Free PE Civil Water Resources and Environmental Practice Problems with Step-by-Step Solutions

If you’re preparing for the PE Civil Water Resources and Environmental Exam, you already know it’s a major step in your engineering career. One of the most effective ways to boost your confidence and sharpen your problem-solving skills is by working through realistic, exam-style practice problems. Why practice problems? Because they push you to actively engage with the material, understand the underlying concepts, and identify exactly where you need improvement. The PE exam requires you to think critically under time pressure, so simulated practice is key. Below are two sample problems with full solutions at the bottom of the page to help you practice.

Sample Problem 1

An engineer is analyzing a small urban watershed that includes the following drainage areas:

• Single-family residential area

• Unimproved open space

• Light industrial area

• Concrete street

Rank these surfaces from largest to smallest runoff coefficient.

A. Unimproved open space > concrete street > light industrial area > concrete street

B. Light industrial area > concrete street > single-family residential area > unimproved open space

C. Light industrial area > single-family residential area > concrete street > unimproved open space

D. Concrete street > light industrial area > single-family residential area > unimproved open space

Sample Problem 2

A completely turbulent mechanical mixing system is being designed for a wastewater

treatment basin using a fan turbine (6 blades at 45°). Assume fully turbulent conditions, and the following parameters apply:

• Impeller diameter, Di = 1.1 m

• Rotational speed, n = 80 rpm

• Fluid: Water at standard conditions ρ = 1,000 kg/cubic meters

What is most nearly the power required to drive the mixer?

A. 7.0 kW

B. 4.0 kW

C. 6.0 kW

D. 5.0 kW

Sample Problem 3

A river segment downstream of 10,000 acres of agricultural land is experiencing persistent algal blooms and dissolved oxygen levels below 4 mg/L, even after a 30% reduction in upstream point-source discharges. What is the most likely explanation for this condition?

A. Groundwater inflow diluting surface nutrients by approximately 15%

B. Intermittent industrial spills

C. Natural background nutrient concentrations near 0.2 mg/L initiating eutrophication

D. Continued high nonpoint source nutrient loading from agricultural runoff

Why practice problems are crucial for PE success

The PE exam allows access to a Reference Handbook and design standards during the test. But don’t let that fool you—success still depends on how well you understand and can apply those references quickly. By working through practice problems with detailed solutions, you’ll develop strategies for efficient problem-solving and effective reference use, both critical for the exam.

To further help you prepare, StrataWay offers a Civil PE Water Resources and Environmental Sample Exam, which features 80 exam-style problems with step-by-step solutions.

Solution to Sample Problem 1

Correct answer is D.

Reference Table 3-1 “Runoff Coefficients for Rational Formula” from the Federal Highway Administration Urban Drainage Design Manual: Hydraulic Engineering Circular No. 22, 3rd edition. This table is also found in the Reference Handbook.

Per the table, the correct order is as follows (ranges are provided):

Concrete street (0.80-0.95) > light industrial area (0.50-0.80) > single-family residential area (0.30- 0.50) > unimproved open space (0.10-0.30).

Hint: If the basin includes a mix of land cover types and other features, a composite runoff coefficient can be determined by areal weighing.

Solution to Sample Problem 2

Correct answer is C.

Reference the NCEES Reference Handbook or the Table “Values of the Impeller Constant KT” from Mixing of Liquids in Chemical Processing by J. Henry Rushton, v. 44, no. 12, p. 2,934. Copyright 1952 American Chemical Society. Based on the table, KT = 1.65 for a fan turbine, 6 blades at 45°.

Convert rotational speed to revolutions per second:

N = 80 rpm/60 = 1.333 rev/s

Apply the equation for turbulent flow impeller mixing power:

P = K_T × (n)³ × (Di)⁵ × ρ_f

P = 1.65 × (1.33 rev/s)³ × (1.1 m)⁵ × 1,000 kg/m³

P = 6,301.2 W

Convert to kilowatts:

P = 6.3 kW

Solution to Sample Problem 3

Correct answer is D.

A is incorrect. Groundwater inflow may affect nutrient concentrations, but in this context, it is unlikely to significantly dilute the large nutrient loads entering from surface runoff. In some cases, groundwater may even carry additional nutrients, depending on subsurface conditions.

B is incorrect. While industrial spills can contribute nutrients, their contribution is typically episodic and small in comparison to diffuse, continuous agricultural runoff, especially in rural or farming-dominated watersheds.

C is incorrect. Natural background nutrient concentrations are generally low and insufficient to trigger eutrophication on their own. Algal blooms typically require nutrient inputs well above natural levels, often from human activities.

D is correct. Agricultural runoff is a major nonpoint source of nutrients such as nitrogen and phosphorus. Even with reductions in point-source discharges, large-scale agricultural activity can continue to drive eutrophication and algal blooms that deplete oxygen levels downstream.