Control Systems PE

The friction factor f must be determined from the Moody diagram or Colebrook equation using Reynolds number and relative roughness (ε/D). Don't confuse this with the Fanning friction factor, which is 1/4 of the Darcy friction factor. Always verify units are consistent throughout the calculation.

Always verify that flow conditions are laminar and soil is saturated. Pay attention to hydraulic conductivity units - often given as cm/day or ft/day and must be converted. The hydraulic gradient (Δh/L) is dimensionless. Cross-sectional area is perpendicular to flow direction.

First-order kinetics appears frequently in environmental and chemical PE problems. Remember that the rate constant k must have units of 1/time to match your time units. When solving for time or rate constant, you'll need natural logarithms. The half-life relationship t₁/₂ = 0.693/k is often useful.

Most fundamental equation in structural analysis. Watch units carefully - stress and modulus must be in same units. Often appears in combined problems with deflection equations. Know typical E values for common materials.

CRITICAL: Manning's equation requires different constants for SI (k=1) and English (k=1.49) units. Always verify which unit system you're using. The equation appears frequently in drainage design and channel analysis problems. Remember that hydraulic radius R = Area/Wetted Perimeter, not the geometric radius.