---
title: "How stage-discharge relationship is established"
subject: "Engineering Hydrology"
chapter: 4
key: "semester_5/engineering_hydrology:stage-discharge-established"
source: https://www.bctengineer.com/q/semester_5/engineering_hydrology/stage-discharge-established
site: BCT Engineering
---

# How stage-discharge relationship is established

Engineering Hydrology · Chapter 4: Surface Runoff

- Asked in: 2073 Shrawan, 4 marks
- Video: [Stage Discharge Rating Curve : Stream Flow Measurement : WRE](https://www.youtube.com/watch?v=RkorkZaEbL8) — The Classroom
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/engineering_hydrology/stage-discharge-established
- Whole chapter: https://www.bctengineer.com/md/semester_5/engineering_hydrology/chapter-4

## Question

Explain how stage discharge relationship is established.

## Short answer

Select stable site, install gauge, measure discharges at various stages by current meter. Plot stage vs discharge, fit Q=C(G-a)^b: determine a (zero-flow stage) by trial or three-point method, log-log regression for C and b, and verify correlation.

## Answer

A **stage-discharge relationship (rating curve)** at a gauging site is established as follows.

1. **Select the site** with a stable, permanent control and a straight reach.
2. **Install a gauge** (staff gauge or automatic recorder) and note the datum.
3. **Measure discharge** at various stages, from low to flood, by the area-velocity (current meter) method, and simultaneously record the stage. A minimum of about 15 to 20 measurements covering the whole range is desirable.
4. **Plot** the stage $G$ against discharge $Q$ on arithmetic paper; draw a smooth curve through the points.
5. **Fit the equation** $Q = C(G-a)^b$:
   - Find $a$, the stage at zero discharge (by trial, or the three-point method $a=\dfrac{G_1G_3-G_2^2}{G_1+G_3-2G_2}$ with $Q_2=\sqrt{Q_1Q_3}$).
   - Plot $\log Q$ against $\log(G-a)$; a straight line is obtained when $a$ is correct; its slope is $b$ and intercept is $\log C$.
6. **Check** the correlation and test the curve by new measurements.
7. **Extrapolate** the curve above the highest measured stage by the log-log straight line or the conveyance (Manning) method.
8. **Review** periodically: if the points depart from the curve (shifting control), apply shift corrections or draw a new curve.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. What kind of site is selected for establishing the rating?
   A. A confluence
   B. A waterfall pool with backwater
   C. Reach with frequently shifting bed
   D. Stable permanent control in a straight reach
   Answer: D. A stable control gives a consistent relation. (Key point: Site selection)

2. On log-log paper, a straight line is obtained when
   A. a is correct
   B. C equals 1
   C. a equals zero
   D. b equals 1
   Answer: A. A correct stage of zero discharge makes log Q vs log(G - a) linear; slope is b. (Key point: Fitting the equation)

3. What is done if points depart from the curve later?
   A. Delete the gauge
   B. Apply shift corrections or draw a new curve
   C. Extrapolate more
   D. Ignore them
   Answer: B. Departures indicate shifting control, so correct or redraw. (Key point: Review)

## Related in Engineering Hydrology

- [Shifting control in stage-discharge relation](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Ashifting-control) — Engineering Hydrology, chapter 4
- [Rating curve equation, zero-discharge stage 161.0 m](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Arating-curve-equation-161-0) — Engineering Hydrology, chapter 4
- [Gauge-discharge relationship and discharge at 10.5 m](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Agauge-discharge-rating-7-5) — Engineering Hydrology, chapter 4
- [Stage at zero discharge from rating data](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Astage-zero-discharge-rating-20-80) — Engineering Hydrology, chapter 4, asked 2×
- [Zero-discharge stage of a smooth rating curve](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Astage-zero-discharge-23-37) — Engineering Hydrology, chapter 4, asked 2×
- [Stage for zero discharge with sketch](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Astage-zero-discharge-sketch) — Engineering Hydrology, chapter 4

## Related in other subjects

- [Stage discharge curve and its application](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Astage-discharge-curve) — Hydro Power, chapter 2
- [Arrester coordination for 40 kA discharge](https://www.bctengineer.com/question.md?key=semester_8%2Fhigh_voltage_engineering%3Aarrester-132kv-40ka-coordination) — High Voltage Engineering, chapter 4, asked 2×