Formula sheet and tables PDF

Preview

Summary

Formula sheet with necessary equations along with all necessary tables....

Description

Conversion Factors Mass and Density

Pressure

1 1 1 1 1 1

1 Pa

kg g/cm3 g/cm3 lb lb/ft3 lb/ft3

5 5 5 5 5 5

2.2046 lb 103 kg/m3 62.428 lb/ft3 0.4536 kg 0.016018 g/cm3 16.018 kg/m3

Length 1 1 1 1

cm m in. ft

5 5 5 5

0.3937 in. 3.2808 ft 2.54 cm 0.3048 m

Velocity 1 km/h 5 0.62137 mile/h 1 mile/h 5 1.6093 km/h

cm3 m3 L L in.3 ft3 gal gal

5 5 5 5 5 5 5 5

0.061024 in.3 35.315 ft3 1023 m3 0.0353 ft3 16.387 cm3 0.028317 m3 0.13368 ft3 3.7854 3 1023 m3

Force 1 1 1 1

N N lbf lbf

5 5 5 5

bar atm lbf/in.2 lbf/in.2 atm

1 N/m2 1.4504 3 1024 lbf/in.2 105 N/m2 1.01325 bar 6894.8 Pa 144 lbf/ft2 14.696 lbf/in.2

Energy and Specific Energy 1 1 1 1 1 1 1 1 1

J kJ kJ kJ/kg ft ? lbf Btu Btu Btu/lb kcal

5 1 N ? m 5 0.73756 ft ? lbf 5 737.56 ft ? lbf 5 0.9478 Btu 5 0.42992 Btu/lb 5 1.35582 J 5 778.17 ft ? lbf 5 1.0551 kJ 5 2.326 kJ/kg 5 4.1868 kJ

Energy Transfer Rate

Volume 1 1 1 1 1 1 1 1

1 1 1 1 1

5 5 5 5 5 5 5

1 kg ? m/s2 0.22481 lbf 32.174 lb ? ft/s2 4.4482 N

1W 1 kW 1 Btu/h 1 hp 1 hp 1 hp

5 5 5 5 5 5

1 J/s 5 3.413 Btu/h 1.341 hp 0.293 W 2545 Btu/h 550 ft ? lbf/s 0.7457 kW

Specific Heat 1 kJ/kg ? K 1 kcal/kg ? K 1 Btu/h ? 8R

5 0.238846 Btu/lb ? 8R 5 1 Btu/lb ? 8R 5 4.1868 kJ/kg ? K

Others 1 ton of refrigeration 5 200 Btu/min 5 211 kJ/min 1 volt 5 1 watt per ampere

Constants Universal Gas Constant

Standard Atmospheric Pressure

8.314 kJ/kmol ? K R 5 • 1545 ft ? lbf /lbmol ? 8R 1.986 Btu /lbmol ? 8R

1.01325 bar 1 atm 5 • 14.696 lbf/in.2 760 mm Hg 5 29.92 in. Hg

Standard Acceleration of Gravity

Temperature Relations

g5 e

9.80665 m /s 32.174 ft/s2

2

T18R2 5 1.8 T1K 2 T18C2 5 T1K2 2 273.15 T18F2 5 T18R2 2 459.67

MEEN315-700 SUMMER 2020

Page 1 of 4

YOU MAY REMOVE FORMULA SHEETS FROM THE EXAM. First Law of Thermodynamics

E = Q − W

(energy balance for closed system)

dE =Q dt

(energy rate balance for closed system)

dE cv = Qcv dt

cv



i

i

i +

i +

i

V2 + 2

−

i

e

e

e+

V2 + 2

e

(energy rate balance for control

volume)

0 = Qcv



cv

i

V2 + 2

i

− e

e

e+

V2 + 2

(energy rate balance for control volume at steady

e

state)

0 = Qcv

  

cv

1 −

2) +

(V1 2 −V2 2 )  + g ( z1 − z2 ) 2 

(1-inlet, 1-exit control volume at

steady state)

Second Law of Thermodynamics 2  Q  S 2 − S1 =    + 1  T b

(closed system entropy balance)

Qj dS = + dt j Tj

(closed system entropy rate balance)

Qj dScv = +  mi dt j Tj i 0= j

Qj Tj

i

−

+  mi i −  i

e e

+ cv

(control volume entropy rate balance)

e

e e

+  cv

(control volume entropy rate balance at steady state)

e

Conservation of Mass

dmcv =  mi −  dt i e

e

m

i

i

=

e e

(Steady State)

MEEN315-700 SUMMER 2020

Page 2 of 4

Properties

E = KE + PE + U =

1 mV 2 + mgz + mu 2

h = u + pv

Thermodynamic Cylce

= =

Wcycle Qin

=

Wcycle

=

(Power cycle)

Qin

Qout Q = out Wcycle Wcycle

Qin Q = in Wcycle Wcycle

(Refrigeration cycle)

(Heat pump cycle)

Quality Equation

x=

mvapor

=

mliquid + mvapor

m vapor m

v = (1− x )vf + xvg = vf + x (vg − vf )

u =(1 − x) u f + xug = u f + x( u g − u f )

h = (1 − x )h f + xhg = h f + x (hg − h f )

s = (1 − x) sf + xsg = sf + x( sg − s f )

Isentropic Efficiencies

t =

Wt (Wt

actual s

(Turbine)

p =

ideal

Flow Relationships

m=

AV v

Boundary Work

W=



V2

V1

p  dV

W = p(V2 − V1)

(Constant Pressure)

(Wp Wp

s

ideal actual

(Pump or compressor)

MEEN315-700 SUMMER 2020

W=

p2V2 − p1V1 1− n

Page 3 of 4

(Polytropic Process, pVn = constant)

V  W = pV ln  2  V 1 

(Polytropic Process, n=1)

Ideal Gas Relationships

pv = RT

pV = nRT

pV = mRT

𝑐𝑝 (𝑇) = 𝑐𝑣 (𝑇) + 𝑅

𝑘=

𝑐𝑝 (𝑇)

𝑐𝑝 (𝑇) =

𝑐𝑣 (𝑇)

𝑘𝑅 𝑘−1

c v (T ) =

du dT

u = cv T (at constant cv)

c p (T ) =

dh dT

h = cp T (at constant cp) T2

s (T2 ,v 2 ) − s (T1 ,v1 ) =  c v (T ) T1

Z=

pv RT

pR =

p pc

T2

dT v + R ln 2 T v1

s (T2 , p 2 ) − s (T1 , p1 ) = s o (T2 ) − s o (T1 ) − R ln

TR =

T Tc

𝑅

𝑐𝑣 (𝑇) = 𝑘−1

s (T2 , p 2 ) − s (T1 , p1 ) =  c p (T ) T1

p2 p1

v'R =

v RTc / p c

Ideal Gas Isentropic Relationships

p2 pr 2 = p1 pr 1 T2  v1  =  T1  v2 

v 2 v r2 = v1 vr 1 k−1

T2  p2  =  T1  p1 

(k −1)/k

Solid / Liquid Relationships

h = u = cT Tds Relations

T  s = c ln  2   T1 

p2  v1  =  p1  v2 

k

dT p − R ln 2 T p1

MEEN315-700 SUMMER 2020

Tds = du + pdv

Page 4 of 4

Tds = dh − vdp

Rankine Cycle

𝜂=

𝑊󰇗 𝑛𝑒𝑡 󰇗 𝑄󰇗𝑖𝑛 𝑊󰇗𝑝/𝑚󰇗 /𝑚󰇗

Back work ratio (bwr) = 𝑊𝑡󰇗

Otto Cycle

𝜂=

𝑊𝑛𝑒𝑡 󰇗 𝑄𝑖𝑛

𝜂 = 1−

1

(cold air-standard basis) r = compression ratio,

𝑟 𝑘−1

𝑛𝑒𝑡 𝑤𝑜𝑟𝑘 𝑓𝑜𝑟 𝑜𝑛𝑒 𝑐𝑦𝑐𝑙𝑒

Mean effective pressure (mep) = 𝑑𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡 𝑣𝑜𝑙𝑢𝑚𝑒

Diesel Cycle

𝜂=

𝑊𝑛𝑒𝑡 𝑄𝑖𝑛

1

𝜂 = 1 − 𝑟 𝑘−1 [

ratio Mean effective pressure (mep) =

𝑟𝑐𝑘 −1

𝑘(𝑟𝑐 −1)

]

(cold air-standard basis) r = compression ratio, rc=cut off

𝑛𝑒𝑡 𝑤𝑜𝑟𝑘 𝑓𝑜𝑟 𝑜𝑛𝑒 𝑐𝑦𝑐𝑙𝑒 𝑑𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡 𝑣𝑜𝑙𝑢𝑚𝑒

Index to Tables in SI Units Table A-1 Table A-2 Table A-3 Table A-4 Table A-5 Table A-6 Table A-7 Table A-8 Table A-9 Table A-10 Table A-11 Table A-12 Table A-13 Table A-14 Table A-15 Table A-16 Table A-17 Table A-18 Table A-19 Table A-20 Table A-21 Table A-22 Table A-23 Table A-24 Table A-25 Table A-26 Table A-27

Atomic or Molecular Weights and Critical Properties of Selected Elements and Compounds 890 Properties of Saturated Water (Liquid–Vapor): Temperature Table 891 Properties of Saturated Water (Liquid–Vapor): Pressure Table 893 Properties of Superheated Water Vapor 895 Properties of Compressed Liquid Water 899 Properties of Saturated Water (Solid–Vapor): Temperature Table 900 Properties of Saturated Refrigerant 22 (Liquid–Vapor): Temperature Table 901 Properties of Saturated Refrigerant 22 (Liquid–Vapor): Pressure Table 902 Properties of Superheated Refrigerant 22 Vapor 903 Properties of Saturated Refrigerant 134a (Liquid–Vapor): Temperature Table 907 Properties of Saturated Refrigerant 134a (Liquid–Vapor): Pressure Table 908 Properties of Superheated Refrigerant 134a Vapor 909 Properties of Saturated Ammonia (Liquid–Vapor): Temperature Table 912 Properties of Saturated Ammonia (Liquid–Vapor): Pressure Table 913 Properties of Superheated Ammonia Vapor 914 Properties of Saturated Propane (Liquid–Vapor): Temperature Table 918 Properties of Saturated Propane (Liquid–Vapor): Pressure Table 919 Properties of Superheated Propane Vapor 920 Properties of Selected Solids and Liquids: cp, r, and k. 924 Ideal Gas Specific Heats of Some Common Gases 925 Variation of cp with Temperature for Selected Ideal Gases 926 Ideal Gas Properties of Air 927 Ideal Gas Properties of Selected Gases 929 Constants for the van der Waals, Redlich–Kwong, and Benedict–Webb–Rubin Equations of State 933 Thermochemical Properties of Selected Substances at 298 K and 1 atm 934 Standard Molar Chemical Exergy, ech (kJ/kmol), of Selected Substances at 298 K and p0 935 Logarithms to the Base 10 of the Equilibrium Constant K 936

889

890

Tables in SI Units

Table A-1

TABLE A-1

Atomic or Molecular Weights and Critical Properties of Selected Elements and Compounds p c vc RTc

Substance

Chemical Formula

Acetylene Air (equivalent) Ammonia

C2H2 — NH3

26.04 28.97 17.03

309 133 406

62.8 37.7 112.8

0.274 0.284 0.242

Argon Benzene Butane

Ar C6H6 C4H10

39.94 78.11 58.12

151 563 425

48.6 49.3 38.0

0.290 0.274 0.274

Carbon Carbon dioxide Carbon monoxide

C CO2 CO

12.01 44.01 28.01

— 304 133

— 73.9 35.0

— 0.276 0.294

Copper Ethane Ethanol

Cu C2H6 C2H5OH

63.54 30.07 46.07

— 305 516

— 48.8 63.8

— 0.285 0.249

Ethylene Helium Hydrogen

C2H4 He H2

28.05 4.003 2.016

283 5.2 33.2

51.2 2.3 13.0

0.270 0.300 0.304

Methane Methanol Nitrogen

CH4 CH3OH N2

16.04 32.04 28.01

191 513 126

46.4 79.5 33.9

0.290 0.220 0.291

Octane Oxygen Propane

C8H18 O2 C3H8

114.22 32.00 44.09

569 154 370

24.9 50.5 42.7

0.258 0.290 0.276

Propylene Refrigerant 12 Refrigerant 22

C3H6 CCl 2F2 CHClF2

42.08 120.92 86.48

365 385 369

46.2 41.2 49.8

0.276 0.278 0.267

Refrigerant 134a Sulfur dioxide Water

CF3CH2F SO2 H2O

102.03 64.06 18.02

374 431 647.3

40.7 78.7 220.9

0.260 0.268 0.233

M (kg/kmol)

Tc (K)

pc (bar)

Zc 5

Sources: Adapted from International Critical Tables and L. C. Nelson and E. F. Obert, Generalized Compressibility Charts, Chem. Eng., 61: 203 (1954).

891

Tables in SI Units TABLE A-2

Properties of Saturated Water (Liquid–Vapor): Temperature Table Specific Volume m3/kg

Internal Energy kJ/kg

Temp. 8C

Press. bar

Sat. Liquid vf 3 10 3

Sat. Vapor vg

Sat. Liquid uf

Sat. Vapor ug

.01 4 5 6 8

0.00611 0.00813 0.00872 0.00935 0.01072

1.0002 1.0001 1.0001 1.0001 1.0002

206.136 157.232 147.120 137.734 120.917

0.00 16.77 20.97 25.19 33.59

2375.3 2380.9 2382.3 2383.6 2386.4

10 11 12 13 14

0.01228 0.01312 0.01402 0.01497 0.01598

1.0004 1.0004 1.0005 1.0007 1.0008

106.379 99.857 93.784 88.124 82.848

42.00 46.20 50.41 54.60 58.79

15 16 17 18 19

0.01705 0.01818 0.01938 0.02064 0.02198

1.0009 1.0011 1.0012 1.0014 1.0016

77.926 73.333 69.044 65.038 61.293

20 21 22 23 24

0.02339 0.02487 0.02645 0.02810 0.02985

1.0018 1.0020 1.0022 1.0024 1.0027

25 26 27 28 29

0.03169 0.03363 0.03567 0.03782 0.04008

30 31 32 33 34 35 36 38 40 45

Enthalpy kJ/kg Sat. Liquid hf

Entropy kJ/kg ? K

Evap. h fg

Sat. Vapor hg

Sat. Liquid sf

Sat. Vapor sg

0.01 16.78 20.98 25.20 33.60

2501.3 2491.9 2489.6 2487.2 2482.5

2501.4 2508.7 2510.6 2512.4 2516.1

0.0000 0.0610 0.0761 0.0912 0.1212

9.1562 9.0514 9.0257 9.0003 8.9501

.01 4 5 6 8

2389.2 2390.5 2391.9 2393.3 2394.7

42.01 46.20 50.41 54.60 58.80

2477.7 2475.4 2473.0 2470.7 2468.3

2519.8 2521.6 2523.4 2525.3 2527.1

0.1510 0.1658 0.1806 0.1953 0.2099

8.9008 8.8765 8.8524 8.8285 8.8048

10 11 12 13 14

62.99 67.18 71.38 75.57 79.76

2396.1 2397.4 2398.8 2400.2 2401.6

62.99 67.19 71.38 75.58 79.77

2465.9 2463.6 2461.2 2458.8 2456.5

2528.9 2530.8 2532.6 2534.4 2536.2

0.2245 0.2390 0.2535 0.2679 0.2823

8.7814 8.7582 8.7351 8.7123 8.6897

15 16 17 18 19

57.791 54.514 51.447 48.574 45.883

83.95 88.14 92.32 96.51 100.70

2402.9 2404.3 2405.7 2407.0 2408.4

83.96 88.14 92.33 96.52 100.70

2454.1 2451.8 2449.4 2447.0 2444.7

2538.1 2539.9 2541.7 2543.5 2545.4

0.2966 0.3109 0.3251 0.3393 0.3534

8.6672 8.6450 8.6229 8.6011 8.5794

20 21 22 23 24

1.0029 1.0032 1.0035 1.0037 1.0040

43.360 40.994 38.774 36.690 34.733

104.88 109.06 113.25 117.42 121.60

2409.8 2411.1 2412.5 2413.9 2415.2

104.89 109.07 113.25 117.43 121.61

2442.3 2439.9 2437.6 2435.2 2432.8

2547.2 2549.0 2550.8 2552.6 2554.5

0.3674 0.3814 0.3954 0.4093 0.4231

8.5580 8.5367 8.5156 8.4946 8.4739

25 26 27 28 29

0.04246 0.04496 0.04759 0.05034 0.05324

1.0043 1.0046 1.0050 1.0053 1.0056

32.894 31.165 29.540 28.011 26.571

125.78 129.96 134.14 138.32 142.50

2416.6 2418.0 2419.3 2420.7 2422.0

125.79 129.97 134.15 138.33 142.50

2430.5 2428.1 2425.7 2423.4 2421.0

2556.3 2558.1 2559.9 2561.7 2563.5

0.4369 0.4507 0.4644 0.4781 0.4917

8.4533 8.4329 8.4127 8.3927 8.3728

30 31 32 33 34

0.05628 0.05947 0.06632 0.07384 0.09593

1.0060 1.0063 1.0071 1.0078 1.0099

25.216 23.940 21.602 19.523 15.258

146.67 150.85 159.20 167.56 188.44

2423.4 2424.7 2427.4 2430.1 2436.8

146.68 150.86 159.21 167.57 188.45

2418.6 2416.2 2411.5 2406.7 2394.8

2565.3 2567.1 2570.7 2574.3 2583.2

0.5053 0.5188 0.5458 0.5725 0.6387

8.3531 8.3336 8.2950 8.2570 8.1648

35 36 38 40 45

Temp. 8C

H2O

ersions: Pressure Conv a MP 0.1 = r 1 ba 2 = 10 kPa

892

Tables in SI Units

TABLE A-2

(Continued )

H2O

Specific Volume m3 /kg Temp. 8C

Press. bar

Sat. Liquid 3 vf 3 10

50 55 60 65 70

.1235 .1576 .1994 .2503 .3119

75 80 85 90 95

.3858 .4739 .5783 .7014 .8455

Internal Energy kJ/kg

Sat. Vapor vg

Sat. Liquid uf

Sat. Vapor ug

1.0121 1.0146 1.0172 1.0199 1.0228

12.032 9.568 7.671 6.197 5.042

209.32 230.21 251.11 272.02 292.95

2443.5 2450.1 2456.6 2463.1 2469.6

1.0259 1.0291 1.0325 1.0360 1.0397

4.131 3.407 2.828 2.361 1.982

313.90 334.86 355.84 376.85 397.88

Enthalpy kJ/kg Sat. Liquid hf

Entropy kJ/kg ? K

Evap. hfg

Sat. Vapor hg

Sat. Liquid sf

Sat. Vapor sg

209.33 230.23 251.13 272.06 292.98

2382.7 2370.7 2358.5 2346.2 2333.8

2592.1 2600.9 2609.6 2618.3 2626.8

.7038 .7679 .8312 .8935 .9549

8.0763 7.9913 7.9096 7.8310 7.7553

50 55 60 65 70

2475.9 2482.2 2488.4 2494.5 2500.6

313.93 334.91 355.90 376.92 397.96

2321.4 2308.8 2296.0 2283.2 2270.2

2635.3 2643.7 2651.9 2660.1 2668.1

1.0155 1.0753 1.1343 1.1925 1.2500

7.6824 7.6122 7.5445 7.4791 7.4159

75 80 85 90 95

Temp. 8C

100 110 120 130 140

1.014 1.433 1.985 2.701 3.613

1.0435 1.0516 1.0603 1.0697 1.0797

1.673 1.210 0.8919 0.6685 0.5089

418.94 461.14 503.50 546.02 588.74

2506.5 2518.1 2529.3 2539.9 2550.0

419.04 461.30 503.71 546.31 589.13

2257.0 2230.2 2202.6 2174.2 2144.7

2676.1 2691.5 2706.3 2720.5 2733.9

1.3069 1.4185 1.5276 1.6344 1.7391

7.3549 7.2387 7.1296 7.0269 6.9299

100 110 120 130 140

150 160 170 180 190

4.758 6.178 7.917 10.02 12.54

1.0905 1.1020 1.1143 1.1274 1.1414

0.3928 0.3071 0.2428 0.1941 0.1565

631.68 674.86 718.33 762.09 806.19

2559.5 2568.4 2576.5 2583.7 2590.0

632.20 675.55 719.21 763.22 807.62

2114.3 2082.6 2049.5 2015.0 1978.8

2746.5 2758.1 2768.7 2778.2 2786.4

1.8418 1.9427 2.0419 2.1396 2.2359

6.8379 6.7502 6.6663 6.5857 6.5079

150 160 170 180 190

200 210 220 230 240

15.54 19.06 23.18 27.95 33.44

1.1565 1.1726 1.1900 1.2088 1.2291

0.1274 0.1044 0.08619 0.07158 0.05976

850.65 895.53 940.87 986.74 1033.2

2595.3 2599.5 2602.4 2603.9 2604.0

852.45 897.76 943.62 990.12 1037.3

1940.7 1900.7 1858.5 1813.8 1766.5

2793.2 2798.5 2802.1 2804.0 2803.8

2.3309 2.4248 2.5178 2.6099 2.7015

6.4323 6.3585 6.2861 6.2146 6.1437

200 210 220 230 240

250 260 270 280 290

39.73 46.88 54.99 64.12 74.36

1.2512 1.2755 1.3023 1.3321 1.3656

0.05013 0.04221 0.03564 0.03017 0.02557

1080.4 1128.4 1177.4 1227.5 1278.9

2602.4 2599.0 2593.7 2586.1 2576.0

1085.4 1134.4 1184.5 1236.0 1289.1

1716.2 1662.5 1605.2 1543.6 1477.1

2801.5 2796.6 2789.7 2779.6 2766.2

2.7927 2.8838 2.9751 3.0668 3.1594

6.0730 6.0019 5.9301 5.8571 5.7821

250 260 270 280 290

85.81 112.7 145.9 186.5 220.9

1.4036 1.4988 1.6379 1.8925 3.155

0.02167 0.01549 0.01080 0.006945 0.003155

1332.0 1444.6 1570.3 1725.2 2029.6

2563.0 2525.5 2464.6 2351.5 2029.6

1344.0 1461.5 1594.2 1760.5 2099.3

1404.9 1238.6 1027.9 720.5 0

2749.0 2700.1 2622.0 2481.0 2099.3