Engineering reference cards
Single-page printable cheat sheets for the values engineers look up over and over — roughness coefficients, discharge coefficients, curve numbers, loss factors, and more. Every card names the source equation and cites a reference, and prints clean on one letter page. No login, no paywall.
Manning's n
Roughness coefficient — concrete to natural streams to floodplains
Hazen-Williams C
Pipe roughness for water mains — new vs. aged values
Runoff Coefficients (C)
Rational Method C by land use, surface, slope, frequency
Curve Numbers (CN)
NRCS / TR-55 CN by land use & hydrologic soil group, with HSG & ARC
Weir Coefficients (Cd)
Sharp-crested, broad-crested, V-notch, ogee, Cipolletti
Tc Methods Compared
Kirpich vs. NRCS Lag vs. TR-55 segmental vs. FAA
Minor Loss Coefficients (K)
Fittings, valves, bends, entrances & exits — h = K·V²/2g
Pipe Roughness (ε)
Absolute roughness by material for Darcy-Weisbach / Moody
Culvert Entrance Loss (Ke)
HDS-5 inlet coefficients — concrete pipe, CMP, box culvert
HDS-5 Inlet Control Coefficients (K, M, c, Y)
Table 9 / A.1 constants for every culvert shape & inlet, with the three equations
SCS Storm Distributions
Type I, IA, II, III 24-hr curves & where each applies
Open Channel Geometry
A, P, R, T formulas by shape + best hydraulic section
Orifice Coefficients (Cd)
Outlet & riser Cd — Q = Cd·A·√(2gh)
Hydraulic Jump
Froude, sequent depth, energy loss, jump types
Riprap Sizing
Isbash / HEC-11 D50, gradation, thickness, filter
Specific Energy & Critical Depth
E = y + V²/2g, critical depth, alternate depths
Storm Sewer Design Criteria
Velocity, slope, n, pipe size, cover, full-flow capacity
Stokes Settling Velocity
Particle settling, overflow rate, Type I settling
Bridge Scour Equations
HEC-18 CSU & Froehlich pier scour, Laursen contraction, K-factors
Dam Breach Parameters
Froehlich, MacDonald & Von Thun equations compared
Water Properties by Temperature
Density, specific weight, viscosity & vapor pressure, SI + US
Reynolds Number Regimes
Laminar/turbulent thresholds + water viscosity
Fitting Equivalent Lengths (L/D)
Crane TP-410 L/D ratios + equivalent feet of pipe by diameter
Unit Weights of Materials
Water, concrete, steel, asphalt, soils — pcf & kN/m³
Presumptive Bearing Values
IBC Table 1806.2 — vertical, lateral & sliding by soil class
Rebar Development Length
ACI 318 simplified ld, Gr60 #3–#11, top-bar & splice factors
Design Rainfall / Atlas 14
PFDS workflow, coverage by state, depth ↔ intensity
USCS Soil Classification
ASTM D2487 group symbols, Cu/Cc, A-line, AASHTO cross-walk
Soil Permeability (k)
k by USCS group, unit conversions, Hazen, test ranges, HSG Ksat
Permissible Velocity & Shear
Channel lining limits — τ = γdS, HEC-15 shear, grass & RECP
Pipe Sizes & Actual ID
Sch 40/80, SDR & DR classes, DIP OD, RCP D-loads, CMP
Rational Method (Q = CiA)
Q = CiA in US and SI, frequency adjustment, composite C, and the limits
Fan & Pump Affinity Laws
Speed, diameter and density relations for flow, head and power
Vertical Curve K Values
AASHTO crest & sag rates by design speed; L = KA, drainage cap
Bearing Capacity Factors
Terzaghi & Meyerhof/Vesić Nc, Nq, Nγ vs friction angle
Hazen-Williams Equation
Every form & unit constant; validity limits and exponent pitfalls
Rebar Sizes & Areas
#3–#18 diameter, area, weight; area/ft by spacing; hooks & cover
How these differ from the calculators
The calculators solve a specific equation for your inputs and print with a PE stamp block. These reference cards are the lookup tables behind them — the coefficient values, gradation limits, and design criteria you reach for first. Print one, tape it to the monitor, and skip digging through Chow or the TR-55 appendix every time. Each card cites where its values come from.