FIFI'H EDITION L E. Lo Houghton PW Carpenter Aerodynamics for Engineering Students Frontispiece (see overleaf) Aircraft wake (photo courtesy of Cessna Aircraft Company). This photograph first appeared in the Gallery of Fluid Motion, Physics of Fluids (published by the American Institute of Physics), Vol. 5, No. 9, Sept. 1993, p. S5, and was submitted by Professor Hiroshi Higuchi (Syracuse University). It shows the wake created by a Cessna Citation VI flown immediately above the fog bank over Lake Tahoe at approximately 313 km/h. Aircraft altitude was about 122 m above the lake, and its mass was approximately 8400 kg. The downwash caused the trailing vortices to descend over the fog layer and disturb it to make the flow field in the wake visible. The photograph was taken by P. Bowen for the Cessna Aircraft Company from the tail gunner’s position in a B-25 flying slightly above and ahead of the Cessna. [...]... layer 7 .10 .8 Turbulence structure in the near-wall region 7 .11 Computational methods 7 .11 .1 Methods based on the momentum integral equation 7 .11 .2 Transition prediction 7 .1 1.3 Computational solution of the laminar boundary-layer equations 7 .11 .4 Computational solution of turbulent boundary layers 7 .11 .5 Zero-equation methods 7 .1 1.6 The k E method - A typical two-equation method 7 .11 .7 Large-eddy simulation... T-l T-2 T-I MLP3 MLT-~ ML-~T-~ 1 ML-~T-~ ML~T-~ ML2TP3 ML~T-~ Kinematic viscosity Bulk elasticity L2TML-~T-~ e L2 L3 LT-I LT-~ 1 ML-IT-I Unit (name and abbreviation) Metre (m) Kilogram (kg) Second (s) Degree Celsius ("C), Kelvin (K) Square metre (m2) Cubic metre (m3) Metres per second (m s-') Metres per second per second (m s-*) Radian or degree (") (The radian is expressed as a ratio and is therefore... (1. 10) But, from the definition of specific heat at constant volume, Eqn (1. 7), Eqn (1. 10) becomes Again from the definition, Eqn (1. 8), Eqn (1. 10) gives c ~ = CVT T +p/p (1. 11) Now the pressure, density and temperature are related in the equation of state, which for perfect gases takes the form p/(pT) = constant = R (1. 12) Substituting for p/p in Eqn (1. 1 1) yields the relationship c p - CY = R (1. 13)... fluids gives + - cpT = cpTO= constant (1. 18) Further, if the flow is unidirectional and cvT = E, Eqn (1. 18) becomes, on cancelling dt, d E +pd(i) =0 (1. 19) but differentiating Eqn (1. 10) gives (1. 20) Combining Eqns (1. 19) and (1. 20) 1 dh = -dp (1. 21) P but (1. 22) R which, together with Eqn (1. 21) , gives the identity *+ypd(j) P =O (1. 23) Integrating gives In p + yln (3 - = constant or p = kpy which is the... p This equation is F - = P(;) A Hence [ML-'T-2] = [p][LT-'L-'] = /p][T-'] Thus [p] = [ML-lT-'] and the units of p are therefore kgm-ls-l; in the SI system the name Poiseuille (Pl) has been given to this combination of fundamental units At 0°C (273K) the kgm-' s-l dynamic viscosity for dry air is 1. 714 x The relationship of Eqn (1. 5) with p constant does not apply for all fluids For an important class... given by T2 A S = S2 - SI = cvln-+ T1 Rln-P I (1. 29) P2 With the use of Eqn (1. 14) this is more usually rearranged to be -= ln-+((yAS T2 cv TI 1) lnPI (1. 30) P2 or in the exponential form (1. 31) Alternatively, for example, by using the equation of state, (1. 32) These latter expressions find use in particular problems 1. 3 Aeronautical definitions 1. 3 .1 Wing geometry The planform of a wing is the shape of the... following expressions are obtained: (1. 14) ~ Replacing C V Tby [ l / ( - l)]p/p in Eqn (1. 1 1) readily gives the enthalpy as cpT Y P 7 -1 P - (1. 15) Basic concepts and definitions It is often convenient to link the enthalpy or total heat above to the other energy of motion, the kinetic energy that for unit mass of gas moving with mean velocity Vis w; - v2 K =- (1. 16) 2 Thus the total energy flux in the... one thousand m (milli) - denoting one one-thousandth part p (micro) - denoting one-millionth part Thus 1 MW = 1 O O O W OOO 1 mm = 0.001m 1 pm = 0.0 01 mm A prefix attached to a unit makes a new unit For example, 1mm2 = 1 (nun>' = m2, not 1 0 - ~ m2 For some purposes, the hour or the minute can be used as the unit of time 1. 1.3 Units of other physical quantities Having defined the four fundamental dimensions... momentum integral equation Laminar-turbulent transition 7.9 7 .10 The physics of turbulent boundary layers 7 .10 .1 Reynolds averaging and turbulent stress 7 .10 .2 Boundary-layer equations for turbulent flows 7 .10 .3 Eddy viscosity 7 .10 .4 Prandtl's mixing-length theory of turbulence 7 .10 .5 Regimes of turbulent wall flow 7 .10 .6 Formulae for local skin-friction coefficient and drag 7 .10 .7 Distribution of Reynolds... therefore (1. 28) Integrating Eqn (1. 28) from datum conditions to conditions given by suffix 1, Tl SI= cvln- 4- Rln-P D T 2 S2 = cvln- 4- Rln-P D TD P1 Likewise, TD P2 *Note that in this passage the unconventional symbol S is used for specific entropy to avoid confusion with the length symbols Basic concepts and definitions and the entropy change from conditions 1 to 2 is given by T2 A S = S2 - SI = cvln-+ . 11 4 11 8 11 9 12 2 12 5 12 6 12 9 13 3 13 6 13 7 13 7 13 8 13 9 14 0 14 2 14 4 14 7 15 2 15 5 15 9 15 9 15 9 16 0 16 2 16 7 16 9 17 1 17 6 17 7 17 8 1 a2 I a4 18 5 18 6 18 6 19 0 19 0 19 3. 97 10 1 10 4 10 4 10 4 10 5 10 6 10 7 10 9 11 0 11 0 11 2 3.3.3 Uniform flow 3.3.4 Solid boundaries and image systems 3.3.5 A source in a uniform horizontal stream 3.3.6 Source-sink. William), 19 4 2- I1 Title. TL570 .H587 2002 629 .13 2’3-dc 21 2002029945 ISBN 0 7506 511 1 3 Contents Preface xlll 1 Basic concepts and defdtions Preamble 1. 1 Units and dimensions 1. 1.1