GATE CE 2023 Set 2 — Question 62
Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.NAT+2 / -0MediumPrecipitationHydrology & PrecipitationWater Resources Engineering
Water Resources Engineering → Hydrology & Precipitation → Precipitation
Last updated
Question
A catchment may be idealized as a circle of radius 30 km. There are five rain gauges, one at the center of the catchment and four on the boundary (equi-spaced), as shown in the figure (not to scale).The annual rainfall recorded at these gauges in a particular year are given below.
Using the Thiessen polygon method, what is the average rainfall (in mm, rounded off to two decimal places) over the catchment in that year?
| Gauge | |||||
|---|---|---|---|---|---|
| Rainfall (mm) | 910 | 930 | 925 | 895 | 905 |
Correct answer
912.28 to 912.82
Solution
1.Identify the positions of the rain gauges: is at the center , and are on the boundary at distance km, spaced apart.
2.Construct Thiessen polygons by drawing perpendicular bisectors between and the boundary gauges. The bisectors are lines at distance from the center: and .
3.These four lines form a square of side centered at . The area assigned to is .
4.The total area of the circular catchment is .
5.The remaining area is divided equally among the four boundary gauges due to symmetry. Thus, .
6.The average rainfall is calculated using the Thiessen polygon formula:
7.Substitute the given rainfall values: , , , , .
Average of boundary rainfalls mm.8.Calculate :
9.Rounded to two decimal places, the average rainfall is mm.
Continue learning with Success Tracker
A step still unclear? Work through it with support
Use Success Tracker to ask about the reasoning, then try another GATE CE question to check your understanding.
AI-powered practice· Unlimited practice on eligible plans
- PYQs with solutions
- Attempt available previous-year questions, then compare your reasoning with the worked solution. Coverage varies by stream.
- Practice that adapts
- Choose a topic, work on weaker areas and bookmark questions to revisit. Your attempts feed your progress tracking.
- AI doubt support
- Ask follow-up questions about a step or concept while practising, instead of stopping at the final answer.
Unlimited practice is available on eligible plans. Free practice and AI usage have limits; check the current plan allowances before choosing.
This page stays readable without an account. AI responses can be wrong; check them against the solution and source material.
More questions on Hydrology & Precipitation
2026 Set 1 Q16Two reservoirs having different water levels are connected by two long parallel pipelines of same…2026 Set 1 Q17An irrigation canal is to be designed to deliver 10 cumec to meet the peak demand of 7500 hectare…2026 Set 2 Q19The Culturable Command Area (CCA) for a canal is 10000 hectares. The base period for a crop in the…2026 Set 2 Q20Following statements are made with respect to the mass curve of rainfall: (I) Slope at a point on…2026 Set 1 Q23Gradually Varied Flow (GVF) profiles in open channels given in Column 1 are to be matched with the…