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Open CalculatorAll Civil: Water Resources and Environmental PE Equations (39)
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Bernoulli (head form)
Total head equality (simplified)
intermediateHigh Frequency -
Chick–Watson Inactivation (log10)
Estimate log inactivation with n≈1.
intermediateHigh Frequency -
First-Order Decay
Residual decay over time.
basicHigh Frequency -
Continuity
Discharge from area and velocity.
basicHigh Frequency -
Critical Depth (rectangular)
Critical depth from unit discharge q = Q/b.
basicHigh Frequency -
Disinfection CT (baffled basin)
Computed CT using T10 = BF·V/Q.
intermediateHigh Frequency -
Darcy–Weisbach Headloss
Headloss due to friction.
intermediateHigh Frequency -
Detention Time
Hydraulic residence time.
basicHigh Frequency -
Energy Slope
Friction slope from headloss and length.
basicHigh Frequency -
F/M Ratio
Food-to-microorganism loading.
intermediateHigh Frequency -
Froude Number (rectangular)
Flow regime indicator (sub/supercritical).
basicHigh Frequency -
Hazen-Williams Head Loss (hf)
Head loss in pressure pipes using selected material C value.
intermediateHigh Frequency -
Filter Loading Rate (HLR)
Hydraulic loading on filters.
basicHigh Frequency -
Water Hammer (head rise)
Joukowsky equation: surge head due to velocity change.
intermediate -
Pounds per Day
Convert mg/L and MGD to lb/day.
basicHigh Frequency -
Manning's Velocity
Average velocity in an open channel.
intermediateHigh Frequency -
Manning's Discharge
Discharge in an open channel.
intermediateHigh Frequency -
Minor Loss (K)
Headloss due to a fitting, valve, entrance, exit, etc.
basicHigh Frequency -
MLSS from MLVSS
Estimate MLSS using volatile fraction.
basic -
NPSH Available
Net Positive Suction Head available.
intermediateHigh Frequency -
Orifice Equation
Flow through an orifice or culvert entrance control
basicHigh Frequency -
Orifice (free discharge)
Flow through a sharp-edged free orifice.
basicHigh Frequency -
Orifice (submerged)
Submerged orifice using differential head.
basicHigh Frequency -
Parshall Flume (generic)
Generic free-flow form Q = C h^n (enter C and n for your flume).
intermediate -
Pump Affinity Laws
Flow, head and power scaling with speed or impeller diameter ratio.
intermediateHigh Frequency -
Pump Power (hp)
Wire-to-water horsepower.
basicHigh Frequency -
Pump Power (kW)
Metric power from flow/head.
basicHigh Frequency -
Rational Method Peak Flow
Peak runoff rate for small watersheds
basicHigh Frequency -
Rational Method
Peak runoff rate.
basicHigh Frequency -
Solids Loading Rate (clarifier)
Mass flux of solids to clarifier.
basicHigh Frequency -
Surface Overflow Rate (SOR)
Clarifier/sed tank overflow rate.
basicHigh Frequency -
Solids Retention Time (approx.)
SRT neglecting effluent solids (quick check).
intermediateHigh Frequency -
Stokes Settling Velocity
Terminal settling in laminar regime.
intermediateHigh Frequency -
Swamee–Jain (f)
Explicit friction factor for turbulent flow.
intermediateHigh Frequency -
Venturi Meter (pipe)
Discharge from venturi differential.
intermediate -
Broad-Crested Weir
Empirical broad-crested weir equation.
basicHigh Frequency -
Weir Loading
Overflow per unit weir length.
basicHigh Frequency -
Rectangular Sharp-Crested Weir
Standard fully contracted rectangular weir.
basicHigh Frequency -
V-Notch Weir (general)
V-notch with included angle θ (degrees).
intermediateHigh Frequency
Frequently Asked Questions
How do I use Bernoulli (head form) on the PE exam?
Always check units carefully - pressure must be converted to head units (divide by specific weight). Remember that gauge pressures are relative to atmospheric pressure. For velocity head calculations, don't forget the factor of 2 in the denominator. When solving for velocity, check that the result under the square root is positive.
How do I use Chick–Watson Inactivation (log10) on the PE exam?
The Chick-Watson model is fundamental for water treatment design. Remember that n≤1 for this form, and different pathogens have vastly different k values. Cryptosporidium is extremely resistant to chlorine (very low k), while bacteria are more susceptible. CT concept (concentration × time) is critical for disinfection credit calculations.
How do I use First-Order Decay on the PE exam?
This equation appears frequently on the PE exam for disinfection problems. Remember that decay constants are often given in different time units (per minute, per hour, per day) - always check units match. The equation assumes first-order kinetics, which is valid for free chlorine in most treated waters.
How do I use Continuity on the PE exam?
The continuity equation is fundamental to all fluid flow problems. Often appears as part of larger problems involving energy equations, pipe networks, or channel design. Remember that velocity is average velocity across the entire cross-section.
How do I use Critical Depth (rectangular) on the PE exam?
Critical depth problems appear frequently on the PE exam. Remember that critical flow occurs at minimum specific energy. When flow depth equals critical depth, the flow transitions from subcritical to supercritical. Always check if the actual depth is above (subcritical) or below (supercritical) critical depth.