Practice Problems: Hydrology
Question 1
A civil engineer is designing a stormwater management system for a 250-acre commercial development. The site has been divided into four distinct land use areas with different runoff coefficients. Given the following information:
Area 1: 80 acres, C = 0.35 (landscaped areas)
Area 2: 95 acres, C = 0.75 (parking lots)
Area 3: 50 acres, C = 0.90 (building rooftops)
Area 4: 25 acres, C = 0.20 (open green space)
Using the Rational Method, what is the composite runoff coefficient for the entire development?
(a) 0.55
(b) 0.59
(c) 0.63
(d) 0.68
Question 2
A hydrologist is analyzing a watershed to determine the time of concentration for a proposed detention basin design. The watershed has three distinct flow segments:
Sheet flow: 100 ft, Manning's n = 0.24, slope = 2.5%
Shallow concentrated flow: 800 ft, slope = 1.8%, unpaved surface
Channel flow: 2,200 ft, velocity = 4.5 ft/s
Using NRCS methods (sheet flow velocity = 16.1345 × S0.5 / n for first 100 ft, shallow concentrated unpaved velocity = 16.1345 × S0.5), what is the total time of concentration?
(a) 16.2 minutes
(b) 18.5 minutes
(c) 20.8 minutes
(d) 22.4 minutes
Question 3
A municipal engineer is designing a culvert for a 25-year storm event. Using the Rational Method, the following data has been collected:
Drainage area = 185 acres
Composite runoff coefficient C = 0.68
Rainfall intensity for 25-year, 15-minute storm = 4.8 in/hr
Time of concentration = 15 minutes
What is the peak discharge for design purposes?
(a) 524 cfs
(b) 603 cfs
(c) 678 cfs
(d) 742 cfs
Question 4
A watershed manager is evaluating streamflow data from a gauging station. A flood event recorded the following measurements:
Peak discharge = 8,500 cfs
Channel bottom width = 45 ft
Side slopes = 2H:1V (both sides)
Flow depth = 8.5 ft
Manning's n = 0.035
Channel slope = 0.0018 ft/ft
What is the calculated discharge using Manning's equation, and does it match the recorded peak discharge within 5%?
(a) 7,850 cfs, No
(b) 8,320 cfs, Yes
(c) 8,680 cfs, Yes
(d) 9,125 cfs, No
Question 5
A stormwater engineer is designing a detention pond for a residential subdivision. The inflow hydrograph has been developed with the following ordinates at 10-minute intervals:
Time (min): 0, 10, 20, 30, 40, 50, 60
Inflow (cfs): 0, 125, 340, 285, 180, 95, 0
The outlet structure provides a constant outflow of 150 cfs when the pond has water.
Using the storage indication method, what is the maximum storage volume required?
(a) 62,500 ft³
(b) 85,000 ft³
(c) 103,000 ft³
(d) 127,500 ft³
Question 6
A consulting engineer is performing a frequency analysis on annual peak flood data for a river. The following statistics have been calculated from 45 years of record:
Mean annual flood = 12,400 cfs
Standard deviation = 3,850 cfs
Skew coefficient = 0.42
Using the Log-Pearson Type III distribution and a frequency factor K = 2.18 for the 100-year event, what is the estimated 100-year flood discharge?
(a) 18,750 cfs
(b) 20,790 cfs
(c) 22,485 cfs
(d) 24,120 cfs
Question 7
A drainage engineer is evaluating infiltration capacity for a bioretention facility. A double-ring infiltrometer test was conducted with the following results:
Initial infiltration rate = 3.2 in/hr
Final constant infiltration rate = 0.65 in/hr
Decay constant k = 0.18 hr⁻¹
Using Horton's infiltration equation f = fc + (f0 - fc)e-kt, what is the infiltration rate after 2.5 hours?
(a) 0.89 in/hr
(b) 1.05 in/hr
(c) 1.28 in/hr
(d) 1.52 in/hr
Question 8
A water resources engineer is analyzing a unit hydrograph for a 450-acre watershed. The 2-hour unit hydrograph has been developed with a peak discharge of 285 cfs occurring 3.5 hours from the start.
If a storm produces 1.8 inches of effective rainfall in the first 2 hours and 1.2 inches in the second 2 hours, what is the peak discharge of the composite hydrograph?
(a) 684 cfs
(b) 745 cfs
(c) 825 cfs
(d) 897 cfs
Question 9
A floodplain manager is determining the 100-year flood elevation for a residential development. The following channel geometry and hydraulic data are provided:
Q₁₀₀ = 15,500 cfs
Channel bottom width = 65 ft
Side slopes = 3H:1V
Channel slope = 0.0025 ft/ft
Manning's n = 0.040
Using normal depth calculations, what is the depth of flow for the 100-year event?
(a) 9.8 ft
(b) 10.6 ft
(c) 11.4 ft
(d) 12.2 ft
Question 10
A hydrologist is calibrating a rainfall-runoff model for a 2,850-acre urban watershed. A storm event produced the following data:
Total rainfall = 3.4 inches
Initial abstraction = 0.6 inches
Total runoff volume = 185 acre-ft
Using the NRCS Curve Number method where Q = (P - 0.2S)²/(P + 0.8S) and S = (1000/CN) - 10, what is the Curve Number for this watershed?
(a) 76
(b) 82
(c) 88
(d) 94
Question 11
A stormwater consultant is designing a grass-lined channel for conveyance of the 10-year storm runoff. The channel specifications are:
Design discharge = 425 cfs
Bottom width = 8 ft
Side slopes = 3H:1V
Channel slope = 0.008 ft/ft
Manning's n = 0.030 (grass lining)
Permissible velocity = 5.0 ft/s (erosion control)
What normal depth satisfies both capacity and velocity requirements?
(a) 3.2 ft
(b) 3.8 ft
(c) 4.4 ft
(d) 5.0 ft
Question 12
An engineer is designing a stormwater pumping station for a low-lying residential area. The pump must handle the runoff from a 50-year, 24-hour storm with the following characteristics:
Drainage area = 95 acres
Composite runoff coefficient = 0.55
50-year, 24-hour rainfall = 8.2 inches
Required pumping duration = 18 hours
If the total runoff volume must be removed in 18 hours, what is the minimum average pumping rate required?
(a) 1.85 cfs
(b) 2.24 cfs
(c) 2.68 cfs
(d) 3.12 cfs
Question 13
A watershed planner is evaluating the impact of urbanization on peak discharge. Pre-development conditions for a 125-acre watershed are:
Time of concentration = 45 minutes
Curve Number = 68
Post-development conditions show:
Time of concentration = 22 minutes
Curve Number = 85
For a 25-year storm with I = 95/(Tc + 20) where I is in in/hr and Tc in minutes, what is the percent increase in peak discharge using the Rational Method with C = (CN - 40)/60?
(a) 168%
(b) 195%
(c) 224%
(d) 251%
Question 14
A hydraulic engineer is analyzing the routing of a flood wave through a reservoir. The reservoir storage-elevation relationship and outflow rating curve are given as:
Storage (acre-ft) = 15 × (Elevation - 100)²
Outflow (cfs) = 8.5 × (Elevation - 100)1.5
where elevation is in feet above datum.
If the peak inflow is 2,500 cfs and the initial reservoir elevation is 112 ft, what is the approximate peak elevation during the flood event using level pool routing?
(a) 118.5 ft
(b) 120.2 ft
(c) 122.8 ft
(d) 125.3 ft
Question 15
A municipal engineer is designing an urban drainage system using the Modified Rational Method for a 340-acre mixed-use development. The design parameters are:
Composite C = 0.72
Time of concentration = 28 minutes
25-year rainfall intensity = 3.8 in/hr
Storage coefficient Cs = 0.85 for detention
What is the required detention storage volume using V = Cs × (Qin - Qout) × T where Qout is limited to 50% of pre-developed flow and T = time of concentration?
(a) 2.8 acre-ft
(b) 3.6 acre-ft
(c) 4.2 acre-ft
(d) 4.9 acre-ft
Question 16
A consulting engineer is evaluating groundwater recharge for a proposed infiltration basin. A falling head permeameter test provides the following data:
Initial head = 85 cm
Final head = 28 cm
Time interval = 12 minutes
Standpipe diameter = 5 cm
Soil sample length = 15 cm
Soil sample diameter = 10 cm
Using k = (aL/At) × ln(h₁/h₂), what is the hydraulic conductivity?
(a) 1.8 × 10⁻³ cm/s
(b) 2.4 × 10⁻³ cm/s
(c) 3.1 × 10⁻³ cm/s
(d) 3.7 × 10⁻³ cm/s
Question 17
A flood control engineer is evaluating a levee design for a riverine flood protection project. The design flood parameters are:
100-year discharge = 45,000 cfs
Water surface elevation at Q₁₀₀ = 485.6 ft
Levee crest elevation = 489.0 ft
Freeboard requirement = 3.0 ft minimum
Wave height estimate = 1.2 ft
Does the proposed levee meet the freeboard requirement including wave runup consideration?
(a) Yes, with 0.2 ft excess freeboard
(b) Yes, with 0.5 ft excess freeboard
(c) No, deficient by 0.8 ft
(d) No, deficient by 1.4 ft
Question 18
A water resources engineer is designing a riprap-lined spillway for an earthen dam. The design criteria are:
Design discharge = 3,200 cfs
Spillway width = 35 ft
Spillway slope = 2H:1V (26.6°)
Average flow depth = 4.8 ft
Using the relationship d₅₀ = 0.01 × V²/(2g × (Ss - 1)) where Ss = 2.65 for stone and V = Q/(width × depth), what median stone size is required?
(a) 8.5 inches
(b) 11.2 inches
(c) 14.8 inches
(d) 18.3 inches
Question 19
A stormwater engineer is analyzing a catch basin inlet capacity on a continuous grade. The inlet parameters are:
Curb opening length = 10 ft
Gutter slope = 3.5%
Cross slope = 2.0%
Gutter flow = 4.2 cfs
Manning's n = 0.016
Using the orifice equation Qi = 0.67 × L × d1.5 where L is length in ft and d is depth at inlet in ft, and gutter flow Q = (Ku/n) × SL0.5 × Sx2.67 × T2.67 where T is top width, what percentage of flow is intercepted?
(a) 68%
(b) 75%
(c) 82%
(d) 89%
Question 20
A hydrologist is performing a water balance analysis for a lake system over a one-year period. The following annual data has been collected:
Surface area = 850 acres (average)
Precipitation on lake = 42 inches
Evaporation = 38 inches
Surface inflow = 8,200 acre-ft
Surface outflow = 7,850 acre-ft
Change in storage = +120 acre-ft
What is the net groundwater exchange (positive indicates groundwater inflow to lake)?
(a) -516 acre-ft (outflow)
(b) -398 acre-ft (outflow)
(c) +286 acre-ft (inflow)
(d) +432 acre-ft (inflow)
