---
title: "Rating curve equation and daily discharge hydrograph"
subject: "Engineering Hydrology"
chapter: 4
key: "semester_5/engineering_hydrology:rating-curve-equation-daily-hydrograph"
source: https://www.bctengineer.com/q/semester_5/engineering_hydrology/rating-curve-equation-daily-hydrograph
site: BCT Engineering
---

# Rating curve equation and daily discharge hydrograph

Engineering Hydrology · Chapter 4: Surface Runoff

- Asked in: 2080 Baisakh, 6 marks
- Video: [Developing stream Rating Curve Equation and curve Using EXCEL [ Step By Step ]](https://www.youtube.com/watch?v=CSPLLGA4c3M) — Hydraulics and Hydrology Tutorials
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/engineering_hydrology/rating-curve-equation-daily-hydrograph
- Whole chapter: https://www.bctengineer.com/md/semester_5/engineering_hydrology/chapter-4

## Question

Write the equation of rating curve and explain it with figure. How is daily discharge hydrograph obtained from daily stage hydrograph?

## Short answer

The rating curve enuation is Q = C(G - a)^b, where G is stage, a is zero-flow gauge height, and C, b are onstants. A daily discharge hydrograph is obtained by converting each day's mean stage to discharge using this curve, applying shift corrections if needed, and plotting Q versus time.

## Answer

#### Equation of the rating curve
The stage-discharge relation at a gauging section is
$$
Q = C\,(G-a)^{b}
$$
where $Q$ = discharge (m$^3$/s), $G$ = gauge height (m), $a$ = gauge height for zero discharge (m), and $C$, $b$ = constants of the section ($b\approx1.5$ to $2.0$). It plots as a smooth, upward-curving line on arithmetic paper and as a straight line on log-log paper.

```text
 G (stage)                 log Q
  |        .'               |       . /
  |      .'                 |     . /  slope = b
  |    .'                   |   . /
  |  .'                     | . /
  |_.'___________ Q         +---------- log(G-a)
  a
```

#### Daily discharge hydrograph from the daily stage hydrograph
1. Obtain the **daily mean stage** for each day, as the average of the observed gauge readings, or from the area under the recorder chart (stage hydrograph).
2. Use the rating curve (equation or table) to read the **discharge corresponding to each day's mean stage**: $Q_i = C(G_i-a)^b$.
3. Where the stage changes rapidly in a day, compute discharge for shorter intervals, or use the discharge for each reading and then average.
4. Apply **shift corrections** if the control has changed in the period.
5. Plot $Q_i$ against time (days) to get the **daily discharge hydrograph**.

```text
 stage G        rating curve      discharge Q
  |   /\                            |   /\
  |  /  \      ---> Q=f(G) --->     |  /  \
  |_/____\___ t                     |_/____\__ t
```

The sum of the daily discharges gives monthly and annual volumes.

## Check yourself

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

1. What is the rating curve equation and how does it plot?
   A. Q = CG^b; straight on arithmetic paper
   B. Q = C + bG; a circle
   C. Q = C(G-a)^b; curved on arithmetic paper, straight on log-log paper
   D. Q = C(G-a)^b; straight on arithmetic paper
   Answer: C. The power form becomes linear after taking logs. (Key point: Rating equation)

2. How is the daily discharge hydrograph obtained?
   A. Average the rainfall each day
   B. Measure discharge daily with a current meter
   C. Use the stage hydrograph unchanged
   D. Convert each day's mean stage to discharge with the rating curve, then plot against time
   Answer: D. Q_i = C(G_i - a)^b applied to the daily mean stage. (Key point: Daily discharge)

3. What corrections may be needed?
   A. Shift corrections if the control has changed, and shorter intervals if stage changes rapidly
   B. Add rainfall
   C. Multiply by 0.85
   D. None ever
   Answer: A. Rating curves shift when the control changes. (Key point: Corrections)

## Related in Engineering Hydrology

- [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
- [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×
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