---
title: "Stage for zero discharge with sketch"
subject: "Engineering Hydrology"
chapter: 4
key: "semester_5/engineering_hydrology:stage-zero-discharge-sketch"
source: https://www.bctengineer.com/q/semester_5/engineering_hydrology/stage-zero-discharge-sketch
site: BCT Engineering
---

# Stage for zero discharge with sketch

Engineering Hydrology · Chapter 4: Surface Runoff

- Asked in: 2072 Chaitra, 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/stage-zero-discharge-sketch
- Whole chapter: https://www.bctengineer.com/md/semester_5/engineering_hydrology/chapter-4

## Question

Explain with sketch how you determine the stage for zero discharge.

## Short answer

The stage for zero discharge a is determined by trial on log-log plot of Q vs (G−a): assume values of a, plot logQ against log(G−a), and choose a that straightens the line. Alternatively, a field survey of the lowest point of the control directly gives a.

## Answer

The **stage of zero discharge** ($a$) is the gauge height at which the flow in the river becomes zero (the level of the lowest point of the control). It is needed in the rating equation $Q = C(G-a)^b$.

#### Methods
**1. Field survey:** survey the level of the lowest point of the channel control (the bed of the riffle or the lowest point of the section) directly. For sand-bed rivers this level may change from time to time.

**2. Trial and error (log-log plot):** assume trial values of $a$ and plot $\log Q$ against $\log(G-a)$. The correct $a$ gives a straight line. If the plot curves upward (concave up), the assumed $a$ is too high; if it curves downward (concave down), $a$ is too low.

```text
  a too low        correct a        a too high
  (concave down)   (straight)       (concave up)
  logQ             logQ             logQ
   |     ___        |      /         |         /
   |   /            |    /           |       /
   |  /             |  /             |   _ -
   | /              | /              |_ -
   +------ log(G-a) +------          +------
```

**3. Extrapolation of the arithmetic curve:** extend the smooth stage-discharge curve down until it meets the stage axis at $Q=0$. This is a first rough estimate.

**4. Three-point (analytical) method:**
Select three points $(G_1,Q_1)$, $(G_2,Q_2)$, $(G_3,Q_3)$ on the smooth curve with $Q_2^2 = Q_1Q_3$. Then
$$
a = \frac{G_1G_3 - G_2^2}{G_1+G_3-2G_2}
$$
Procedure: choose the lowest and highest points $Q_1$, $Q_3$; compute $Q_2=\sqrt{Q_1Q_3}$; read $G_2$ on the curve; substitute.

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

## Check yourself

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

1. The stage of zero discharge is
   A. Bank-full stage
   B. Highest flood level
   C. Mean water level
   D. Gauge height at which flow becomes zero (lowest point of the control)
   Answer: D. It is the level of the lowest point of the control. (Key point: Meaning of a)

2. On the log-log plot, if the curve bends upward, a trial a is
   A. Too high
   B. Irrelevant
   C. Exactly correct
   D. Too low
   Answer: A. As given in the answer: curves up means a is too high; correct a gives a straight line. (Key point: Log-log trial)

3. In the three-point method, Q2 is chosen as
   A. Q3 - Q1
   B. sqrt(Q1 Q3)
   C. (Q1 + Q3)/2
   D. Q1 x Q3
   Answer: B. Q2^2 = Q1 Q3, and then a = (G1 G3 - G2^2)/(G1 + G3 - 2 G2). (Key point: Three-point condition)

## Related in Engineering Hydrology

- [Rating curve and stage for zero discharge](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Arating-curve-zero-stage) — 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×
- [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
- [Shifting control in stage-discharge relation](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Ashifting-control) — Engineering Hydrology, chapter 4
- [How stage-discharge relationship is established](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Astage-discharge-established) — 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