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Twelve-line unit pad: a rod stress, a pipe flow, a car's kinetic energy and the head of one atmosphere, every factor from NIST SP 811

Tool	Unit Calculator Pad
Source	Thompson, A., and Taylor, B. N. (2008). Guide for the Use of the International System of Units (SI). NIST Special Publication 811, National Institute of Standards and Technology, Gaithersburg, MD. Appendix B.8 (conversion factors: foot, inch, pound, pound-force, psi, gallon, mile, Btu, horsepower, degree Fahrenheit interval) and Section B.7 (rounding).
Level	Undergraduate

Problem

On one scratch pad: a tie rod carries 12 kN over 0.5 in², find its stress in MPa and ksi; 250 US gal/min flows through a 2-inch pipe, find the velocity in ft/s; a 3,000-lbm car travels at 60 mi/h, find its kinetic energy in Btu and ft·lbf; one standard atmosphere (14.696 psi) is to be expressed as a head of water in ft; a length of 3 ft + 4 in is covered at 2 m/s, find the time; and convert 60 mi/h to ft/s. Every unit is reduced to the SI base units, each operation is checked dimensionally and the results are named by the unit dictionary.

Inputs to Enter

Pad lines: F = 12 kN; A = 0.5 in^2; sigma = F / A in MPa; sigma -> ksi; Q = 250 gal/min; v = Q / (pi * (2 in)^2 / 4) in ft/s; E_k = 0.5 * 3000 lbm * (60 mi/h)^2 in Btu; E_k -> ft-lbf; h = 14.696 psi / (1000 kg/m^3 * g_0) in ft; L = 3 ft + 4 in; t = L / (2 m/s); 60 mi/h in ft/s
Digits 5; Show steps off

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Answers

sigma = 12,000 N / (0.5 × 0.0254² m²) = 37.200 MPa = 5.3954 ksi (pint 37.2000744 MPa, 5.395414634 ksi)
Q = 250 × 231 in³ / 60 s = 0.015773 m³/s = 33.420 cfm; v = Q / (π (0.0508 m)²/4) = 7.7819 m/s = 25.531 ft/s (handbook rule 0.4085 Q/d² = 25.53 ft/s)
E_k = ½ × 3,000 × 0.45359237 kg × (26.8224 m/s)² = 489.50 kJ (dictionary name kN-m, also kJ) = 463.96 Btu (IT, 1,055.056 J) = 361,036 ft·lbf
h = 14.696 × 6,894.757 Pa / (1,000 kg/m³ × 9.80665 m/s²) = 10.332 m = 33.899 ft of water
L = 0.9144 + 0.1016 = 1.0160 m = 40.000 in; t = 1.016 m / (2 m/s) = 0.50800 s; 60 mi/h = 26.822 m/s = 88.000 ft/s exactly

Notes

The tool's default pad is this case; press Submit. Every value is checked in test_unit_calculator.php (227 checks) against the SP 811 Appendix B.8 factors, closed forms from the exact definitions (1 ft = 0.3048 m, 1 lb = 0.453 592 37 kg, 1 gal = 231 in³, g_n = 9.806 65 m/s²) and an independent pint 0.24.4 computation (References/Unit-Calculator/pint_check.py); pint prints 463.95596 Btu with the rounded 1,055.056 J, the tool 463.95602 with the exact IT Btu.