Water Resources and Hydraulics for the FE Exam
Water resources and hydraulics is a major topic area on the FE Civil exam. It covers the behavior of water in natural and engineered systems, from pipe flow and open channel flow to hydrology and stormwater design. The equations are well-established and are available in the reference handbook.
Fluid Properties Review
- Density of water: 1,000 kg/m^3 (62.4 lb/ft^3) at standard conditions.
- Specific weight of water: 9,810 N/m^3 (62.4 lb/ft^3).
- Dynamic viscosity: Temperature-dependent. At 20 degrees C, approximately 1.0 x 10^(-3) Pa*s for water.
- Kinematic viscosity: nu = mu / rho. At 20 degrees C, approximately 1.0 x 10^(-6) m^2/s for water.
Pipe Flow
Reynolds Number
The Reynolds number determines whether flow is laminar or turbulent:
Re = V * D / nu
Where V is flow velocity, D is pipe diameter, and nu is kinematic viscosity. For pipe flow: Re less than 2,100 is laminar; Re greater than 4,000 is turbulent; between these values is the transition zone.
Energy Equation (Bernoulli's Equation)
For steady, incompressible flow between two points along a streamline:
P1/(gamma) + V1^2/(2g) + z1 = P2/(gamma) + V2^2/(2g) + z2 + h_L
Where P is pressure, gamma is specific weight, V is velocity, z is elevation, g is gravitational acceleration, and h_L is the total head loss between the two points.
Head Losses
Head losses in pipe systems come from two sources:
- Major losses (friction): h_f = f * L * V^2 / (D * 2g), where f is the Darcy friction factor (found from the Moody diagram), L is pipe length, and D is pipe diameter.
- Minor losses: h_m = K * V^2 / (2g), where K is the loss coefficient for each fitting, valve, or transition. Common K values are in the reference handbook.
Moody Diagram
The Moody diagram relates the Darcy friction factor to the Reynolds number and relative roughness (epsilon/D). Practice reading the Moody diagram quickly, as pipe flow problems often require looking up friction factors.
Open Channel Flow
Manning's Equation
Manning's equation is the most commonly used equation for open channel flow:
V = (1/n) * R^(2/3) * S^(1/2) (SI units)
V = (1.486/n) * R^(2/3) * S^(1/2) (US customary units)
Where V is velocity, n is Manning's roughness coefficient, R is the hydraulic radius (A/P, where A is cross-sectional area and P is wetted perimeter), and S is the slope of the energy grade line (approximately the channel bed slope for uniform flow).
Flow rate: Q = V * A
Froude Number
The Froude number classifies open channel flow:
Fr = V / sqrt(g * y)
Where y is the flow depth.
- Fr less than 1: Subcritical flow (deep, slow)
- Fr = 1: Critical flow
- Fr greater than 1: Supercritical flow (shallow, fast)
Specific Energy
Specific energy is the energy per unit weight relative to the channel bottom:
E = y + V^2 / (2g) = y + Q^2 / (2g * A^2)
The specific energy diagram shows the relationship between depth and energy. At critical depth, specific energy is minimized for a given flow rate.
Hydrology
Rational Method
The rational method estimates peak runoff for small watersheds:
Q = C * i * A
Where Q is peak discharge, C is the runoff coefficient (0 to 1), i is the rainfall intensity for the design storm (corresponding to the time of concentration), and A is the drainage area.
Time of Concentration
The time of concentration (t_c) is the time for runoff to travel from the hydraulically most distant point in the watershed to the outlet. Several empirical formulas are used to estimate t_c (Kirpich, FAA, SCS methods).
SCS Curve Number Method
The SCS (now NRCS) curve number method estimates total runoff from a rainfall event:
Q = (P - 0.2S)^2 / (P + 0.8S)
Where Q is direct runoff, P is total precipitation, and S = (1000/CN) - 10 (in inches). CN is the curve number, which depends on soil type, land use, and antecedent moisture condition.
Unit Hydrograph
A unit hydrograph represents the runoff from one unit of excess rainfall over the watershed. It is used to predict the hydrograph from any rainfall event by convolution (scaling and superposition).
Stormwater Management
- Detention basins: Temporarily store stormwater and release it at a controlled rate to reduce peak flows downstream.
- Retention basins: Permanently store stormwater, allowing it to infiltrate or evaporate.
- Storm sewer design: Size pipes to carry design storm flows using Manning's equation or the rational method.
Water resources and hydraulics problems are formula-driven and very scoreable. Know the key equations (Bernoulli, Manning, rational method, SCS curve number), practice using the Moody diagram, and you will be well prepared for this section of the FE exam.