---
title: "Stage discharge curve and its application"
subject: "Hydro Power"
chapter: 2
key: "semester_6/hydro_power:stage-discharge-curve"
source: https://www.bctengineer.com/q/semester_6/hydro_power/stage-discharge-curve
site: BCT Engineering
---

# Stage discharge curve and its application

Hydro Power · Chapter 2: Introduction to Hydrology

- Asked in: 2070 Bhadra, 6 marks
- Video: [Stage Discharge Rating Curve : Stream Flow Measurement : WRE](https://www.youtube.com/watch?v=RkorkZaEbL8) — The Classroom
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/hydro_power/stage-discharge-curve
- Whole chapter: https://www.bctengineer.com/md/semester_6/hydro_power/chapter-2

## Question

Define with application of stage discharge curve in hydropower project.

## Short answer

A stage–discharge curve relates water level G to discharge Q by Q = Cr(G−a)^β. In hydropower, it transforms gauge records into flow series for design discharge, tailwater level, flood level estimation for structures, and real-time operation.

## Answer

A **stage–discharge curve** (rating curve) is a graph or equation relating the **stage** (water surface level, G) at a gauging site to the **discharge** (Q) of the river at that site. Once it is established from a number of current-meter measurements over a range of flows, discharge can be read directly from a simple daily water level reading.

#### Development
1. Measure Q (by current meter) and the stage G at the same time, many times over low, medium and high flows.
2. Plot G against Q; fit a smooth curve.
3. Usual equation:
$$
Q = C_r(G - a)^{\beta}
$$
   where $a$ = gauge reading for zero flow, and $C_r$, $\beta$ are found by plotting $\log Q$ against $\log(G - a)$ (least squares).
4. Extend to high flood levels by log-log extrapolation, or by Stevens or conveyance methods.

```text
 Stage G (m)
   |                  .  *
   |             *  .
   |         * .
   |      *.
   |   *.
 a |*_____________________ Q (m3/s)
```

#### Applications in a hydropower project
- Converts long records of daily gauge readings into a **discharge series**, from which hydrographs, flow duration curves and firm flow are drawn for fixing the design discharge and installed capacity.
- Gives the **tailwater level** for each discharge, needed for net head, turbine setting and draft tube design.
- Gives water levels at the **headworks/intake** for different flows: intake sill level, weir crest, freeboard.
- Gives **flood levels** for design of the dam/weir, spillway, river training works and powerhouse floor level.
- Used in **real-time operation**: estimating inflow, managing pondage and spills.

Limitations: a shifting river bed (common in Nepal's sediment-laden rivers) changes the curve, so it must be checked regularly.

## Check yourself

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

1. What does a stage-discharge (rating) curve relate?
   A. Rainfall and runoff
   B. Stage at a gauging site and the river discharge
   C. Head and power
   D. Velocity and depth only
   Answer: B. It relates the water level (stage) at a site to the discharge, so discharge can be read from daily stage. (Key point: Definition)

2. In Q = Cr (G - a)^beta, what is 'a'?
   A. Catchment area
   B. Maximum flood level
   C. The gauge reading at zero flow
   D. The channel width
   Answer: C. a is the gauge reading for zero discharge; Cr and beta are found from a log-log plot. (Key point: Rating equation)

3. How does the curve help in fixing the installed capacity of a hydropower project?
   A. It gives the turbine efficiency
   B. It fixes the penstock diameter
   C. It gives soil strength
   D. It converts daily gauge readings into a discharge series for flow duration and firm flow
   Answer: D. A long discharge series gives hydrographs, flow duration curves and firm flow, used for the design discharge and capacity. (Key point: Application: design)

4. Why is the curve needed at the powerhouse and weir sites?
   A. To get tailwater level for net head and flood levels for structure design
   B. To measure sediment
   C. To find rainfall losses
   D. To compute evaporation
   Answer: A. It gives the tailwater for each discharge (net head, draft tube) and flood levels for weir, spillway and powerhouse floor. (Key point: Tailwater and floods)

## Related in Hydro Power

- [Stages of hydropower project study](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Ahydropower-study-stages) — Hydro Power, chapter 3, asked 3×
- [Bernoulli's equation limitations and application](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Abernoulli-limitations-application) — Hydro Power, chapter 1
- [Flow duration curve and planning parameters](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Afdc-planning-parameters) — Hydro Power, chapter 3

## Related in other subjects

- [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
- [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×