工程系热力学3

Fluid properties which should be understood
• See Chapter 1 of Potter and Wiggert • specific weight ( γ = ρg - weight per unit volume), • compressibility (define bulk modulus of elasticity) ∂p β ≡ −V ∂V T • surface tension ( σ - force per unit length), • vapor pressure (equilibrium pressure reached by a liquid vapor mixture in the absence of other substances), • viscosity ( µ -‘stickiness of fluid’).
Pv n = PV = nR T
• dividing by the mass:
PV nR T R T = Pv = = ≡ RT m m M
Heat Transfer
• Conduction • Convection Correlations for • Radiation: Emit
∂T q = −kA ∂x
For an introductory course we restrict attention to: “those liquids and gases that move under the action of a shear stress, no matter how small that shear stress may be.” • In studying fluid dynamics, fluids are treated as a continuum. • This is OK if the linear dimensions of infinitesimal volumes over which fluid properties are constant are >> the mean free path • Eg 10-9 mm3 of air contains 3 x 107 molecules •
e
µ
υ
is a dimensionless number which represents the ratio of inertial forces to viscous forces. • L is the appropriate “characteristic length” • Re is used to predict the transition from laminar to turbulent flow. • Transition occurs at a critical Reynolds number which is a function of the flow geometry/situation,eg Recrit=2000 for flow in rough walled pipe.
Ideal Gases
• Low density gases behave as “ideal gases”, to a good approximation the molecules can be modeled as if they don’t interact • The equation of state is Pv = R T ( R is the universal gas constant = 8.3144 kJ kmol-1K-1 ) • multiplying both sides by the number of moles gives;
For a liquid, µ decreases with temperature, cohesive forces are reduced as average molecular kinetic energy increases
• For a gas, µ increases with temperature as the frequency of molecular collisions increases
Fluids are gases or liquids, ie a liquid is: • “A state of matter in which the molecules are relatively free to change their positions with respect to each other but restricted by cohesive forces so as to maintain relatively fixed volume.” And a gas is: • “A state of matter in which the molecules are practically unrestricted by cohesive forces. A gas has neither definite shape or volume.”
Classification of Flows
Flows can be classified according to whether they can be modeled as: • 3D/2D/1D. • Viscid/Inviscid. • Laminar/turbulent. Need to be familiar with definitions of; • plane flow, • developed flow, • uniform flow, • stagnation point.
Some reminders from 2222
Problem solving methodology
Developing an effective problem solving methodology is essential: • Think explicitly about exactly what is the system being studied, drawing sketches is almost essential in this process. • The hardest part of thermodynamics is usually converting a real world situation into a problem that can be analysed avoid the temptation to start analysing before you know what it is you want to analyse. • Where manipulation of formulas is required, don't substitute numerical values until all manipulation is complete. • Try to develop a habit of self verifying analysis (in the real world there are no solutions in the back of the book).
Physical Laws
• Fluid dynamics is governed by the same basic physical laws as other mechanical systems, ie given the continuum assumption and assuming non-relativistic velocities (<< the speed of light!): − Conservation of mass. dp − Newton's second law; ∑ F = . dt − First law of thermodynamics (conservation ∆Q = ∆Ε + ∆W of energy); . • An equation of state (eg tables or ideal gas) may also be needed if temperature changes are expected. • The study of fluid dynamics is essentially the formulation of these laws for the general case of fluid flow, after that it is just special cases and examples!
τ =µ
• Kinematic viscosity is;
du dr
ν=
µ ρ
• For a Newtonian fluid µ is independent of du/dr. Silly putty and hair cream are Non-newtonian fluids, where viscosity increases and decreases respectively, with increasing shear stress.
Good techniques include: • Carrying all units through a calculation when substituting numerical values in order to check the final result has the right unit dimensions and order of magnitude. • Using simplified analysis to check the order of magnitude of the final result. • Checking that derived formula have the right behavior in limiting situations. • Reversing analysis or taking it around a ‘full circle’ to check for self consistency. • Checking that results are consistent with common sense expectations where appropriate.