f12_sp - Fluids – Lecture 12 Notes 1. Energy Conservation...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

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.

Page1 / 4

f12_sp - Fluids – Lecture 12 Notes 1. Energy Conservation...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online