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Unformatted text preview: Fluids – Lecture 12 Notes 1. Energy Conservation Reading: Anderson 2.7, 7.4, 7.5 Energy Conservation Application to fixed finite control volume The first law of thermodynamics for a fixed control volume undergoing a process is V Q . W . E(t) . E out . E in dE = δQ + δW dE ˙ + E ˙ out − E ˙ in = Q ˙ + W (1) dt where the second rate form is obtained by dividing by the process time interval dt , and including the contribution of ﬂow in and out of the volume. Total energy ˙ In general, the work rate W will go towards the kinetic energy as well as the internal energy of the ﬂuid inside the CV, in some unknown proportion. This is ambiguity is resolved by defining the total specific energy , which is simply the sum of internal and kinetic specific energies. 1 1 V 2 e o = e + V 2 = c v T + 2 2 This is the overall energy/mass of the ﬂuid seen by a fixed observer. The e part corresponds to the molecular motion, while the V 2 / 2 part corresponds to the bulk motion. = + total energy internal energy kinetic energy We now define the overall system energy E to include the kinetic energy E = ρe o d V ˙ so that W can now include all work. Energy ﬂow The E ˙ out and E ˙ in terms in equation (1) account for mass ﬂow through the CV boundary, which carries not only momentum, but also thermal and kinetic energies. The internal energy ﬂow and kinetic energy ﬂow can be described as internal energy ﬂow = (mass ﬂow) × (internal energy / mass) kinetic energy ﬂow = (mass ﬂow) × (kinetic energy / mass) 1 where the mass ﬂow was defined earlier. The internal energy/mass is by definition the specific internal energy e , and the kinetic energy/mass is simply V 2 / 2. Therefore ˙ vector n A e = ρV n A e internal energy ﬂow = me = ρ V · ˆ 1 1 1 kinetic energy ﬂow = m V 2 = ρ V...
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This note was uploaded on 01/28/2012 for the course AERO 16.01 taught by Professor Markdrela during the Fall '05 term at MIT.
- Fall '05