Open Channel Flow - Sediment Transport in Irrigation Canals: A New Approach - page 19

Critical flow
For open channel flow the specific energy (Bakhmeteff, 1912) is the
energy per unit weight with respect to the channel bottom. The piezometric
head in a point of the cross section is ( p / ρg )

+

z , which is equal to the water
depth y in that particular cross section: ( p / ρg ) y . Therefore, the

specific energy E s is the sum of the water depth and the velocity head
(assuming that the streamlines are straight and parallel):

+ z =

v 2 / 2 g E s = y + α ¯ (2.19)

αQ 2 / 2 gA 2 E s = y + (2.20)

where:
y = water depth (m)

discharge (m 3 /s) Q =

area of the cross section (m 2 )

A =

v ¯ = mean velocity in a cross-section (m/s)

E s = specific energy with respect to the bottom (m)

For a given cross-section and a constant discharge Q , the specific energy E s
is a function of the water-depth y only. Plotting this water-depth y against
the specific energy E s gives a specific energy curve for the discharge Q
(see Figure 2.6).

Specific energy E s function of water depth y

0

Specific energy E s in m

Figure 2.6. Specific energy as
function of the water depth y .

E s

Q 2 /2 gA 2 follows that for a given dis-
charge Q and a specific energy E s , which should be larger than a certain

From this figure with E s = y +