American electricians' handbook

1.1 DIVISION 1 FUNDAMENTALS Useful Tables 1.2 Conversion Factors 1.9 Graphical Electrical Symbols 1.12 Principles of Electricity and Magnetism: Units . 1.21 Measuring, Testing, and Instruments . 1.70 Harmonics . 1.100 Source: AMERICAN ELECTRICIANS’ HANDBOOK Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. 1.2 USEFUL TABLES 1. Natural Trigonometric Functions Angle ( ␪ or lag angle), deg Sine (or reactive factor) Cosine (or power factor) Tangent Cotangent Secant Cosecant Angle ( ␪ or lag angle), deg 0 1 2 3 4 5 0.00000 0.01774 0.03490 0.05234 0.06976 0.08715 1.00000 0.99985 0.99939 0.99863 0.99756 0.99619 0.00000 0.01745 0.03492 0.05241 0.06993 0.08749 Infinite 57.290 28.636 19.081 14.301 11.430 1.0000 1.0001 1.0006 1.0014 1.0024 1.0038 Infinite 57.299 28.654 19.107 14.335 11.474 180 179 178 177 176 175 6 7 8 9 10 0.10453 0.12187 0.13917 0.15643 0.17365 0.99452 0.99255 0.99027 0.98769 0.98481 0.10510 0.12278 0.14054 0.15838 0.17633 9.5144 8.1443 7.1154 6.3137 5.6713 1.0055 1.0075 1.0098 1.0125 1.0154 9.5668 8.2055 7.1853 6.3924 5.7588 174 173 172 171 170 11 12 13 14 15 0.19081 0.20791 0.22495 0.24192 0.25882 0.98163 0.97815 0.97437 0.97029 0.96592 0.19438 0.21256 0.23087 0.24933 0.26795 5.1445 4.7046 4.3315 4.0108 3.7320 1.0187 1.0223 1.0263 1.0306 1.0353 5.2408 4.8097 4.4454 4.1336 3.8637 169 168 167 166 165 16 17 18 19 20 0.27564 0.29237 0.30902 0.32557 0.34203 0.96126 0.95630 0.95106 0.94552 0.93969 0.28674 0.30573 0.32492 0.34433 0.36397 3.4874 3.2708 3.0777 2.9042 2.7475 1.0403 1.0457 1.0515 1.0576 1.0642 3.6279 3.4203 3.2361 3.0715 2.9238 164 163 162 161 160 21 22 23 24 25 0.35837 0.37461 0.39073 0.40674 0.42262 0.93358 0.92718 0.92050 0.91354 0.90631 0.38386 0.40403 0.42447 0.44523 0.46631 2.6051 2.4751 2.3558 2.2460 2.1445 1.0711 1.0785 1.0864 1.0946 1.1034 2.7904 2.6695 2.5593 2.4586 2.3662 159 158 157 156 155 26 27 28 29 30 0.43837 0.45399 0.46947 0.48481 0.50000 0.89879 0.89101 0.88295 0.87462 0.86603 0.48773 0.50952 0.53171 0.55431 0.57735 2.0503 1.9626 1.8807 1.8040 1.7320 1.1126 1.1223 1.1326 1.1433 1.1547 2.2812 2.2027 2.1300 2.0627 2.0000 154 153 152 151 150 31 32 33 34 35 0.51504 0.52992 0.54464 0.55919 0.57358 0.85717 0.84805 0.83867 0.82904 0.81915 0.60086 0.62487 0.64941 0.67451 0.70021 1.6643 1.6003 1.5399 1.4826 1.4281 1.1666 1.1792 1.1924 1.2062 1.2208 1.9416 1.8871 1.8361 1.7883 1.7434 149 148 147 146 145 36 37 38 39 40 0.58778 0.60181 0.61566 0.62932 0.64279 0.80902 0.79863 0.78801 0.77715 0.76604 0.72654 0.75355 0.78128 0.80978 0.83910 1.3764 1.3270 1.2799 1.2349 1.1917 1.2361 1.2521 1.2690 1.2867 1.3054 1.7013 1.6616 1.6243 1.5890 1.5557 144 143 142 141 140 41 42 43 44 45 0.65606 0.66913 0.68200 0.69466 0.70711 0.75741 0.74314 0.73135 0.71934 0.70711 0.86929 0.90040 0.93251 0.96569 1.0000 1.1504 1.1106 1.0724 1.0355 1.0000 1.3250 1.3456 1.3673 1.3902 1.4142 1.5242 1.4945 1.4663 1.4395 1.4142 139 138 137 136 135 DIVISION 1 FUNDAMENTALS Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. 1.3 Natural Trigonometric Functions Angle ( ␪ or lag angle), deg Sine (or reactive factor) Cosine (or power factor) Tangent Cotangent Secant Cosecant Angle ( ␪ or lag angle), deg 46 47 48 49 50 0.71934 0.73135 0.74314 0.75471 0.76604 0.69466 0.68200 0.66913 0.65606 0.64279 1.0355 1.0724 1.1106 1.1504 1.1917 0.96569 0.93251 0.90040 0.86929 0.83910 1.4395 1.4663 1.4945 1.5242 1.5557 1.3902 1.3673 1.3456 1.3250 1.3054 134 133 132 131 130 51 52 53 54 55 0.77715 0.78801 0.79863 0.80902 0.81915 0.62932 0.61566 0.60181 0.58778 0.57358 1.2349 1.2799 1.3270 1.3764 1.4281 0.80978 0.78128 0.75355 0.72654 0.70021 1.5890 1.6243 1.6616 1.7013 1.7434 1.2867 1.2690 1.2521 1.2361 1.2208 129 128 127 126 125 56 57 58 59 60 0.82904 0.83867 0.84805 0.85717 0.86603 0.55919 0.54464 0.52992 0.51504 0.50000 1.4826 1.5399 1.6003 1.6643 1.7230 0.67451 0.64941 0.62487 0.60086 0.57735 1.7883 1.8361 1.8871 1.9416 2.0000 1.2062 1.1922 1.1792 1.1666 1.1547 124 123 122 121 120 61 62 63 64 65 0.87462 0.88295 0.89101 0.89879 0.90631 0.48481 0.46947 0.45399 0.43837 0.42262 1.8040 1.8807 1.9626 2.0503 2.1445 0.55431 0.53171 0.50952 0.48773 0.46631 2.0627 2.1300 2.2027 2.2812 2.3662 1.1433 1.1326 1.1223 1.1126 1.1034 119 118 117 116 115 66 67 68 69 70 0.91354 0.92050 0.92718 0.93358 0.93969 0.40674 0.39073 0.37461 0.35837 0.34202 2.2460 2.3558 2.4751 2.6051 2.7475 0.44523 0.42447 0.40403 0.38386 0.36397 2.4586 2.5593 2.6695 2.7904 2.9238 1.0946 1.0864 1.0785 1.0711 1.0642 114 113 112 111 110 71 72 73 74 75 0.94552 0.95106 0.95630 0.96126 0.96592 0.32557 0.30902 0.29237 0.27564 0.25882 2.9042 3.0777 3.2708 3.4874 3.7320 0.34433 0.32492 0.30573 0.28647 0.26795 3.0715 3.2361 3.4203 3.6279 3.8637 1.0576 1.0515 1.0457 1.0403 1.0353 109 108 107 106 105 76 77 78 79 80 0.97029 0.97437 0.97815 0.98163 0.98481 0.24192 0.22495 0.20791 0.19081 0.17365 4.0108 4.3315 4.7046 5.1445 5.6713 0.24933 0.23087 0.21256 0.19438 0.17633 4.1336 4.4454 4.8097 5.2408 5.7588 1.0306 1.0263 1.0223 1.0187 1.0154 104 103 102 101 100 81 82 83 84 85 0.98769 0.99027 0.99255 0.99452 0.99619 0.15643 0.13917 0.12187 0.10453 0.08715 6.3137 7.1154 8.1443 9.5144 11.430 0.15838 0.14054 0.12278 0.10510 0.08749 6.3924 7.1853 8.2055 9.5668 11.474 1.0125 1.0098 1.0075 1.0055 1.0038 99 98 97 96 95 86 87 88 89 90 0.99756 0.99863 0.99939 0.99985 1.00000 0.06976 0.05234 0.03490 0.01745 0.00000 14.301 19.081 28.634 57.290 Infinite 0.06993 0.05241 0.03492 0.01745 0.00000 14.335 19.107 28.654 57.299 Infinite 1.0024 1.0014 1.0006 1.0001 1.0000 94 93 92 91 90 DIVISION 1 FUNDAMENTALS Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. 1.4 DIVISION ONE 2. Fractions of Inch Reduced to Decimal Equivalents Halves 4ths 8ths 16ths 32ds 64ths Decimal equivalents Halves 4ths 8ths 16ths 32ds 64ths Decimal equivalents . . . . . . . . . . 1 ⁄ 16 . 1 ⁄ 32 . . . 1 ⁄ 64 3 ⁄ 64 5 ⁄ 64 0.015625 0.03125 0.046875 0.0625 0.078125 . . . . . . . . . . 9 ⁄ 16 . 17 ⁄ 32 . . . 33 ⁄ 64 35 ⁄ 64 37 ⁄ 64 0.515625 0.53125 0.546875 0.5625 0.578125 . . . . . . . 1 ⁄ 8 . . 3 ⁄ 32 . . . 5 ⁄ 32 7 ⁄ 64 9 ⁄ 64 0.09375 0.109375 0.125 0.140625 0.15625 . . . . . . . 5 ⁄ 8 . . 19 ⁄ 32 . . . 21 ⁄ 32 39 ⁄ 64 41 ⁄ 64 0.59375 0.609375 0.625 0.640625 0.65625 . . . . . . . . . . 3 ⁄ 16 . . . 7 ⁄ 32 . 11 ⁄ 64 13 ⁄ 64 15 ⁄ 64 0.171875 0.1875 0.203125 0.21875 0.234375 . . . . . . . . . . 11 ⁄ 16 . . . 23 ⁄ 32 . 43 ⁄ 64 45 ⁄ 64 47 ⁄ 64 0.671875 0.6875 0.703125 0.71875 0.734375 1 ⁄ 4 . . . . . . . . . 5 ⁄ 16 . . 9 ⁄ 32 . . 17 ⁄ 64 19 ⁄ 64 0.25 0.265625 0.28125 0.296875 0.3125 3 ⁄ 4 . . . . . . . . . 13 ⁄ 16 . . 25 ⁄ 32 . . 49 ⁄ 64 51 ⁄ 64 0.75 0.765625 0.78125 0.796875 0.8125 . . . . . . . . 3 ⁄ 8 . . 11 ⁄ 32 . . . 21 ⁄ 64 23 ⁄ 64 25 ⁄ 64 0.328125 0.34375 0.359375 0.375 0.390625 . . . . . . . . 7 ⁄ 8 . . 27 ⁄ 32 . . . 53 ⁄ 64 55 ⁄ 64 57 ⁄ 64 0.828125 0.84375 0.859375 0.875 0.890625 1 ⁄ 2 . . . . . . . . . . . . . . 7 ⁄ 16 13 ⁄ 32 . . . 15 ⁄ 32 . . 27 ⁄ 64 29 ⁄ 64 31 ⁄ 64 0.40625 0.421875 0.4375 0.453125 0.46875 0.484375 0.5 . . . . . . . . . . . . 15 ⁄ 16 29 ⁄ 32 . . . 31 ⁄ 32 . 59 ⁄ 64 61 ⁄ 64 63 ⁄ 64 0.90625 0.921875 0.9375 0.953125 0.96875 0.984375 3. In figuring discounts on electrical equipment, it is often necessary to ap- ply primary and secondary discounts. By using the values in Table 4, time and labor may be conserved. To find the net price, multiply the list or gross price by the multiplier from the table which corresponds to the discounts. EXAMPLE The discount on iron conduit may be quoted as 25 and 10 with 2 percent for cash in 10 days. To obtain the actual cost, 25 percent would be deducted from the list price, then 10 percent from that result, and finally 2 percent from the second result. If we assume that the list price of 1 ⁄ 2 -in conduit is $12 per 100 ft, its actual price with the 25, 10, and 2 percent discounts would be $12.00 Ϫ 0.25 ϫ $12.00 ϭ $12.00 Ϫ $3.00 ϭ $9.00 $9.00 Ϫ 0.10 ϫ $9.00 ϭ $9.00 Ϫ $0.90 ϭ $8.10 $8.10 Ϫ 0.02 ϫ $8.10 ϭ $8.10 Ϫ $0.16 ϭ $7.94 Therefore, the net cost of the conduit would be $7.94 per 100 ft. Now by using the multiplier from Table 4 corresponding to a primary discount of 25 percent and secondary discounts of 10 and 2 percent, which is 0.661, $12.00 ϫ 0.661 ϭ $7.94 This is the same result as that obtained by using the longer method. DIVISION 1 FUNDAMENTALS Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. FUNDAMENTALS 1.5 4. Table for Figuring Total Discount Multiplier by Combining Primary and Secondary Discounts Primary discount, percent Secondary discounts 2% 5% 10% 15% 5 and 2% 10 and 2% 10 and 5% Multiplier 0 5 10 11 12 0.980 0.931 0.882 0.872 0.862 0.950 0.902 0.855 0.845 0.836 0.900 0.855 0.810 0.801 0.792 0.850 0.807 0.765 0.756 0.748 0.931 0.884 0.838 0.829 0.819 0.882 0.838 0.794 0.785 0.776 0.855 0.812 0.769 0.761 0.752 13 14 15 16 17 0.853 0.843 0.833 0.823 0.813 0.826 0.817 0.807 0.798 0.788 0.783 0.774 0.765 0.756 0.747 0.740 0.731 0.722 0.714 0.705 0.810 0.801 0.791 0.782 0.773 0.767 0.758 0.750 0.741 0.732 0.744 0.735 0.727 0.718 0.710 18 19 20 25 30 0.803 0.794 0.784 0.735 0.686 0.779 0.770 0.760 0.712 0.665 0.738 0.729 0.720 0.675 0.630 0.697 0.688 0.680 0.638 0.595 0.763 0.754 0.745 0.698 0.652 0.723 0.714 0.705 0.661 0.617 0.701 0.692 0.684 0.641 0.598 35 40 45 50 55 0.637 0.588 0.539 0.490 0.441 0.617 0.570 0.522 0.475 0.427 0.585 0.540 0.495 0.450 0.405 0.552 0.510 0.468 0.425 0.382 0.605 0.559 0.512 0.465 0.419 0.573 0.529 0.485 0.441 0.397 0.556 0.513 0.470 0.428 0.385 60 65 70 0.392 0.343 0.294 0.380 0.333 0.285 0.360 0.315 0.270 0.340 0.298 0.255 0.372 0.326 0.279 0.353 0.309 0.265 0.342 0.299 0.256 DIVISION 1 FUNDAMENTALS Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. 1.6 DIVISION ONE 5. Multipliers for Computing Selling Prices Which Will Afford a Given Percentage Profit Percentage profit desired To obtain selling price, multiply actual cost (invoice cost ϩ freight) by the following value When per- centage profit is based on cost When per- centage profit is based on selling price Percentage profit desired To obtain selling price, multiply actual cost (invoice cost ϩ freight) by the following value When per- centage profit is based on cost When per- centage profit is based on selling price 5 6 7 8 9 10 1.05 1.06 1.07 1.08 1.09 1.10 1.053 1.064 1.075 1.087 1.100 1.111 36 37 38 39 40 41 1.36 1.37 1.38 1.39 1.40 1.41 1.563 1.588 1.613 1.640 1.667 1.695 11 12 13 14 15 1.11 1.12 1.13 1.14 1.15 1.124 1.136 1.149 1.163 1.176 42 43 45 46 47 1.42 1.43 1.45 1.46 1.47 1.725 1.754 1.818 1.852 1.887 16 17 18 19 20 1.16 1.17 1.18 1.19 1.20 1.190 1.204 1.220 1.235 1.250 48 49 50 52 54 1.48 1.49 1.50 1.52 1.54 1.923 1.961 2.000 2.084 2.174 21 22 23 24 25 1.21 1.22 1.23 1.24 1.25 1.267 1.283 1.299 1.316 1.334 56 58 60 62 64 1.56 1.58 1.60 1.62 1.64 2.272 2.381 2.500 2.631 2.778 26 27 28 29 30 1.26 1.27 1.28 1.29 1.30 1.352 1.370 1.390 1.409 1.429 66 68 70 72 74 1.66 1.68 1.70 1.72 1.74 2.941 3.126 3.333 3.572 3.847 31 32 33 34 35 1.31 1.32 1.33 1.34 1.35 1.450 1.471 1.493 1.516 1.539 76 78 80 90 100 1.76 1.78 1.80 1.90 2.00 4.168 4.545 5.000 10.000 Infinity DIVISION 1 FUNDAMENTALS Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. FUNDAMENTALS 1.7 6. Table Showing Percentage Net Profit Percentage markup above cost Percentage overhead 10% 12% 14% 16% 18% 20% 22% 24% Percentage net profit based on selling price for a given percentage overhead based on gross sales 10 15 20 25 30 Ϫ 0.90 3.05 6.67 10.00 13.08 Ϫ 2.90 1.05 4.67 8.00 11.08 Ϫ 4.90 Ϫ 0.95 2.67 6.00 9.08 Ϫ 6.90 Ϫ 2.95 0.67 4.00 7.08 Ϫ 8.90 Ϫ 4.95 Ϫ 1.33 2.00 5.08 Ϫ 10.90 Ϫ 6.95 Ϫ 3.33 0.00 3.08 Ϫ 12.90 Ϫ 8.95 Ϫ 5.33 Ϫ 2.00 1.08 Ϫ 14.90 Ϫ 10.95 Ϫ 7.33 Ϫ 4.00 Ϫ 0.92 33 1 ⁄ 3 35 40 45 50 15.00 15.93 18.57 21.00 23.33 13.00 13.93 16.57 19.00 21.33 11.00 11.93 14.57 17.00 19.33 9.00 9.93 12.57 15.00 17.33 7.00 7.93 10.57 13.00 15.33 5.00 5.93 8.57 11.00 13.33 3.00 3.93 6.57 9.00 11.33 1.00 1.93 4.57 7.00 9.33 55 60 65 70 75 25.50 27.50 29.40 31.18 32.85 23.50 25.50 27.40 29.18 30.85 21.50 23.50 25.40 27.18 28.85 19.50 21.50 23.40 25.18 26.85 17.50 19.50 21.40 23.18 24.85 15.50 17.50 19.40 21.18 22.85 13.50 15.50 17.40 19.18 20.85 11.50 13.50 15.40 17.18 18.85 80 85 90 95 100 34.45 35.95 37.37 38.72 40.00 32.45 33.95 35.37 36.72 38.00 30.45 31.95 33.37 34.72 36.00 28.45 29.95 31.37 32.72 34.00 26.45 27.95 29.37 30.72 32.00 24.45 25.95 27.37 28.72 30.00 22.45 23.95 25.37 26.72 28.00 20.45 21.95 23.37 24.72 26.00 NOTE Minus ( Ϫ ) values indicate a net loss. 7. Net profits. In figuring the net profit of doing business, Table 6 will be found to be very useful. The table may be used in three ways, as explained below. To Determine the Percentage of Net Profit on Sales That You are Making. Locate, at the top of one of the vertical columns, your percentage overhead—your ‘‘cost of doing business’’ in percentage of gross sales. Locate, at the extreme left of one of the horizontal columns, your percentage markup. The value at the inter- section of these two columns will be the percentage profit which you are making. EXAMPLE If your cost of doing business is 18 percent of your gross sales and you mark your goods at 35 percent above cost, your net profit is 7.93 percent of gross sales, obtained by carrying down from the column headed 18 percent and across from the 35 percent markup. To Determine the Percentage Overhead Cost of Doing Business That Would Yield a Certain Net Profit for a Given Markup Percentage. Locate in the extreme left- hand column the percentage that the selling price is marked above the cost price. Trace horizontally across from this value until the percentage net profit desired is located. At the top of the column in which the desired net profit is located will be found the percentage overhead cost of doing business that will allow this profit to be made. DIVISION 1 FUNDAMENTALS Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. 1.8 DIVISION ONE EXAMPLE If the markup is 45 percent and the profit desired is 15 percent, an overhead cost of doing business of 16 percent can be allowed, obtained by carrying across from the 45 percent markup to the 15 percent profit and finding that this column is headed by 16 percent overhead. To Determine the Percentage That Should Be Added to the Cost of Goods to Make a Certain Percentage Net Profit on Sales. Select the vertical column which shows the percentage cost of doing business at its top. Trace down the column until the desired percentage profit is found; from this value trace horizontally to the extreme left-hand column, in which will be found the markup percentage—the percentage to be added to the cost to afford the desired profit. EXAMPLE It is desired to make a 12 percent net profit when the cost of doing business is 20 percent of gross sales. Select the vertical column with 20 percent at its top. Trace down the column to locate the net profit desired of 12 percent. This will be partway between 11.00 and 13.33. Carrying across to the left from these values gives a required markup between 45 and 50, or approximately 47 percent. For values which do not appear in the table, approximate results can be obtained by estimation from the closest values in the table. If more accurate results are desired for these intermediate values, the following formulas may be used: or or 10,000 P ϭ 100 Ϫ h Ϫ 100 ϩ m 100(P ϩ h) m ϭ 100 Ϫ (P ϩ h) 10,000 h ϭ 100 Ϫ P Ϫ 100 ϩ m (1) (2) (3) where m ϭ percentage markup based on cost of goods, h ϭ percentage overhead based on gross sales, and P ϭ percentage net profit based on selling price. If you sell your goods at the retail list prices set by the manufacturers, you can use the table by converting the trade discount which you receive to an equivalent percentage markup, according to the following table: Manufacturer’s Discount Equivalent per- centage Markup Manufacturer’s Discount Equivalent per- centage Markup 10 15 20 25 30 11 17 1 ⁄ 2 25 33 1 ⁄ 3 43 35 40 45 50 54 66 2 ⁄ 3 81 3 ⁄ 4 100 Intermediate values may be calculated from the following formula: 100Q m ϭ (4) 100 Ϫ Q where m ϭ percentage markup based on cost of goods and Q ϭ manufacturer’s discount. DIVISION 1 FUNDAMENTALS Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. FUNDAMENTALS 1.9 CONVERSION FACTORS (Standard Handbook for Electrical Engineers) These factors were calculated with a double-length slide rule and checked with those given by Carl Hering in his ‘‘Conversion Tables.’’ 8. Length 1 mil ϭ 0.0254 mm ϭ 0.001 in 1mm ϭ 39.37 mils ϭ 0.03937 in 1cm ϭ 0.3937 in ϭ 0.0328 ft 1in ϭ 25.4 mm ϭ 0.083 ft ϭ 0.0278 yd ϭ 2.54 cm 1ft ϭ 304.8 mm ϭ 12 in ϭ 0.333 yd ϭ 0.305 m 1yd ϭ 91.44 cm ϭ 36 in ϭ 3ft ϭ 0.914 m 1m ϭ 39.37 in ϭ 3.28 ft ϭ 1.094 yd 1km ϭ 3281 ft ϭ 1094 yd ϭ 0.6213 mi 1mi ϭ 5280 ft ϭ 1760 yd ϭ 1609 m ϭ 1.609 km 9. Surface 1 cmil ϭ 0.7854 mil 2 ϭ 0.0005067 mim 2 ϭ 0.0000007854 in 2 1 mil 2 ϭ 1.273 cmil ϭ 0.000645 mm 2 ϭ 0.000001 in 2 1mm 2 ϭ 1973 cmil ϭ 1550 mil 2 ϭ 0.00155 in 2 1cm 2 ϭ 197,300 cmil ϭ 0.155 in 2 ϭ 0.00108 ft 2 1in 2 ϭ 1,273,240 cmil ϭ 6.451 cm 2 ϭ 0.0069 ft 2 1ft 2 ϭ 929.03 cm 2 ϭ 144 in 2 ϭ 0.1111 yd 2 ϭ 0.0929 m 2 1yd 2 ϭ 1296 in 2 ϭ 9ft 2 ϭ 0.8361 m 2 ϭ 0.000207 acre 1m 2 ϭ 1550 in 2 ϭ 10.7 ft 2 ϭ 1195 yd 2 ϭ 0.000247 acre 1 acre ϭ 43,560 ft 2 ϭ 4840 yd 2 ϭ 4047 m 2 ϭ 0.4047 ha ϭ 0.004047 km 2 ϭ 0.001562 mi 2 1mi 2 ϭ 27,880,000 ft 2 ϭ 3,098,000 yd 2 ϭ 2,590,000 m 2 ϭ 640 acres ϭ 2.59 km 2 10. Volume 1 cmil ⅐ ft ϭ 0.0000094248 in 3 1cm 3 ϭ 0.061 in 3 ϭ 0.0021 pt (liquid) ϭ 0.0018 pt (dry) 1in 3 ϭ 16.39 cm 3 ϭ 0.0346 pt (liquid) ϭ 0.0298 pt (dry) ϭ 0.0173 qt (liquid) ϭ 0.0148 qt (dry) ϭ 0.0164 L or dm 3 ϭ 0.0036 gal ϭ 0.0005787 ft 3 1 pt (liquid) ϭ 473.18 cm 3 ϭ 28.87 in 3 1 pt (dry) ϭ 550.6 cm 3 ϭ 33.60 in 3 1 qt (liquid) ϭ 946.36 cm 3 ϭ 57.75 in 3 ϭ 8 gills (liquid) ϭ 2 pt (liquid) ϭ 0.94636 Lordm 3 ϭ 0.25 gal 1 liter (L) ϭ 1000 cm 3 ϭ 61.025 in 3 ϭ 2.1133 pt (liquid) ϭ 1.8162 pt (dry) ϭ 0.908 qt (dry) ϭ 0.2642 gal (liquid) ϭ 0.03531 ft 3 1 qt (dry) ϭ 1101 cm 3 ϭ 67.20 in 3 ϭ 2 pt (dry) ϭ 0.03889 ft 3 1 gal ϭ 3785 cm 3 ϭ 231 in 3 ϭ 32 gills ϭ 8pt ϭ 4 qt (liquid) ϭ 3.785 L ϭ 0.1337 ft 3 ϭ 0.004951 yd 3 DIVISION 1 FUNDAMENTALS Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. 1.10 DIVISION ONE 1ft 3 ϭ 28,317 cm 3 ϭ 1728 in 3 ϭ 59.84 pt (liquid) ϭ 51.43 pt (dry) ϭ 29.92 qt (liquid) ϭ 28.32 L ϭ 25.71 qt (dry) ϭ 7.48 gal ϭ 0.03704 yd 3 ϭ 0.02832 m 3 or stere 1yd 3 ϭ 46.656 in 3 ϭ 27 ft 3 ϭ 0.7646 m 3 or stere 1m 3 ϭ 61,023 in 3 ϭ 1001 L ϭ 35.31 ft 3 ϭ 1.308 yd 3 11. Weight 1mg ϭ 0.01543 gr ϭ 0.001 g 1gr ϭ 64.80 mg ϭ 0.002286 oz (avoirdupois) 1g ϭ 15.43 gr ϭ 0.03527 oz (avoirdupois) ϭ 0.002205 lb 1 oz (avoirdupois) ϭ 437.5 gr ϭ 28.35 g ϭ 16 drams (avoirdupois) ϭ 0.0625 lb 1lb ϭ 7000 gr ϭ 453.6 g ϭ 256 drams ϭ 16 oz ϭ 0.4536 kg 1kg ϭ 15,432 gr ϭ 35.27 oz ϭ 2.205 lb 1 ton (short) ϭ 2000 lb ϭ 907.2 kg ϭ 0.8928 ton (long) 1 ton (long) ϭ 2240 lb ϭ 1.12 tons (short) ϭ 1.016 tons (metric) 12. Energy Torque units should be distinguished from energy units: thus, foot pound and kilogram-meter for energy, and pound-foot and meter-kilogram for torque (see Sec. 67 for further information on torque). 1ft ⅐ lb ϭ 13,560,000 ergs ϭ 1.356 J ϭ 0.3239 g ⅐ cal ϭ 0.1383 kg ⅐ m ϭ 0.001285 Btu ϭ 0.0003766 Wh ϭ 0.0000005051 hp ⅐ h 1kg ⅐ m ϭ 98,060,000 ergs ϭ 9,806 J ϭ 7.233 ft ⅐ lb ϭ 2.34 g ⅐ cal ϭ 0.009296 Btu ϭ 0.002724 Wh ϭ 0.000003704 hp ⅐ h (metric) 1 Btu ϭ 1055 J ϭ 778.1 ft ⅐ lb ϭ 252 g ⅐ cal ϭ 107.6 kg ⅐ m ϭ 0.5555 lb Celsius heat unit ϭ 0.2930 Wh ϭ 0.252 kg ⅐ cal ϭ 0.0003984 hp ⅐ h (metric) ϭ 0.0003930 hp ⅐ h 1Wh ϭ 3600 J ϭ 2,655.4 ft ⅐ lb ϭ 860 g ⅐ cal ϭ 367.1 kg ⅐ m ϭ 3.413 Btu ϭ 0.001341 hp ⅐ h 1hp ⅐ h ϭ 2,684,000 J ϭ 1,980,000 ft ⅐ lb ϭ 273,700 kg ⅐ cm ϭ 745.6 Wh 1 kWh ϭ 2,655,000 ft ⅐ lb ϭ 367,100 kg ⅐ m ϭ 1.36 hp ⅐ h (metric) ϭ 1.34 hp ⅐ h 13. Power 1g ⅐ cm/s ϭ 0.00009806 W 1ft ⅐ lb/min ϭ 0.02260 W ϭ 0.00003072 hp (metric) ϭ 0.00000303 hp 1W ϭ 44.26 ft ⅐ lb/min ϭ 6.119 kg ⅐ m/min ϭ 0.001341 hp 1hp ϭ 33,000 ft ⅐ lb/min ϭ 745.6 W ϭ 550 ft ⅐ lb/s ϭ 76.04 kg ⅐ m/s ϭ 1.01387 hp (metric) 1kW ϭ 44,256.7 ft ⅐ lb/min ϭ 101.979 kg ⅐ m/s ϭ 1.3597 hp (metric) ϭ 1.341 hp ϭ 1000 W 14. Resistivity 1 ⍀ /cmil ⅐ ft ϭ 0.7854 ⍀ /mil 2 ⅐ ft ϭ 0.001662 ⍀ /mm 2 ⅐ m ϭ 0.0000001657 ⍀ / cm 3 ϭ 0.00000006524 ⍀ /in 3 DIVISION 1 FUNDAMENTALS Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. . . 1.100 Source: AMERICAN ELECTRICIANS’ HANDBOOK Downloaded from Digital Engineering Library @ McGraw-Hill. secondary discounts. By using the values in Table 4, time and labor may be conserved. To find the net price, multiply the list or gross price by the multiplier