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Civil Engineering (CE) Exam > Civil Engineering (CE) Notes > Topic wise GATE Past Year Papers for Civil Engineering > Past Year Questions: Infiltration, Runoff and Hydrographs

Past Year Questions: Infiltration, Runoff and Hydrographs | Topic wise GATE Past Year Papers for Civil Engineering - Civil Engineering (CE) PDF Download

Q1: A storm with a recorded precipitation of 11.0 cm, as shown in the table, produced a direct run-off of 6.0 cm.

The ϕ-index of this storm is ____ cm/hr (rounded off to 2 decimal places) (2024 SET-2)
Ans: 0.64 to 0.65

Sol: Assume ϕ ≤ i_lowest

Past Year Questions: Infiltration, Runoff and Hydrographs | Topic wise GATE Past Year Papers for Civil Engineering - Civil Engineering (CE) Assume 0.625 < ϕ ≤ 0.8

Past Year Questions: Infiltration, Runoff and Hydrographs | Topic wise GATE Past Year Papers for Civil Engineering - Civil Engineering (CE)

Q2: The ordinates of a 1-hour unit hydrograph (UH) are given below.
These ordinates are used to derive a 3-hour UH. The peak discharge (in m³/s ) for the derived 3-hour UH is ______(rounded off to the nearest integer). (2024 SET-1)
Ans: 86 to 88
Sol: Past Year Questions: Infiltration, Runoff and Hydrographs | Topic wise GATE Past Year Papers for Civil Engineering - Civil Engineering (CE)

Maximum ordinate of 3HUH is 86.67 m³/s
Maximum ordinate is 87 m³/s (to nearest integer)

Q1: Which one of the following options provides the correct match of the terms listed in Column-I and Column-II? (2023 SET-2)

(a) P-IV, Q-V, R-III
(b) P-III, Q-IV, R-I
(c) P-IV, Q-III, R-II
(d) P-III, Q-I, R-IV
Ans: (a)
Sol: Horton's equation is used to calculate total infiltration.
Muskingum method is used in flood response analysis in channels.
Penman equation is used to calculate potential evapotranspiration.

Q2: In Horton's equation fitted to the infiltration data for a soil, the initial infiltration capacity is 10 mm/h; final infiltration capacity is 5 mm/h; and the exponential decay constant is 0.5 h. Assuming that the infiltration takes place at capacity rates, the total infiltration depth (in mm ) from a uniform storm of duration 12 h is ____. (round off to one decimal place) (2023 SET-1 )
Ans: 69.7 to 70.1
Sol: f₀ = 10 meter
f_c = 5 meter
K = 0.5hr⁻¹
Past Year Questions: Infiltration, Runoff and Hydrographs | Topic wise GATE Past Year Papers for Civil Engineering - Civil Engineering (CE) At capacity rates i.e. t→∞
f = 5 + 5e^−0.5×∞
= 5 meters
Infiltration in 12hr. = 5 × 12 = 60 mm
If above is not the case :
then
Infiltration = ∫ fdt
Past Year Questions: Infiltration, Runoff and Hydrographs | Topic wise GATE Past Year Papers for Civil Engineering - Civil Engineering (CE) = 60 + 10 (1 - e^{0.5 x 12})
= 69.795 mm = 70 mm.

Q3: A 12-hour storm occurs over a catchment and results in a direct runoff depth of 100 mm. The time-distribution of the rainfall intensity is shown in the figure (not to scale). The ϕ-index of the storm is (in mmmm, rounded off to two decimal places)_____ (2023 SET-1)
Ans: 3.6 to 3.6
Sol: D = 12 hrs.
Direct runoff (R) = 100 mm = 10 cm
P = total rainfall
P = Area under above diagram
P = (1/2)×(12+2)×20
= 14 × 10 = 140 mm = 14 cm
Total Infiltration = Total rainfall − runoff
=140 − 100 = 40 mm
Assuming infiltration rate as x mm/hr.
Past Year Questions: Infiltration, Runoff and Hydrographs | Topic wise GATE Past Year Papers for Civil Engineering - Civil Engineering (CE)

x/y₁= 20/4
y₁ = x/5
y₂ = x/y₂ = 20/6
y₂ = 3x/10
Total Infiltration
= Area under rainfall intensity duration curve Area of same curve below ϕ-index line.
Past Year Questions: Infiltration, Runoff and Hydrographs | Topic wise GATE Past Year Papers for Civil Engineering - Civil Engineering (CE) ⇒x2−48x+160=0
⇒ x = 3.6 and x = 44.39 [Discarded]
⇒ ϕ = 3.6 mm/hr.

Q4: The ordinates of a one-hour unit hydrograph for a catchment are given below :
Using the principle of superposition, a D-hour unit hydrograph for the catchment was derived from the one-hour unit hydrograph. The ordinate of the D-hour unit hydrograph were obtained as 3 m³/s at t = 1 hour and 10 m³/s at t = 2 hour. the value of D (in integer) is _____ (2023 SET-1)
Ans: 3 to 3
Sol: Past Year Questions: Infiltration, Runoff and Hydrographs | Topic wise GATE Past Year Papers for Civil Engineering - Civil Engineering (CE) Clearly seen
The duration D = 3 hours

Q1: A two-hour duration storm event with uniform excess rainfall of 3 cm occurred on a watershed. The ordinates of streamflow hydrograph resulting from this event are given in the table.
Considering a constant baseflow of 10 m³/s, the peak flow ordinate (in m³/s) of one-hour unit hydrograph for the watershed is ________ . (in integer) (2022 SET-1)
Ans: 12 to 12
Sol: C₁ = Time
C₂ = Ordinates of 2hr DRH
C₃ = Ordinates of 2hr UH = (Ordinates of 2hr DRH)/(Rianfall excess of 3cm)
C₄= S-curve lag by 2hr
C₅= S-curve ordinates S₂
C₆= S₁ curve
C₇= Ordinates of 1hr UH = (S₂−S−1)/1/2
Past Year Questions: Infiltration, Runoff and Hydrographs | Topic wise GATE Past Year Papers for Civil Engineering - Civil Engineering (CE)
Q1: The hyetograph in the figure corresponds to a rainfall event of 3 cm.

If the rainfall event has produced a direct runoff of 1.6 cm, the ϕ-index of the event (in mm/hour, round off to one decimal place) would be (2021 SET-2)
Ans: 4.2 to 4.2
Sol: Past Year Questions: Infiltration, Runoff and Hydrographs | Topic wise GATE Past Year Papers for Civil Engineering - Civil Engineering (CE) Total rainfall = 3 cm
Total runoff = 1.6 cm
∴ Total infiltration = 3 − 1.6 = 1.4 cm
∴ W-index = Total infiltration /Total duration of storm
= 1.4/(210/60) cm/hr
= 0.4 cm/hr = 4 mm/hr
As ∅-index > W-index
Hence storm of intensities 4 mm/hr and 3 mm/hr will not produce rainfall exam.
ϕ -index = Total infiltration in which rainfall excess occur / Time period in which rainfall excess occur
= Total infiltration − Infiltration in which no rainfall excess occur / T_excess
Past Year Questions: Infiltration, Runoff and Hydrographs | Topic wise GATE Past Year Papers for Civil Engineering - Civil Engineering (CE) = 4.2 mm/hr

Q2: A 12-hour unit hydrograph (of 1 cm excess rainfall) of a catchment is of a triangular shape with a base width of 144 hour and a peak discharge of 23 m³/s. The area of the catchment (in km², round off to the nearest integer) is _______ (2021 SET-2 )
Ans: 595 to 598
Sol: Past Year Questions: Infiltration, Runoff and Hydrographs | Topic wise GATE Past Year Papers for Civil Engineering - Civil Engineering (CE) Area of hydrograph = Total direct runoff volume
⇒ (1/2) × 23 m³/sec × 144 × 3600 sec= Area of catchment × Runoff depth
⇒ (1/2) × 23 x 144 x 3600 m³ = A x (1/100) m
A = 596.16 x 10⁶ m²
∴ Area of catchment = 596.16 km²

Q3: The value of abscissa (x) and ordinate (y) of a curve are as follows:
By Simpson's 1/3^rd rule, the area under the curve (round off to two decimal places) is ______ (2021 SET-1)
Ans: 20 to 21
Sol: d = 0.5 unit
Past Year Questions: Infiltration, Runoff and Hydrographs | Topic wise GATE Past Year Papers for Civil Engineering - Civil Engineering (CE)

A = d/3 [(y₁+ y₅) + 4(y₂+ y₄) + 2y₃]
= 0.5/3 [(5 + 17) + 4(7.25 + 13.25) + 2 × 10]
= 20.67 unit²

Q1: A triangular direct runoff hydrograph due to a storm has a time base of 90 hours. The peak flow of 60 m³/s occurs at 20 hours from the start of the storm. The area of catchment is 300 km². The rainfall excess of the storm (in cm), is (2020 SET-2 )
(a) 2
(b) 3.24
(c) 5.4
(d) 6.48
Ans: (b)
Sol: Past Year Questions: Infiltration, Runoff and Hydrographs | Topic wise GATE Past Year Papers for Civil Engineering - Civil Engineering (CE)

Past Year Questions: Infiltration, Runoff and Hydrographs | Topic wise GATE Past Year Papers for Civil Engineering - Civil Engineering (CE)

Rainfall excess = 3.24 cm

Q2: The probability that a 50 year flood may NOT occur at all during 25 years life of a project (round off to two decimal places), is _______. (2020 SET-1)
Ans: 0.59 to 0.61
Sol: Past Year Questions: Infiltration, Runoff and Hydrographs | Topic wise GATE Past Year Papers for Civil Engineering - Civil Engineering (CE)

q = 1 - P = 0.98
∴ Probability of non-occurance of an event is given by
Assurance = qⁿ
= (0.98)²⁵
= 0.603

Q1: The ordinates, u, of a 2-hour unit hydrograph (i.e., for 1 cm of effective rain), for a catchment are shown in the table.
A 6-hour storm occurs over the catchment such that the effective rainfall intensity is 1 cm/hour for the first two hours, zero for the next two hours, and 0.5 cm/hour for the last two hours. If the base flow is constant at 5 m³/s, the peak flow due to this storm (in m³/s, round off to 1 decimal place) will be _____ (2019 SET-2)
Ans: 96.5 to 97.5
Sol: Rainfall excess in 1st two hours,
R₁ = 1 cm/hr × 2hr = 2cm
Rainfall excess in 2nd two hours
R₂ = 0
Rainfall excess in 3rd two hours,
R₃ = 0.5 cm/hr × 2hr = 1cm
Past Year Questions: Infiltration, Runoff and Hydrographs | Topic wise GATE Past Year Papers for Civil Engineering - Civil Engineering (CE)

Q2: An inflow hydrograph is routed through a reservoir to produce an outflow hydrograph. The peak flow of the inflow hydrograph is P_Iand the time of occurrence of the peak is tItI. The peak flow of the outflow hydrograph is P_O and the time of occurrence of the peak is t_O. Which one of the following statements is correct? (2019 SET-2)
(a) P_I< P_O and t_I < t_O
(b) P_I < P_O and t_I> t_O
(c) P_I > P_O and t_I < t_O
(d) P_I> P_O and t_I> t_O
Ans: (c)
Sol: Past Year Questions: Infiltration, Runoff and Hydrographs | Topic wise GATE Past Year Papers for Civil Engineering - Civil Engineering (CE)

The outflow from the reservoir is uncontrolled therefore peak of outflow hydrograph will occur at the junction of inflow and outflow hydrograph.
P_I> P₀
t_I < t₀

Q3: The hyetograph of a storm event of duration 140 minutesis shown in the figure.

The infiltration capacity at the start of this event (t = 0) is 17 mm/hour, which linearly decreases to 10 mm/hour after 40 minutes duration. As the event progresses, the infiltration rate further drops down linearly to attain a value of 4 mm/hour at t = 100 minutes and remains constant thereafter till the end of the storm event. The value of the infiltration index, ϕ (in mm/hour, round off to 2 decimal places), is _______ (2019 SET-1)
Ans: 7 to 7.3
Sol: P = (4 + 8 + 15 + 10 + 8 + 3 + 1) × (20/60)
= 16.33 minute
Past Year Questions: Infiltration, Runoff and Hydrographs | Topic wise GATE Past Year Papers for Civil Engineering - Civil Engineering (CE) = 4mm
Since, ∅ ≥ W
Assume, ∅ = 5.28 mm/hr
⇒ Corrected, ∅ =
= 7.2475 mm/hr

Q1: The total rainfall in a catchment of area 1000 km², during a 6 h storm, is 19 cm. The surface runoff due to this storm computed from triangular direct runoff hydrograph is 1 × 10⁸m³. The ϕ_index for this storm (in cm/h, up to one decimal place) is ______ (2018 SET-2)
Ans: 1.5 to 1.5
Sol: Surface runoff = 1×10⁸m³/1000×10⁶m² = 0.1 m = 10 cm
Total rainfall = 19 cm
Rainfall intensity = 19/6 = 3.167 cm/hr
w-Index = P − Q/t = Total Infiltration/Total duration of storm
∴ w−Index = (19-10)/6 = 1.5 cm/hr
As intensity of rainfall > w-Index
And rainfall intensity is uniform therefore ϕ-index = w-Index = 1.5 cm/hr.

Q2: The infiltration rate f in a basin under ponding condition is given by f = 30 + 10e^−2t, where, f is in mm/h and t is time in hour. Total depth of infiltration (in mm, up to one decimal place) during the last 20 minutes of a storm of 30 minutes duration is ______ (2018 SET-1)
Ans: 11 to 12
Sol: Infiltration rate f(t) = 30 + 10e^−2t
Total infiltration depth in time 10 min. to 30 min.
i.e., 0.166 hour to 0.5 hour
Past Year Questions: Infiltration, Runoff and Hydrographs | Topic wise GATE Past Year Papers for Civil Engineering - Civil Engineering (CE)

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FAQs on Past Year Questions: Infiltration, Runoff and Hydrographs - Topic wise GATE Past Year Papers for Civil Engineering - Civil Engineering (CE)

1. What is infiltration and how does it affect runoff in civil engineering?

Ans. Infiltration is the process by which water enters the soil surface and moves into the ground. It plays a crucial role in the water cycle and affects runoff by reducing the amount of water that flows over the surface. When infiltration rates are high, more water is absorbed into the ground, leading to less runoff. Conversely, low infiltration rates can increase runoff, potentially causing flooding and erosion.

2. What factors influence the rate of infiltration in a given area?

Ans. The rate of infiltration is influenced by several factors, including soil type, soil moisture content, vegetation cover, land use, and the presence of impermeable surfaces. Sandy soils typically allow for higher infiltration rates compared to clayey soils. Additionally, areas with dense vegetation can enhance infiltration by breaking up the soil surface and creating channels for water to enter.

3. How can hydrographs be used to analyze runoff from a watershed?

Ans. Hydrographs are graphical representations that show the flow of water over time at a specific point in a watershed. They are used to analyze runoff by plotting discharge against time, allowing engineers to observe how runoff responds to rainfall events. By comparing hydrographs from different storms, engineers can assess the watershed's response, including peak flow rates and time to peak, which are essential for designing drainage systems.

4. What is the difference between direct runoff and baseflow in hydrology?

Ans. Direct runoff refers to the portion of rainfall that flows directly into streams and rivers, usually occurring shortly after precipitation events. Baseflow, on the other hand, is the portion of streamflow that is sustained by groundwater discharge, occurring over a longer period. Understanding the distinction between the two is vital for effective water resource management and flood control.

5. How can land use changes impact infiltration and runoff patterns in urban areas?

Ans. Land use changes, such as urbanization, typically lead to increased impervious surfaces like roads and buildings, which reduce infiltration rates and increase runoff. This can result in higher peak flows and more frequent flooding. To mitigate these effects, civil engineers often implement green infrastructure solutions, such as permeable pavements and bioretention systems, to enhance infiltration and manage runoff effectively.

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