# Specific energy and critical depth

Wednesday, March 13, 2013 14:54## Specific energy

Specific energy at a particular section is defined as

The total head with respect to the bed of the channel.

Or

The total head at a cross section by taking the datum passing through the bed of section at that section.

Or

## Critical depth

Critical depth may be defined as

The depth corresponding to the minimum value of Specific energy, provided that the discharge remaining constant is known as critical depth.

## Alternate depths

As we can see the graphical relation between specific energy and depth. For any E value, q remaining constant, there are two possible “y” values, say y1 and y2. These two depths are called as *alternate depths*.

However for minimum specific energy Ec, there is only one corresponding depth “yc” which is called as *critical depth*. The velocity at this point is known as *critical velocity.*

## Upper part of the curve

- If the value of “E” increases on the upper part of the curve, then “y” increases.
- For upper part, “y” is greater than ”yc”.
- For upper part of the curve, velocity is less than critical velocity.
- The flow in this portion is termed as
*sub-critical flow.* - The channel is called as deep channel for sub-critical flow.

## Lower part of the curve

- If the value of “E” increases, we can see that the value of “y” decreases in lower part of the curve.
- For lower part of the curve, “y” is less than “yc”.
- For lower part of the curve, velocity is greater than critical velocity.
- For lower part of the curve, the flow is termed as
*super critical flow*. - The channel is called as shallow channel for super critical flow.

## Critical depth (Alternate approach)

There is another way of defining the critical depth as well, which is :

The depth corresponding to maximum discharge, E remaining constant.

At point e, in the above figure, the depth is critical depth.