---
title: "Flow and power duration curves"
subject: "Hydro Power"
chapter: 3
key: "semester_6/hydro_power:flow-power-duration-curves"
source: https://www.bctengineer.com/q/semester_6/hydro_power/flow-power-duration-curves
site: BCT Engineering
---

# Flow and power duration curves

Hydro Power · Chapter 3: Planning of Hydropower Projects

- Asked in: 2081 Asoj, 6 marks
- Video: [Flow Duration Curve Explained with Practical Example #energy #generated #flow](https://www.youtube.com/watch?v=dMetbSB7orw) — Hydropower
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/hydro_power/flow-power-duration-curves
- Whole chapter: https://www.bctengineer.com/md/semester_6/hydro_power/chapter-3

## Question

Describe flow duration and power duration curves with their significance in estimating power potential of a hydropower project.

## Short answer

A flow duration curve plots discharge against percent of time it is equaled or exceeded; a power duration curve converts flow to power. They are used to determine firm power, select design discharge (e.g., Q40), estimate annual energy from the area under the curve, and assess plant factor and storage needs.

## Answer

#### Flow duration curve (FDC)
A **flow duration curve** is a plot of discharge (on the y-axis) against the percentage of time that discharge is **equalled or exceeded** (on the x-axis). It is a cumulative frequency curve of the river flow.

**How it is drawn**
1. Collect a long record of daily or monthly flows.
2. Arrange the flows in descending order and give each a rank $m$ (1 for the largest).
3. Compute the exceedance probability $P = \frac{m}{N+1}\times100\%$ (N = number of values).
4. Plot Q against P.

#### Power duration curve (PDC)
A **power duration curve** is obtained by converting each flow of the FDC to power:

$$
P = 9.81\,Q\,H\,\eta\ \text{kW}
$$

It shows the percentage of time a given power is equalled or exceeded. Where the head is nearly constant, the PDC has the same shape as the FDC with a different scale.

```text
Q or P
  |*
  | *
  |  **
  |    ***  installed capacity
  |=======*****======   (e.g. Q40)
  |   secondary  ****
  |                 *****
  |--- firm (Q100) -------****
  +---------------------------->
  0        50             100
       % time equalled/exceeded
```

#### Significance in estimating power potential
- **Firm power:** the power at 100% (or 90–95% in practice) of time gives the firm (dependable) power of a run-of-river plant.
- **Installed capacity selection:** the design discharge is chosen at a certain exceedance, e.g. Q40 to Q65 for Nepalese run-of-river projects; the PDC shows the power at that level.
- **Energy estimation:** the area under the PDC (capped at the installed capacity) gives the annual energy; the area below firm power is primary energy and the rest is secondary energy.
- **Plant factor:** mean power from the capped curve divided by installed capacity.
- **Flow character:** a steep curve shows a flashy river (needs storage); a flat curve shows a well-regulated, groundwater-fed river.
- **Storage and pondage:** shows how much storage is needed to raise the firm flow.
- **Environmental flow and spill:** shows how often water is spilled and how much is left for downstream use.

## Check yourself

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

1. What does the FDC plot?
   A. Discharge against the percentage of time it is equalled or exceeded
   B. Discharge against calendar months
   C. Cumulative volume against time
   D. Head against discharge
   Answer: A. The FDC is a cumulative frequency curve of flow against percent time equalled or exceeded. (Key point: Flow duration curve definition)

2. How is the exceedance probability computed after ranking?
   A. P = m/N x 100 with ascending rank
   B. P = N/m
   C. P = m/(N+1) x 100 with flows in descending order
   D. P = (N+1)/m
   Answer: C. Rank flows in descending order and use P = m/(N+1) x 100. (Key point: Drawing the FDC)

3. What does the PDC give for a run-of-river plant?
   A. Firm power at 100% (or 90-95%) of time
   B. Peak power at 0% of time
   C. Mean annual flood
   D. Reservoir volume only
   Answer: A. Power at 100% (or 90-95%) exceedance is the firm power. (Key point: Firm power from curve)

4. What does a steep FDC indicate?
   A. A well-regulated groundwater-fed river
   B. A flashy river that needs storage
   C. A river with no floods
   D. A river with constant flow
   Answer: B. A steep curve means flows vary greatly (flashy); a flat curve means regulated flow. (Key point: Interpreting curve shape)

## Related in Hydro Power

- [Flow duration curve and planning parameters](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Afdc-planning-parameters) — Hydro Power, chapter 3
- [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×
- [Power duration curve and primary/secondary energy](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Apower-duration-curve-energy) — Hydro Power, chapter 3
- [Layout of hydropower scheme components](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Ahydropower-scheme-layout) — Hydro Power, chapter 5
- [Advantages and limitations of hydropower](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Ahydropower-advantages-limitations) — Hydro Power, chapter 3
- [Flow depth in triangular channel](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Atriangular-channel-depth-1-in-2000) — Hydro Power, chapter 1, asked 2×

## Related in other subjects

- [Quartz significance for hydropower project](https://www.bctengineer.com/question.md?key=semester_4%2Fengineering_geology_ii%3Aquartz-hydropower-significance) — Engineering Geology II, chapter 1
- [Flow duration curve and power at mean flow](https://www.bctengineer.com/question.md?key=semester_7%2Fhydropower_engineering%3Aror-capacity-fdc-flow-table-79) — Hydropower Engineering, chapter 3
- [Load duration curve; diesel plant; ROR flow duration](https://www.bctengineer.com/question.md?key=semester_7%2Fhydropower_engineering%3Aload-duration-diesel-import-fdc) — Hydropower Engineering, chapter 3
- [Flow duration curve; firm and secondary energy](https://www.bctengineer.com/question.md?key=semester_7%2Fhydropower_engineering%3Afdc-firm-secondary-energy-69) — Hydropower Engineering, chapter 3