EAS 327: Various TABLES

Note: There are many books of tables in the library. Tables given here are brief; there may be occasions when you need to visit the library (or meteorology text books) for more detailed data.

• Specific gas constants for dry air and for water vapour

  Rd	287	J / (kg.K)
  Rv	462	J / (kg.K)

• Miscellaneous properties of air which we shall treat as roughly constant over the environmental temperature range.

  specific heat	cp	1010	J / (kg . K)
  Ltnt heat vap	Lv	2.5e6	J / kg

• Kinematic viscosity (n) and thermal diffusivity (D_H or k) of air versus temperature, at standard pressure P=100 kPa; and the variation with temperature of the latent heat of vapourization (L_v).

  Temperature	kinematic viscosity	thermal diffusivity	latent heat of vaporization
  T	n	DH (or k)	Lv
  [C]	[m .m/s]	[m.m/s]	[J.kg]
  -5	1.29e-5	1.83e-5	2.513e6
  0	1.33e-5	1.89e-5	2.501e6
  5	1.37e-5	1.95e-5	2.489e6
  10	1.42e-5	2.02e-5	2.477e6
  15	1.46e-5	2.08e-5	2.465e6
  20	1.51e-5	2.15e-5	2.454e6
  25	1.55e-5	2.22e-5	2.442e6
  30	1.60e-5	2.28e-5	2.430e6
  35	1.64e-5	2.35e-5	2.418e6
  40	1.69e-5	2.42e-5	2.406e6
  45	1.74e-5	2.49e-5	2.394e6

• Saturation vapour pressure e_S(T) in [millibars] versus temperature T in [^oC] can be calculated from the following formula (range of validity unknown, but certainly ok over range 0 - 30^oC; T is to be inserted in degrees Celcius; see also Table below):

  e_S(T) = 6.112 exp [ 17.67 T / (243.5+T) ]

• It is useful to have the inverse of this formula, which for example will give us the depoint temperature for a given value of the actual vapour pressure. Rearrangement of the above formula gives

  T(e) = 243.5 / [ 17.67 / ln(e / 6.112) - 1 ]

  where e is to be inserted in millibars, and T will be in degrees Celcius. When using this formula, you might want to check at least once against the table given below, just to be sure you are doing the operations in the correct order. Note that ln( ) denotes the natural logarithm.

• Saturation vapour pressure e_S(T) in [millibars] versus temperature T at 1^oC intervals (you may perform a linear interpolation for intermediate values; for a wider range of temperatures refer to a textbook on meteorology or more comprehensive tables of data, such as the Handbook of Physics and Chemistry, held by the library). Note: 1mb = 100 Pa.

  T [oC]	es(T)	T [oC]	es(T)
  -5	4.21	15	17.04
  -4	4.55	16	18.17
  -3	4.90	17	19.37
  -2	5.28	18	20.63
  -1	5.68	19	21.96
  0	6.11	20	23.37
  1	6.57	21	24.86
  2	7.05	22	26.43
  3	7.58	23	28.09
  4	8.13	24	29.83
  5	8.72	25	31.67
  6	9.35	26	33.61
  7	10.01	27	35.65
  8	10.72	28	37.80
  9	11.47	29	40.06
  10	12.27	30	42.43
  11	13.12	31	44.93
  12	14.02	32	47.55
  13	14.97	33	50.31
  14	15.98	34	53.20

• Formulae for Nusselt number N_u versus Reynolds number R_e for air flow around various types of body. These formulae apply to the case of forced convection. The Reynolds number is R_e = U d / n , where d is the characteristic dimension of the body and U is the airspeed. Please note that N_u - R_e relations such as those given below are empirical correlations, obtained on the basis of physical experiments. The formulae ought not to be regarded as highly accurate - they do not have the status of basic physical laws (such as the ideal gas law, for example). Realistically, one probably ought to think of these correlations as being accurate to within about ± 10%.

  {These N_u-R_e formulae have been taken from a textbook by J.L. Monteith,"Principles of Environmental Physics."}

  • Flat Plates

  • Cylinder

  • Sphere

• Formula for Nusselt number N_u for forced convection to/from a sphere (valid for any fluid).

  Nu = 2 + Pr^0.4 (0.4 R_e ^0.5 + 0.06 R_e ^2/3)

  where P_r= n / k is the "Prandtl number," ratio of kinematic viscosity n to thermal diffusivity k of the fluid. This formula is valid for 3.5 <= R_e <= 8 x 10⁴, 0.7 <= P_r <= 380 ; taken from "Heat Transfer," by White.

• Formula for Nusselt number N_u for free convection to/from a sphere (valid for any fluid).

  Nu = 2 + 0.589 (R_a)^1/4 [1 + (0.469/P_r)^9/16] ^-4/9

  where the Rayleigh number R_a = G_r P_r. Taken from "Fundamentals of Heat and Mass Transfer," by Incropera and de Witt.

• Properties of metals (source: "Handbook of Physics & Chemistry"; "Physics," by Reimann).

  Metal	density	specific heat capacity at 25 oC	Conductivity
  	r, kg m-3	c, J kg-1 K-1	k, W m-1 K-1
  Copper	8900	172	385
  Aluminum	2700	900	239
  Gold	19300	129	310
  Brass	8400-8700	370-400	111

  (Note: brass is an alloy of copper and zinc, typically in the ratio of 70% / 30%, but very often containing a fraction of other metals, such as aluminum. There is a huge range of brass alloys, fabricated for a range of purposes; properties given here are generic and do not accurately represent any particular alloy).

• Table of the area of a standard Gaussian (normal) distribution N(0,1), ie. the normal distribution f(x) having mean m_x=0 and standard deviation s_x=1. The equation for the probability density function is:

  f(x) = 1/(2p)^0.5 exp ( - x²/2)

  The table gives the area lying between x=0 and x=X:

  X	Area	X	Area
  0.1	0.03983	2.1	0.48214
  0.2	0.07296	2.2	0.48610
  0.3	0.11791	2.3	0.48928
  0.4	0.15542	2.4	0.49180
  0.5	0.19146	2.5	0.49379
  0.6	0.22575	2.6	0.49534
  0.7	0.25804	2.7	0.49653
  0.8	0.28814	2.8	0.49744
  0.9	0.31594	2.9	0.49813
  1.0	0.34134	3.0	0.49865
  1.1	0.36433	3.1	0.49903
  1.2	0.38493	3.2	0.49931
  1.3	0.40320	3.3	0.49952
  1.4	0.41924	3.4	0.49966
  1.5	0.43319	3.5	0.49977
  1.6	0.44520	3.6	0.49984
  1.7	0.45543	3.7	0.49989
  1.8	0.46407	3.8	0.49993
  1.9	0.47128	3.9	0.49995
  2.0	0.47725	4.0	0.49997

• Resistance versus temperature, R_T(T), for Fenwal UUT51J1 thermistor:

  T	R	T	R
  -40	4015500	8	230260
  -38	3503500	10	207850
  -36	3062000	12	187840
  -34	2680400	14	169950
  -32	2350200	16	153950
  -30	2064000	18	139610
  -28	1815500	20	126740
  -26	1599400	22	115190
  -24	1411100	24	104800
  -22	1246900	26	95447
  -20	1103400	28	87022
  -18	977910	30	79422
  -16	867910	32	72560
  -14	771370	34	66356
  -12	686530	36	60743
  -10	611870	38	55658
  -8	546070	40	51048
  -6	488000	42	46863
  -4	436680	44	43062
  -2	391270	46	39605
  0	351020	48	36458
  2	315320	50	33591
  4	283600	52	30976
  6	255390	54	28590

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Last Modified: 20 Mar., 2003