The concept of specific energy finds its application for solving many open channel problems.

1. SUBJECT :- APPLIED FLUID MECHANICS
APPLICATION OF SPECIFIC
ENERGY

2. APPLICATION OF SPECIFIC ENERGY
•The concept of specific energy finds its application for
solving many open channel problems.
•Important applications are :-
I. Analysis of flow through channel transition
II. Flow over raised channel floor
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3. 1. Flow through a rectangular channel transition :-
• The width of channel can be reduce either by
suddenly contracting or gradually reducing the width of
the channel.
• The loss of energy in flow through a gradual contraction
is much smaller than in sudden contraction.
• Therefore, in actual practice the reduction in the width
of the channel is made gradual. In case the size of the
channel to be enlarged increase in width of the channel
is also obtained gradually. In both the cases, the portion
of two the channel in which the width changes gradually
is known as the transition.
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4. • Let us consider a rectangular channel of width b1
gradually reducing to width b2, as shown in Fig.
• Let the now approaching the transition be sub-critical(d1
> dc). For a constant discharge Q.
• The discharge per unit width in the approach channel is
• 𝑞1 =
𝑄
𝑏1
• The discharge per unit width in the throat portion is
• 𝑞2 =
𝑄
𝑏2
• Now, since 𝑏2 < 𝑏1, 𝑞2 > 𝑞1
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6. •from the discharge diagram, fig , it can be observed that for
sub-critical flow when discharge q increase, the depth of
flow d decreases, hence in the transition as well as in the
throat the water surface will be lowered as show in fig.
•Specific energy at section 1 = Specific energy at section 2
• 𝐸1 = 𝐸2
• 𝑑1 +
( 𝑄 𝑏1)2
2𝑔𝑑1
2 = 𝑑2 +
( 𝑄 𝑏2)2
2𝑔𝑑2
2
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7. •In the case the flow in the approach channel happens
to be super critical (𝑑′
1 < 𝑑 𝑐) the depth 𝑑′
1 is the
lower alternate depth corresponding to specific
energy
𝐸1 = 𝑑′
1 +
( 𝑄 𝑏1)2
2𝑔𝑑′
1
2 . 𝑑1 and 𝑑′
1 are alternate depths.
•Since 𝑞2 > 𝑞1, from the discharge diagram, it can
be observed that for supercritical flow now when
discharge q increases, the depth of flow d also
increases. Thus, in the transition as well as in the
throat the water surface will rise as shown in fig.
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8. 2. Flow over raised channel floor :-
• Flow over raised floor which is also sometimes
called a hump is analyzed by using specific energy
curve. Let us consider a rectangular channel having
its bottom raised by an amount ∆z as shown in fig.
•As the channel width remains constant, the critical
depth will be some throughout.
•Let the channel be carrying a discharge Q under
subcritical flow conditions.
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10. •Specific energy at section 1 is,
𝐸1 = 𝑑1 +
𝑄2
2𝑔𝐴1
2 𝑉1 =
𝑄
𝐴1
•The hump of height ∆z is provided at section 2, the
specific energy at section 2 will be less by the
amount ∆z.
• 𝐸1 = 𝐸2 + ∆z
• 𝑑1 +
𝑄2
2𝑔𝐴1
2 = 𝑑2 +
𝑄2
2𝑔𝐴2
2 + ∆z
•
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11. •When flow is subcritical, the water surface over the
raised floor or the hump is depressed. The
maximum height of hump will be obtained when
point 2 on the specific energy curve coincides with
the point representing the critical depth. The flow
over the raised floor will then be critical.
•In case the flow in the channel is super critical the
depth of flow and the specific energy of the
approaching flow are represented by point 3 on the
specific energy curve. The depth of flow over the
raised floor will be greater than the depth of the
approaching flow.
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12. •The maximum height of hump is obtained as
• 𝐸1 = 𝐸𝑐 + ∆𝑧 𝑚𝑎𝑥 𝐸𝑐 = 𝐸 𝑚𝑖𝑛
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