---
title: "Definition: specific energy"
subject: "Hydro Power"
chapter: 1
key: "semester_6/hydro_power:specific-energy"
source: https://www.bctengineer.com/q/semester_6/hydro_power/specific-energy
site: BCT Engineering
---

# Definition: specific energy

Hydro Power · Chapter 1: Introduction to Basic Fluid Mechanics and Hydraulics

- Asked in: 2072 Asoj, 3 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/hydro_power/specific-energy
- Whole chapter: https://www.bctengineer.com/md/semester_6/hydro_power/chapter-1

## Question

Define specific energy.

## Short answer

Specific energy is the total energy per unit weight of fluid relative to the channel bed, E = y + V²/(2g). For a given discharge, it has a minimum at critical depth yc = (q²/g)^(1/3) where Emin = 1.5yc, with two possible alternate depths (subcritical and supercritical) for any E > Emin.

## Answer

**Specific energy** ($E$) is the total energy per unit weight of liquid at a channel section, measured **with respect to the channel bed** as datum.

$$
E = y + \frac{V^2}{2g} = y + \frac{Q^2}{2gA^2}
$$

For a rectangular channel with discharge per unit width $q$: $E = y + \dfrac{q^2}{2gy^2}$.

Key points:
- A plot of $E$ against $y$ for constant $q$ is the **specific energy curve**.
- For a given $E$ there are two possible depths (alternate depths): one subcritical, one supercritical.
- $E$ is minimum at **critical depth** $y_c = \left(\dfrac{q^2}{g}\right)^{1/3}$, where $E_{min} = 1.5\,y_c$.

```text
 y |      /  subcritical
   |     /
   |    /
yc |---*  (Emin, Fr = 1)
   |    \
   |     \___ supercritical
   +-----------------------> E
```

Example: $q = 2$ m²/s, $y = 1$ m: $E = 1 + \dfrac{4}{2 \times 9.81 \times 1} = 1.204$ m.

## Check yourself

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

1. Specific energy in an open channel is measured with respect to:
   A. A fixed horizontal datum
   B. The water surface
   C. The channel bed
   D. The energy line
   Answer: C. It is the energy per unit weight with the channel bed as datum: E = y + V^2/2g. (Key point: Definition)

2. For a given E greater than Emin and constant q, how many depths are possible?
   A. One
   B. Two (subcritical and supercritical)
   C. Three
   D. None
   Answer: B. The specific energy curve gives two alternate depths for each E above the minimum. (Key point: Alternate depths)

3. At critical depth in a rectangular channel, Emin equals:
   A. yc
   B. 2 yc
   C. 1.5 yc
   D. 0.5 yc
   Answer: C. Emin = 1.5 yc, where yc = (q^2/g)^(1/3) and Fr = 1. (Key point: Minimum energy)

## Related in other subjects

- [Specific energy, minimum value and critical flow](https://www.bctengineer.com/question.md?key=semester_4%2Fhydraulics%3Aspecific-energy-minimum-critical-curve) — Hydraulics, chapter 7, asked 2×
- [Specific energy of 400 t train on 1% up-gradient](https://www.bctengineer.com/question.md?key=semester_7%2Futilization_of_electrical_energy%3Atrain-400t-up-gradient-specific-energy) — Utilization of Electrical Energy, chapter 4
- [Minimum specific energy for triangular channel](https://www.bctengineer.com/question.md?key=semester_4%2Fhydraulics%3Aminimum-specific-energy-triangular-5-4-yc) — Hydraulics, chapter 7
- [Specific energy from alternate depths](https://www.bctengineer.com/question.md?key=semester_4%2Fhydraulics%3Aspecific-energy-in-terms-of-alternate-depths) — Hydraulics, chapter 7