Engine Power Rating
A gasoline-powered engine produces a peak output of 10 hp. Express the given power P in the SI.
Approach
As listed in Table 3.5
Certain Derived Units in the USCS
| Quantity | Derived Unit | Abbreviation | Definition |
| Length | mil | mil | 1 mil = 0.001 in. |
| inch | in. | 1 in. = 0.0833 ft | |
| mile | mi | 1 mi = 5280 ft | |
| Volume | gallon | gal | 1 gal = 0.1337 ft^3 |
| Mass | slug | slug | 1 slug = 1 (lb . S^2)/ft |
| pound-mass | lbm | 1 lbm = 3.1081 \times 10^{-2}(lb s^{2})/ft | |
| Force | ounce | oz | 1 oz = 0.0625 lb |
| ton | ton | 1 ton = 2000 lb | |
| Torque, or moment of a force | foot-pound | ft · lb | — |
| Pressure or stress | pound/inch^2 | psi | 1 psi = 1 lb/in^2 |
| Energy, work, or heat | foot-pound | ft · lb | — |
| British thermal unit | Btu | 1 Btu = 778.2 ft . lb | |
| Power | horsepower | hp | 1 hp = 550 (ft . lb)/s |
| Temperature | degree Fahrenheit | °F | °F = °R-459.67 |
| Although a change in temperature of 1° Rankine also equals a change of 1 °F, numerical , numerical values are converted using the formula. | |||
for derived units in the USCS, the abbreviation “hp” refers to horsepower. The SI unit for power is the watt (W).The final row of Table 3.6
Table 3.6 Conversion Factors between Certain Quantities in the USCS and SI
| Quantity | Conversion |
| Length | 1 in. = 25.4 mm |
| 1 in. = 0.0254 m | |
| 1 ft = 0.3048 m | |
| 1 mi = 1.609 km | |
| 1 mm = 3.9370 ×10^{-2} in. | |
| 1 m = 39.37 in. | |
| 1 m = 3.2808 ft | |
| 1 km = 0.6214 mi | |
| Area | 1 in^2 = 645.16 mm^2 |
| 1 ft^2 = 9.2903 × 10^{-2} m^2 | |
| 1 mm^2 = 1.5500 × 10^{-3 }in^2 | |
| 1 m^2 = 10.7639 ft^2 | |
| Volume | 1 ft^3 = 2.832 × 10^{-2} m^3 |
| 1 ft^3 = 28.32 L | |
| 1 gal = 3.7854 × 10^{-3} m^3 | |
| 1 gal = 3.7854 L | |
| 1 m^3 = 35.32 ft^3 | |
| 1 L = 3.532 × 10^{-2} ft^3 | |
| 1 m^3 = 264.2 gal | |
| 1 L = 0.2642 gal | |
| Mass | 1 slug = 14.5939 kg |
| 1 lbm = 0.45359 kg | |
| 1 kg = 6.8522 × 10^{-2} slugs | |
| 1 kg = 2.2046 lbm | |
| Force | 1 lb = 4.4482 N |
| 1 N = 0.22481 lb | |
| Pressure or stress | 1 psi = 6895 Pa |
| 1 psi = 6.895 kPa | |
| 1 Pa = 1.450 × 10^{-4 }psi | |
| 1 kPa = 0.1450 psi | |
| Work, energy, or heat | 1 ft · lb = 1.356 J |
| 1 Btu = 1055 J | |
| 1 J = 0.7376 ft · lb | |
| 1 J = 9.478 × 10^{-4} Btu | |
| Power | 1 (ft · lb)/s = 1.356 W |
| 1 hp = 0.7457 kW | |
| 1 W = 0.7376 (ft · lb)/s | |
| 1 kW = 1.341 hp |
lists the conversions for power, and we read off the factor 1 hp = 0.7457 kW. Here the “kilo” prefix in Table 3.3
Table 3.3 Order-of-Magnitude Prefixes in the SI
| Name Symbol Multiplicative Factor | ||
| tera | T | 1,000,000,000,000 = 10^{12} |
| giga | G | 1,000,000,000 = 10^9 |
| mega | M | 1,000,000 = 10^6 |
| kilo | k | 1000 = 10^3 |
| hecto | h | 100 = 10^2 |
| deca | da | 10 = 10^1 |
| deci | d | 0.1 = 10^{-1} |
| centi | c | 0.01 = 10^{-2} |
| milli | m | 0.001 = 10^{-3} |
| micro | μ | 0.000,001 = 10^{-6} |
| nano | n | 0.000,000,001 = 10^{-9} |
| pico | p | 0.000,000,000,001 = 10^{-12} |
denotes a multiplier of 1000.
