Qwestrum Engineering360 · Civil Engineering · Hydrology & Irrigation
Hydrograph Analysis
Separate base flow from the total hydrograph to get direct runoff, derive the unit hydrograph (response to 1 cm of excess rainfall in duration D), then convolve it with the excess rainfall to predict a flood hydrograph.
Exam tip: keep SI units consistent end-to-end, write the governing relation symbolically before substituting, and sanity-check magnitude and sign.
Key formulas & points
Skim these first — then read the full notes below.
- UH ordinates multiply by excess rainfall depth for direct runoff
- S-curve for deriving UH of different duration
- Clark storage routing uses time of concentration
Topic details
Introduction
A hydrograph plots discharge against time at a stream section, and its analysis lets engineers predict flood flows from rainfall. The total hydrograph is separated into direct runoff (the storm response) and base flow (groundwater contribution).
Scope in B.Tech and GATE syllabus
The unit hydrograph (UH) is the direct-runoff hydrograph produced by 1 cm of excess rainfall spread uniformly over the catchment in a specified duration D. Its power comes from linearity and time-invariance: the response to any excess rainfall is obtained by scaling and superposing UH ordinates.
Why this topic matters in practice
The S-curve (S-hydrograph) is the response to continuous excess rainfall and is used to convert a UH of one duration into a UH of another duration, a standard exam manipulation.
Key relations & formulas
Formulas (Indian textbook notation)
Formulas (Indian textbook notation)
Formulas (Indian textbook notation)
Notation and sign conventions
Relation 1 —
Formulas (Indian textbook notation)
Write this relation with symbols exactly as in Irrigation & Water Power Engineering — BC Punmia before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.
Relation 2 —
Formulas (Indian textbook notation)
Write this relation with symbols exactly as in Irrigation & Water Power Engineering — BC Punmia before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.
Relation 3 —
Formulas (Indian textbook notation)
Write this relation with symbols exactly as in Irrigation & Water Power Engineering — BC Punmia before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.
Fundamentals and definitions
Base-flow separation isolates the storm-driven direct runoff from the slowly varying groundwater base flow; the straight-line or N-day methods approximate where the base flow rejoins the recession after the storm peak. The area under the direct-runoff hydrograph equals the volume of excess rainfall.
Governing relations in practice
The unit hydrograph embodies two assumptions: linearity (doubling excess rainfall doubles the direct runoff ordinates) and time-invariance (the shape depends only on the catchment, not when the storm occurs). These let a complex storm be handled as a sum of unit responses.
Design and analysis considerations
Convolution applies the UH: each block of excess rainfall generates a scaled, time-shifted UH, and summing them gives the total direct-runoff hydrograph — the core operation in flood prediction.
Advanced theory and extensions
The S-curve is generated by applying successive UHs at intervals equal to the UH duration until the discharge stabilises; lagging one S-curve behind another and scaling gives the UH for a different rainfall duration, essential when the available UH duration does not match the design storm.
Assumptions and validity limits
State assumptions explicitly before using any relation for hydrograph analysis — steady state, uniform properties, linear elastic material, ideal gas, incompressible flow, etc., as applicable.
Wrong assumptions invalidate the entire solution even when the formula is correct. In Hydrology viva and GATE descriptive questions, listing valid assumptions often earns separate marks.
Step-by-step problem approach
1. Read the question and list given data with SI units (common in Hydrology papers).
2. Draw a neat labelled diagram where applicable — examiners in Indian universities award diagram marks even when arithmetic slips.
3. Identify which relation from this topic applies to hydrograph analysis.
4. Use equation 1:
5. Use equation 2:
6. Substitute values, compute, and verify units and sign (direction).
7. State conclusion in one line — e.g. safe/unsafe, stable/unstable, feasible/infeasible.
2. Draw a neat labelled diagram where applicable — examiners in Indian universities award diagram marks even when arithmetic slips.
3. Identify which relation from this topic applies to hydrograph analysis.
4. Use equation 1:
.
5. Use equation 2:
.
6. Substitute values, compute, and verify units and sign (direction).
7. State conclusion in one line — e.g. safe/unsafe, stable/unstable, feasible/infeasible.
Applications & exam relevance
Hydrograph Analysis appears in dam design and irrigation planning. In Indian civil curricula this topic is tested because it connects theory to precipitation, runoff, and floods.
GATE and semester exams often combine hydrograph analysis with earlier units — revise prerequisites before attempting mixed problems.
Industry interview panels sometimes ask: "Where did you use hydrograph analysis?" — answer with a lab, mini-project, or plant visit example if possible.
Common mistakes in exams
• Forgetting to separate base flow before deriving the direct-runoff hydrograph.
• Applying a UH of the wrong rainfall duration without S-curve conversion.
• Violating the unit-hydrograph linearity by scaling non-uniformly.
• Misaligning the time offsets when convolving rainfall blocks.
• Applying a UH of the wrong rainfall duration without S-curve conversion.
• Violating the unit-hydrograph linearity by scaling non-uniformly.
• Misaligning the time offsets when convolving rainfall blocks.
Quick revision checklist
Before attempting hydrograph analysis problems, confirm you can:
1. UH ordinates multiply by excess rainfall depth for direct runoff
2. S-curve for deriving UH of different duration
3. Clark storage routing uses time of concentration
2. S-curve for deriving UH of different duration
3. Clark storage routing uses time of concentration
Revise the solved examples in Irrigation & Water Power Engineering — BC Punmia and one previous-year GATE or university paper for this unit.
Worked examples
Try the problem first — open the solution when you are ready to check.
Direct runoff peak from a unit hydrograph
Problem
A 1 cm, 3-hour unit hydrograph has a peak ordinate of 25 m³/s. A storm produces 4 cm of excess rainfall in 3 hours. Estimate the peak of the direct-runoff hydrograph (assume a single rainfall block).
Solution
By linearity, the direct-runoff ordinates equal the UH ordinates multiplied by the excess rainfall depth: peak direct runoff = 25 × 4 = 100 m³/s. Adding base flow (say 10 m³/s) would give a total peak of about 110 m³/s. For multi-block storms, each block’s scaled UH would be lagged and summed before reading the peak.
Conceptual check — Hydrograph Analysis
Problem
In a Hydrology semester or GATE paper you are asked: "State the main assumption, the governing relation, and one practical consequence of hydrograph analysis." What should a complete answer include?
Exams & GATE
BC Punmia — derive 3-h UH from 1-h UH by S-curve method.
📖 Standard books (India)
Irrigation & Water Power Engineering — BC Punmia
Read: Syllabus unit
Hydrology, canals, and water resources
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