Specific Energy | Irrigation Engineering - Civil Engineering (CE) PDF Download

Total energy head at a section in an open channel flow is given by:
E = z + h + (v²/2g)
Where, z is the elevation of the bottom of the channel from an arbitrary datum. If we take the datum as the bottom of the channel itself, the equation becomes.
E = h + (v²/2g)
This represents the specific energy of the channel flow.
Thus the specific energy at any section of a channel is the sum of the depth of flow and the kinetic head at that section.
In the case of a steady uniform flow, depth of flow and velocity is same at all sections. Therefore specific energy head is same at all sections.

Considering a non-uniform flow taking place in an open channel of rectangular cross-section of width b, at a steady rate Q.
Discharge per unit width,
q = Q/b = Constant.
Velocity at the section,
v = Q/bh
= q/h
or q = vh
Thus the product of velocity and depth of flow is constant at all sections.
E = h + (v²/2g)

Where, K = q²/2g.

Thus, for a given value of q specific energy head is a function of depth as follows.
E = E₁ + E₂
Here, E₁ = h
and
Where
E₁ = Static energy head
E₂ = Kinetic energy head

If we plot static energy head, kinetic energy head and specific energy head against depth flow, the graph obtained is as follows:

From the above, it follows that specific energy head first becomes lesser and lesser when depth increases and reaches a minimum and then it increases as the depth is increased.

The depth corresponding to minimum specific energy is called the critical depth (h_c). When the depth of flow is greater than the critical depth, the flow is called streaming flow or tranquil flow or sub-critical flow.

Critical flow: When the flow is such that specific energy is minimum, the flow is called a critical flow. Therefore at critical flow, depth of flow is equal to the critical depth (h_c).
The velocity of flow at critical depth is called the critical velocity.