Definition: specific energy

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 $E_{min} = 1.5\,y_c$.

 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.