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Colorado State University

Mechanical Engineering

MECH 237

Daniel B.Olsen

Spring

Description

MECH 237 Exam II Review
CHAPTER 5: MASS AND ENERGY ANALYSIS OF CONTROL VOLUMES
β’ 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 π -in =out systemdt
β’ Where Ξm system = mfinalβ minitial the change in the mass of the system during
the process, π iinand π 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.
β’ The amount of mass flowing through a cross section per unit time is called the
mass flow rate, and is expressed as:
π = Ο πA
β’ Where Ο = 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:
π = VA = π/ Ο
β’ 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:
β― β―
ΞΈ = h + ke + pe = h + + gz
β―
β’ The total energy transported by a flowing fluid of mass m with uniform
properties is mΞΈ. The rate of energy transport by a fluid with a mass flow rate of
π is πΞΈ. When the kinetic and potential energies of a fluid stream are negligible,
the amount and rate of energy transport become E mass = mh and πΈ mass = πh,
respectively.
β’ 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:
Einβ Eout = ΞE system
β’ Where the net energy transfer by heat, work and mass = the change in internal,
kinetic, potential, etc. energy.
β’ 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:
Ξ£ in = Ξ£ outπ
β― β― β― β―
π - π = Ξ£ out (h + + gz) - Ξ£ πin + + gz)
β― β―
β’ These are the most general forms of the equations for steady-flow processes.
For single-stream (one-inletβone-exit) systems such as nozzles, diffusers,
turbines, compressors, and pumps, they simplify to
β― β―
π 1= π 2 Γ β― A 1 1V Aβ― 2 2
β― β― β― β―
π - π = π[(h β 2 ) +1 β―β―β― β― β― + g(z2 β z1)]
β―
β’ In these relations, subscripts 1 and 2 denote the inlet and exit states,
respectively.
β’ 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 β W = Ξ£ out- Ξ£ mhin (m u β m2 2) 1 1 system
β’ Where Q = Q net, in Qinβ Q out is the net heat input and W= W net, out W outW in
is the net work output.
β’ When solving thermodynamic problems, it is recommended that the general
form of the energy balance E β E in out = ΞE 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
β’ 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.
β’ 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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