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

# Rating curve and stage for zero discharge

Engineering Hydrology · Chapter 4: Surface Runoff

- Asked in: 2081 Bhadra, 2+6 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/rating-curve-zero-stage
- Whole chapter: https://www.bctengineer.com/md/semester_5/engineering_hydrology/chapter-4

## Question

What is rating curve? Explain with sketch how would you determine stage for zero discharge.

## Short answer

A rating curve is the stage-discharge relation Q=C(G-a)^b. The stage for zero discharge a is found by extrapolating the G-Q curve to Q=0, applying the three-point formula a=(G1G3-G2^2)/(G1+G3-2G2) with Q2=√(Q1Q3), or by trial values of a to obtain a straight line on log-log plot.

## Answer

#### Rating curve
A **rating curve** (stage-discharge curve) is the graph or equation that gives the discharge corresponding to the stage at a river gauging section, usually $Q=C(G-a)^b$.

#### Stage for zero discharge
The **stage for zero discharge ($a$)** is the gauge height at which flow stops, i.e. the level of the lowest point of the control. It is found as follows.

```text
  G ^
    |           .
 G3-|        .
 G2-|      .        (Q2 = sqrt(Q1*Q3))
 G1-|   .
  a-| .
    +----------------> Q
```

1. **Extrapolation:** draw the smooth stage-discharge curve and extend it downward to cut the stage axis at $Q = 0$ (a rough value).
2. **Three-point method:** pick three points on the smooth curve such that $Q_2=\sqrt{Q_1Q_3}$, read $G_1$, $G_2$, $G_3$, and compute
$$
a=\frac{G_1G_3-G_2^2}{G_1+G_3-2G_2}
$$
3. **Trial on log-log paper:** assume several $a$, plot $\log Q$ against $\log(G-a)$. The value that gives a straight line is the stage for zero discharge. If the plotted curve is concave upward, $a$ is too large; if concave downward, $a$ is too small.

```text
 log Q
   |       . (a too small: concave down)
   |     . ____ straight (correct a)
   |   ._.-'
   | .' (a too large: concave up)
   +------------------ log(G - a)
```
4. **Field survey** of the lowest point of the control, where possible.

## Check yourself

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

1. What is the stage for zero discharge?
   A. The highest flood level
   B. The mean annual stage
   C. The stage at maximum velocity
   D. The gauge height at which flow stops, the lowest point of the control
   Answer: D. It marks the datum of the control for the rating relation. (Key point: Meaning of a)

2. What is required of the three chosen points?
   A. Q2 = sqrt(Q1 Q3), then a = (G1G3 - G2^2)/(G1+G3-2G2)
   B. Q2 = (Q1+Q3)/2
   C. Q1 = Q2 = Q3
   D. G2 = sqrt(G1 G3)
   Answer: A. The discharges must be in geometric progression. (Key point: Three-point method)

3. What does a concave-upward log Q vs log(G-a) plot indicate?
   A. The assumed a is too small
   B. The assumed a is too large
   C. The assumed a is correct
   D. The discharge is wrong
   Answer: B. Concave upward means a too large, concave downward too small; a straight line is correct. (Key point: Log-log trial)

## Related in Engineering Hydrology

- [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×
- [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
- [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×
- [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
- [Rating curve equation and daily discharge hydrograph](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Arating-curve-equation-daily-hydrograph) — Engineering Hydrology, chapter 4
- [Current meter discharge, rating equation](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Acurrent-meter-0-53n) — 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