Distinguishing Pound-Force from Pound-Mass

In the U.S. Customary System (USCS), it is critical to distinguish between pound-force ( $lbf$lbf) and pound-mass ( $lbm$lbm).

Force Unit Conversion Factor ( gcg_cgc​):
$g_c$gc​ is used to maintain unit consistency in equations involving mass and force in USCS.

$$g_c = 32.174 \, \frac{lbm\cdot ft}{lbf\cdot sec^2}$$gc​=32.174lbf⋅sec2lbm⋅ft​

Key Engineering Equations in USCS:

• Newton’s Second Law: $F = \frac{ma}{g_c}$F=gc​ma​ where $F$F is in $lbf$lbf, $m$m is in $lbm$lbm, and $a$a is in $ft/sec^2$ft/sec2.
• Kinetic Energy: $KE = \frac{mv^2}{2g_c}$KE=2gc​mv2​ (Units: $ft\cdot lbf$ft⋅lbf)
• Potential Energy: $PE = \frac{mgh}{g_c}$PE=gc​mgh​ (Units: $ft\cdot lbf$ft⋅lbf)
• Fluid Pressure: $p = \frac{\rho gh}{g_c}$p=gc​ρgh​ (Units: $lbf/ft^2$lbf/ft2)
• Specific Weight: $SW = \frac{\rho g}{g_c}$SW=gc​ρg​ (Units: $lbf/ft^3$lbf/ft3)
• Shear Stress: $\tau = \left(\frac{\mu}{g_c}\right)\left(\frac{dv}{dy}\right)$τ=(gc​μ​)(dydv​) (Units: $lbf/ft^2$lbf/ft2)

Note: Do not confuse gcg_cgc​ (conversion factor) with ggg (local acceleration due to gravity, e.g., 9.807 m/s29.807 \, m/s^29.807m/s2 or 32.174 ft/sec232.174 \, ft/sec^232.174ft/sec2).

Significant Figures Rules

1. Non-zero digits: Always significant.
2. Zeros between non-zeros: Always significant.
3. Leading Zeros: Never significant.
4. Trailing Zeros: Significant if a decimal point is present.
5. Addition/Subtraction: Result matches the least number of decimal places in inputs.
6. Multiplication/Division: Result matches the least number of total significant figures in inputs.
7. Engineering Convention: Retain $3-4$3−4 significant digits in final results.

Fundamental Constants and Gas Constants

• Universal Gas Constant ( Rˉ\bar{R}Rˉ):
  • Metric: $8,314 \, J/(kmol \cdot K)$8,314J/(kmol⋅K) or $8.314 \, kPa \cdot m^3/(kmol \cdot K)$8.314kPa⋅m3/(kmol⋅K)
  • USCS: $1,545 \, ft\cdot lbf/(lb \, mole \cdot {}^\circ R)$1,545ft⋅lbf/(lbmole⋅∘R) or $0.08206 \, L\cdot atm/(mole \cdot K)$0.08206L⋅atm/(mole⋅K)
• Standard Gravity ( ggg): $9.807 \, m/s^2$9.807m/s2 (Metric) or $32.174 \, ft/sec^2$32.174ft/sec2 (USCS).
• Speed of Light ( ccc): $299,792,458 \, m/s$299,792,458m/s.
• Electron Charge ( eee): $1.6022 \times 10^{-19} \, C$1.6022×10−19C.