Advanced Water Engineering: Energy Depth Relationship in Open Channel Flow

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E1: The flow is subcritical
The total energy here remains constant but the flow per unit width changes
q p= Q
B1
qQ= Q
B2
; Hence B1>B2
and q p <qQ
So as the flow width increases at a particular specific energy, the depth value decreases as shown
in the figure
q=flow over unit width
q1> q2 >q3

It is different from E2 since in E2 the flow over the depth does not change the specific energy but
here specific energy does not change while there is a change in the flow over the width. Still, this
is a subcritical flow because V (wave velocity) < C0 (wave celerity) and under this condition the
wave will travel in the upstream direction. Hence, F= V
C0
, Fr < 1 (where Fr is the Froude
number) (Hager & Castro-Orgaz 2015).
E2: Energy depth relationship in a rectangular channel
In open channel flow, the specific energy is the energy drops relative to the channel bottom. The
specific energy is expressed in terms of kinetic energy and potential energy and total energy
(Kabiri-Samani, Bakhshian & Chamani 2017). The Bernoulli’s equation which originates from a
control volume analysis is used in the description of the specific energy relationships in fluids.
The three components of energy in Bernoulli’s equation are density, pressure and velocity. The
velocity of the flow is linear and the depth of the flow can be determined using the equation
v1
2
2 g + y1 + P1
r −h p= v2
2
2 g + y2 + P2
r (Viero & Defina 2017)
Where y is the vertical distance
P=pressure
V= velocity
Hp=head pressure due to friction
r=the specific weight of the fluid; and
g=the acceleration due to gravity