SPECIFIC ENERGY CURVES
GAURAV VERMA
Civil Engineering Department (2nd Year)
Dayalbagh Educational Institute, Dayalbagh, Agra.
August, 2018
Submitted To: Mr. Gurumukh Das.
gaurav170350@dei.ac.in
https://www.linkedin.com/in/gauravverma-5663b0174
OUTLINE:
Introduction.
Channel Flow.
Specific Energy Curves.
Critical Depth and Velocity.
Condition For Minimum Specific Energy.
Condition For Maximum Discharge.
INTRODUCTION:
 In the solution of many problems of channel flow
the concept of specific energy is quite useful ,
which was first introduced by Bakhmettef in
1912.
 The specific energy of flow at any channel section
is defined as the energy per unit weight of water
measured with respect to the channel bottom as
the reference or datum. Thus the specific energy
at any section is the sum of the depth of flow at
that section and the velocity head.
Channel flow:
 A channel may be defined as a passage through
which water flows under atmospheric pressure. As
such in channels the flow of water takes place with
a free surface which is subjected to atmospheric
pressure.
 No pressure difference can be built up between
any two sections along the channel.
 The flow in channels is carried out as a result of
the earth’s gravity.
 For e.g., rivers, streams, underground drains,
tunnels,etc.
Specific energy curves:
 The specific energy E at any section is given by
E = y + V2/(2g).
Or
E = y + Q2/(2gA2). ….. Eq.n(1)
 For a given channel section and discharge the
above equation may be represented graphically in
which specific energy is plotted against the depth
of flow. The curve so obtained is known as
specific energy curve. The curve has two limbs AC
and BC.
 The lower limb AC approaches the specific energy
axis towards the right.
Specific energy curves:
 The upper limb BC approaches asymptotically to
the line OD which passes through the origin and
has an angle of inclination equal to 45°.
 At any point on this curve the ordinate
represents the depth of flow and the abscissa
represents the specific energy which is equal to
the sum of the depth of flow and the velocity
head.
Critical depth and velocity:
 The depth of flow at which the specific energy
is minimum is called critical depth. Similarly,
the velocity of flow at the critical depth is
known as the critical velocity.
 The flow at the depths greater than the critical
depth is known as subcritical flow or tranquil
flow.
 The flow at the depths smaller than the critical
depth is known as supercritical flow or rapid
flow.
Condition for minimum specific energy:
 For a given discharge the condition for minimum
specific energy can be obtained by differentiating
equation (1) with respect to y and then considering
(dE/dY)= 0. This will results in
V2 =gD
This is the condition for minimum specific energy.
Where,
Hydraulic Depth D = A/T,
&
T = Top width of flow.
Condition for minimum specific energy:
 We may also written it as V2/sqrt(gD) = 1.
 Froude number : The quantity V2/sqrt(gD) is known
as the Froude number. Thus,
 For critical flow, Froude number = 1.
 For subcritical flow, Froude number < 1.
 For supercritical flow, Froude number >1.
Condition for maximum discharge:
 Solving Eqn.(1) for Q we get,
Q = sqrt[2A2g(E-y)].
….. Eq.n(2)
In a given channel section for a given value of specific
energy E, the condition for maximum discharge is
obtained by putting (dQ/dy) = 0. Thus differentiating
eq(2) with respect to y and equating it to zero, we get
E = A/(2T).
Substituting the value of E obtained above in eq(2), it
may be simplified as
Q2/g = A3/T
Condition for maximum discharge:
 The above equation which we get in the
previous slide is the criterion for the critical
state of flow.
 It is thus observed that for a given specific
energy the discharge in a given channel
section is maximum when the flow is in the
critical state.
References:
 Modi, P.N., and Seth, S.M.,”Hydraulics and
Fluid Machines”.
 Slideshare.net.
Thank yOu !