thermodynamics states that processes occur in a certain direction, not in any direction. A process does not occur unless it satisfies both the first and the second laws of thermodynamics. Bodies that can absorb or reject finite amounts of heat isothermally are called thermal energy reservoirs or heat reservoirs. • Work can be converted to heat directly, but heat can be converted to work only by some devices called heat en
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