Free PE Civil — WRE practice problems

Ten real questions from our PE Civil: Water Resources and Environmental bank — one from each knowledge area, with the same exam-realistic figures and fully worked solutions our members get. No signup, no email. Try each one first, then reveal the solution.

5 with figures10 knowledge areasFull worked solutions

1
medium
A. Uniform flow, specific energy & critical depth
An earthen trapezoidal irrigation canal has a bottom width $b=4\,\text{m}$ , side slopes $z=2$ (H:V), and runs at a normal depth $y=1.5\,\text{m}$ on a slope $S=0.0008$ with Manning $n=0.025$ . Using $Q=\frac{1}{n}AR^{2/3}S^{1/2}$ , the uniform discharge is most nearly:
1. 11.7 m³/s
2. 4.61 m³/s
3. 15.6 m³/s
4. 0.293 m³/s
Show the answer & worked solution
Answer: A.11.7 m³/s
$A=(b+zy)y=(4+2\cdot1.5)1.5=10.5$ , $P=b+2y\sqrt{1+z^2}=4+2(1.5)\sqrt{1+2^2}=10.708$ m, $R=0.981$ . $Q=\frac{1}{0.025}(10.5)(0.981)^{2/3}(0.0008)^{1/2}=11.7$ m³/s. Distractors: used the RECTANGLE area $b y$ , dropping the side triangles ( $4.61$ ); used $P=b+2y$ , omitting $\sqrt{1+z^2}$ on the slanted sides ( $15.6$ ); and dropped the conveyance constant, computing $AR^{2/3}\sqrt{S}$ without $\frac{1}{n}$ ( $0.293$ ).
2
medium
A. Lateral earth pressure & bearing capacity
A continuous (strip) footing of width $B=6\,\text{ft}$ is founded at depth $D_f=4\,\text{ft}$ in soil with cohesion $c=500\,\text{psf}$ and unit weight $\gamma=120\,\text{pcf}$ (same above and below the base, no water). The Terzaghi bearing-capacity factors are $N_c=37.2$ , $N_q=22.5$ , $N_\gamma=19.7$ . The ultimate (gross) bearing capacity $q_{ult}$ is most nearly:
1. 25700 psf
2. 39500 psf
3. 36500 psf
4. 43600 psf
Show the answer & worked solution
Answer: C.36500 psf
$q_{ult}=cN_c+\gamma D_f N_q+\tfrac12\gamma B N_\gamma=500(37.2)+120(4)(22.5)+\tfrac12(120)(6)(19.7)=18600+10800+7090=36500$ psf. Distractors: DROPPED the ½ on the $\gamma B N_\gamma$ term ( $43600$ ); SWAPPED $B$ and $D_f$ between the $N_q$ and $N_\gamma$ terms ( $39500$ ); and omitted the $\gamma D_f N_q$ surcharge term, reporting a net-like value ( $25700$ ).
3
medium
A. Storms, IDF, time of concentration & runoff
A commercial parking catchment of $A=12\,\text{acres}$ has a runoff coefficient $C=0.65$ and a time of concentration $T_c=18\,\text{min}$ . The 10-yr IDF curve is $i=a/(t_d+b)^c$ with $a=64.1$ , $b=11$ , $c=0.81$ . Using the Rational method with the design storm set at $t_d=T_c$ , the peak discharge is most nearly:
1. 50.3 cfs
2. 15.8 cfs
3. 48.1 cfs
4. 32.7 cfs
Show the answer & worked solution
Answer: D.32.7 cfs
$i=\dfrac{64.1}{(18+11)^{0.81}}=4.19$ in/hr at $t_d=T_c=18$ min; $Q=C\,i\,A=0.65(4.19)(12)=32.7$ cfs. Distractors: OMITTED $C$ (used $i\,A=50.3$ , $C=1$ ); read $i$ at the wrong duration $t_d=60$ min instead of $T_c$ , giving $Q=15.8$ ; and DROPPED the $b$ offset in $i$ , $Q=C(a/T_c^{\,c})A=48.1$ .
4
medium
A. Soil classification, properties, concrete & piping
A specimen of a compacted lean clay has a water content $w=14\%$ , a void ratio $e=0.55$ , and $G_s=2.68$ . The degree of saturation $S$ is most nearly:
1. 68.2 %
2. 25.5 %
3. 24.2 %
4. 20.6 %
Show the answer & worked solution
Answer: A.68.2 %
$S=\dfrac{wG_s}{e}=\dfrac{(0.14)(2.68)}{0.55}=0.682=68.2\%$ . Distractors: DROPPED $G_s$ ( $w/e=25.5\%$ ); divided by $(1+e)$ instead of $e$ , confusing the void ratio with the bulk-volume term ( $wG_s/(1+e)=24.2\%$ ); and MULTIPLIED by $e$ instead of dividing ( $wG_se=20.6\%$ ).
5
medium
A. Collection, primary & secondary treatment
Raw wastewater with $S_0=220\,\text{mg/L}$ BOD $_5$ passes through primary settling then activated sludge. The primary unit removes 35% of the BOD and the secondary unit removes 85% of the BOD reaching it. The final effluent BOD $_5$ is most nearly:
1. 88 mg/L
2. 143 mg/L
3. 33 mg/L
4. 21.5 mg/L
Show the answer & worked solution
Answer: D.21.5 mg/L
After primary: $220(1-0.35)=143$ mg/L; after secondary: $\times(1-0.85)=21.5$ mg/L (overall removal $1-(1-r_1)(1-r_2)=90.3\%$ ). Distractors: used the AVERAGE removal $(r_1+r_2)/2$ applied once, $88$ ; applied SECONDARY removal only to the raw BOD ( $33$ ); and applied PRIMARY removal only ( $143$ ).
6
medium
A. Energy/continuity & pipe losses
A ductile-iron distribution main carries $Q=700\,\text{gpm}$ over $L=2000\,\text{ft}$ of $d=8\,\text{in}$ pipe with Hazen-Williams $C=120$ . Using $h_f=\dfrac{10.44\,L\,Q^{1.852}}{C^{1.852}\,d^{4.87}}$ , the friction head loss is most nearly:
1. 640 ft
2. 0.0824 ft
3. 1290 ft
4. 21.9 ft
Show the answer & worked solution
Answer: D.21.9 ft
$h_f=\dfrac{10.44(2000)(700)^{1.852}}{(120)^{1.852}(8)^{4.87}}=21.89$ ft. Distractors: used a LINEAR flow term $Q^{1}$ instead of $Q^{1.852}$ ( $0.08$ ft); used $C^{1}$ instead of $C^{1.852}$ in the denominator ( $1293.07$ ft); and used the RADIUS $d/2$ for the diameter ( $639.99$ ft — the $d^{4.87}$ term makes this enormous).
7
medium
A. Demand, storage & distribution
A suburban distribution system has an average-day demand of 4.2 MGD. Design factors (referenced to the average day) are a max-day factor of 1.8 and a peak-hour factor of 2.7. The peak hour demand is most nearly:
1. 20.4 MGD
2. 4.2 MGD
3. 11.3 MGD
4. 7.56 MGD
Show the answer & worked solution
Answer: C.11.3 MGD
Apply the peak-hour factor to the average day: $Q=4.2\times2.7=11.3$ MGD. Distractors: used the OTHER factor (the max-day factor, $4.2\times1.8=7.56$ ); STACKED both factors, $Q_{avg}\times\text{MDF}\times\text{PHF}=20.4$ (peak-hour is already referenced to the average day, not the max day); and FORGOT the peaking factor entirely, reporting the average day $4.2$ .
8
medium
A. Aquifers, Darcy flow & well drawdown
A conservative tracer moves through an aquifer of hydraulic conductivity $K=30\,\text{m/day}$ and effective porosity $n_e=0.3$ . The water-table gradient is set by a head drop of $\Delta h=1.8\,\text{m}$ over $L=600\,\text{m}$ . The actual seepage (pore-water) velocity that governs how fast the front advances is most nearly:
1. 0.09 m/day
2. 0.027 m/day
3. 0.3 m/day
4. 0.129 m/day
Show the answer & worked solution
Answer: C.0.3 m/day
$i=\Delta h/L=0.003$ ; Darcy flux $q=Ki=30\times0.003=0.09\,\text{m/day}$ . Seepage velocity $v_s=q/n_e=0.09/0.3=0.3\,\text{m/day}$ . Distractors: reported the specific discharge $q$ itself, FORGETTING to divide by $n_e$ ( $0.09$ ); MULTIPLIED by $n_e$ instead of dividing, $q\,n_e=0.027$ (which wrongly slows the front); and divided by the SOLID fraction $(1-n_e)$ instead of the pore fraction $n_e$ ( $0.129$ ).
9
medium
A. Earthwork, curves & retaining sitework
An embankment for a detention-basin berm requires 12,000 CY of compacted (in-place) fill. The borrow soil has a shrinkage of 18% (compacted volume = bank volume × (1 − shrinkage)). The bank (in-situ) volume that must be excavated from borrow is most nearly:
1. 14200 CY
2. 9840 CY
3. 14600 CY
4. 12000 CY
Show the answer & worked solution
Answer: C.14600 CY
Bank $=\dfrac{\text{compacted}}{1-\text{shrinkage}}=\dfrac{12000}{1-0.18}=14634$ CY. Distractors: MULTIPLIED by $(1-s)$ instead of dividing (9840 CY, the wrong direction — this gives a bank volume smaller than the fill); applied $(1+s)$ as if it were a SWELL factor (14160 CY); and IGNORED shrinkage altogether (12000 CY).
10
medium
A. DO dynamics, TMDL & contaminants
For a phosphorus TMDL on an impaired lake tributary, the loading capacity is the load that just meets the in-stream standard $C_{std}=5\,\text{mg/L}$ at a critical flow $Q=50\,\text{MGD}$ ( $\text{load}=Q\cdot C\cdot8.34$ in lb/day). The nonpoint load allocation is $\Sigma LA=600\,\text{lb/day}$ and a margin of safety of 10% of the loading capacity is reserved. The allowable point-source waste-load allocation $\Sigma WLA$ is most nearly:
1. 1880 lb/day
2. 1340 lb/day
3. 1280 lb/day
4. 1490 lb/day
Show the answer & worked solution
Answer: C.1280 lb/day
Loading capacity $\text{TMDL}=Q\,C_{std}(8.34)=50(5)(8.34)=2085$ lb/day; $\text{MOS}=10\%$ of TMDL $=209$ lb/day. $\Sigma WLA=\text{TMDL}-\Sigma LA-\text{MOS}=2085-600-209=1277$ lb/day. Distractors: FORGOT the margin of safety ( $1485$ ); FORGOT the nonpoint $\Sigma LA$ ( $1877$ ); and reserved the MOS off the LEFTOVER pool $(\text{TMDL}-\Sigma LA)$ instead of the full loading capacity ( $1337$ ).

That was ten. There are thousands.

The full PE Civil: Water Resources and Environmental bank covers every knowledge area at this depth, with timed mock exams that mirror the real 80-question paper and an AI tutor grounded in the PE Civil Reference Handbook + Ten States Standards (water & wastewater) — so it can't confidently feed you a wrong answer.

Explore PE Civil — WRE See pricing

Studying for a different exam? See free practice problems for all 11 exams, or read our FE & PE study guides.

These are the same free sample questions available to anyone with an account — the paid bank is separate. Independent study resource; not affiliated with, endorsed by, or sponsored by NCEES.