APPLICATION OF SPECIFIC ENERGY IN FLUID MECHANICS
- 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 Gandhinagar Institute of Technology : Department of Civil Engineering 2
- 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. Gandhinagar Institute of Technology : Department of Civil Engineering 3
- 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 Gandhinagar Institute of Technology : Department of Civil Engineering 4
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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 Gandhinagar Institute of Technology : Department of Civil Engineering 6
- 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. Gandhinagar Institute of Technology : Department of Civil Engineering 7
- 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. Gandhinagar Institute of Technology : Department of Civil Engineering 8
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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 • Gandhinagar Institute of Technology : Department of Civil Engineering 10
- 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. Gandhinagar Institute of Technology : Department of Civil Engineering 11
- 12. •The maximum height of hump is obtained as • 𝐸1 = 𝐸𝑐 + ∆𝑧 𝑚𝑎𝑥 𝐸𝑐 = 𝐸 𝑚𝑖𝑛 Gandhinagar Institute of Technology : Department of Civil Engineering 12