**MILD SLOPE CHANNEL HYDRO POWER GENERATION HYDRO POWER GENERATION FROM SUBCRITICALCANALS**

GOPALAKRISHNA, Krishnaji, Rao (# 530, Sudeendra Krupa 1st Cross, 1st Main,Maruthi Temple Road, Kuvempunagar,Mysore 3, Karnataka, 570 02, IN)

**E02B9/00**US4014173A | 1977-03-29 | |||

US3593527A | 1971-07-20 | |||

US2025722A | 1935-12-31 | |||

US2605616A | 1952-08-05 |

I Claim, 1. A mild slope hydro power generation system for use with fluid flow channels containing subcritical fluid flow, pre accelerated before the chute, Final accelerated at chute to supercritical flow , increases upstream ambient flow velocities thereby creating kinetic energy at chute and convert the kinetic energy in to head or potential energy by hydraulic jump at downstream of chute. The hydraulic jump holding the back tail water within the free board reach i.e. last reach of the system, created by a gated weir, positioned at end of the system. The potential energy at free board reach of irrigation canal diverted in to power house located on the banks of the canal through a intake channel for power generation and leave back to the irrigation canal through tail race channel after the power generation. 2. A mild slope hydro power generation as in claim 1 wherein the acceleration zone comprises a pre-acceleration zone, Final-acceleration zone, hydraulic jump and weir at end of system. 3. A mild slope hydropower generation system as in claim lwhere the system comprises an open channel structure. 4. A mild slope hydropower generation system as in claim 3 wherein the open channel has a rectangle cross-sectional shape or circular cross section or U shaped cross sectional shape. 5. A mild slope hydropower generation system as in claim 3 wherein the open channel has a trapezoidal cross-sectional shape or Elongated circular cross section shape. 6. A mild slope hydropower generation system as in claim 1 wherein the bed slope of the channel is modified suitably to control the normal depth of the channel. 7. A mild slope hydropower generation system as in claim 1 wherein the acceleration zone is obtained by creating sill height i.e. by putting hump of sufficient height on the existing canal bed and diverging or modifying the bed width of control section to avoid the chocking effect at upstream depth of existing canal. 8. A mild slope hydropower generation system as in claim 1 wherein the acceleration zone is comprised of a pre-accelerated zone defined by a supercritical bed width contraction on chute or inclined plane of the channel and Final-acceleration zone, positioned downstream of pre- accelerated zone, comprised of a chute. 9. A mild slope hydropower generation system as in claim 8 wherein the chute or inclined plane has a trapezoidal or rectangle or circular or U shaped or elongated circular shape. 10. A mild slope hydropower generation system as in claim Iwherein conversion of kinetic energy in to potential energy or head comprised of a hydraulic jump. 11. A mild slope hydropower generation system as in claim 1 wherein the concept is implemented in flow channel with predetermined existing free board location all along the flow channel. Page No. 18 12. A mild slope hydropower generation system as in claim 1 wherein the concept also implemented in flow channel without free board location by creating free board all along the flow channel by way of rising embankment on either side of the channel. 13. A mechanism for mild slope hydropower generation for subcritical flow comprising pre and Final-acceleration section to increase flow velocity above ambient upstream velocities, convert in to potential energy by hydraulic jump and weir positioned at end of system. The intake structure on side of weir and a penstock to convey the water in to power house positioned on the banks of the channel and also comprising tail race channel. 14. The mechanism in claim 13 where in the power house consists of electro-mechanical equipments for power generation. 15. The mechanism in claim 13 wherein after power generation, the tail race channel convey the water back to the irrigation canal. The depth at tail race canal is lesser than or lower than the depth at existing irrigation canal to achieve and improve the head of the power generation system. 16. A mild slope hydropower generation system as in claim 1 wherein the tail race channel comprised of hydraulic jump at end of the tail race channel that connects the irrigation canal to recover the normal depth of irrigation canal. 17. The mechanism as in claim 16 wherein the hydraulic jump working as buffer between irrigation channel and tail race channel i.e. the recovered normal depth of irrigation channel should not reflect to the upstream tail race channel. Page No. 19 |

HYDRO POWER GENERATION FROM SUBCRITICALCANALS

The present inventions concerns the generation of power in subcritical channels by accelerating subcritical flow in to supercritical hydraulic jump and converting or transferred the kinetic energy in to required potential energy for hydro power generation.

The need for power is on the increase and this need influences the feasibility of generating electricity using cost - effective techniques, from a variety of water sources and especially from direct flowing waters in manmade canals, tailraces, diversion channels, or other fluid flow channels, is very desirable. The driving impetus for this undertaking is the recognition that there exists an enormous, worldwide potential for the generation of power in subcritical channel of manmade canal in to useful hydro electric power. At the present time this potential for power generation remains untapped.

The present invention herewith addresses the unique challenge interest in the cost effective extraction of hydro electric power from the canals, especially in the manmade conveyance systems. The first and foremost, since the primary function of these water conveyance systems is the conveyance of water for drinking or irrigation purposes, it is imperative that the installation and operation of a power generation facility in these subcritical canal must not have an adverse impact on their capability to deliver water in a desired flow and at an expected quality. Usually power generation is possible in the canal drops however in the subcritical channel so far no power generation was through of due to mild bed slope in the channel. The present invention addresses that power generation is possible in subcritical mild slope channel without canal drops by suitably modifying subcritical channel to create hydraulic jump and converting kinetic energy in to potential energy.

The philosophy mentioned above addresses only the potential energy created at upstream side by raising of FRL. However in irrigation canals the tail water depth can also be reduced to a certain extent by suitable modification of tail race canal i.e. It is obvious that after power generation the water has to go back into original ^{1 } canal to obtain the original FSL so that irrigation is not affected. However whenever possible and no irrigation is envisaged for a certain length downstream then it is possible to lower the tail race water level after the power house by suitable modification in tailrace canal . The theory consists of creating hydraulic jump at the end of tailrace channel where tail race joins to original channel.

The present invention is based upon a design philosophy and criteria for a hydraulic jump of the subcritical channel that will accomplish this objective cost effectively, and without adversely impacting the primary function of these waterways, i.e., to convey water for irrigation or drinking purpose.

A Subcritical channel with sufficient free board is identified and briefly evaluated for potential deployment in Irrigation canals to generate power cost effectively. For example, a 16.45 m width,285 cumecs flow canal with a depth 2.131 m and velocity of 16.71 m/s before hydraulic jump and sequent depth 10 m can generate 9505 kW or 9.5 MW power.

Page No. 1 Brief description of the Drawings

FIGURE 1: Specific-energy curve

FIGURE 2: Hydraulic jump interpreted by specific-energy and specific force curves. FIGURE 3: Definition sketch of a hydraulic jump.

FIGURE 4: Relation between Fl and Y2 Y1 for a hydraulic jump in a horizontal channel. FIGURE 5: Various types of hydraulic jump.

FIGURE 6: Effect of tail water depth on the formation of hydraulic jump below a weir.

FIGURE 7: Graphical method to find location of hydraulic jump.

FIGURE 8: Gassification of flow profiles for gradually varied flow.

FIGURE 9: Plan and elevation of existing canal.

FIGURE 10: Trapezoidal cross section of the canal.

FIGURE 11: Water surface profile for existing canal for length .

FIGURE 12: Plan and elevation of proposed canal in mild slope canal.

FIGURE 13: Initial 2 profile in reach 1.

FIGURE 14: Initial M2 profile in reach 2.

FIGURE 15: S2 profile in reach 3 and M2 profile in reach 2.

FIGURE 16: M2 water surface profile of reach land 2 S2 profile of reach 3.

FIGURE 17: S2 profile in reach 4.

FIGURE 18: M3 profile in reach 5.

FIGURE 19: Final profile from reach 1 to 5.

FIGURE 20: Graphical method to find location and length of hydraulic jump for 6 m downstream water depth.

[027] FIGURE 21: Graphical method to find location and length of hydraulic jump for 8 m downstream water depth.

[028] FIGURE 22: Graphical method to find location and length of hydraulic jump for 9.5 m downstream water depth.

[029] FIGURE 23: Hydraulic Jump for 6 m downstream normal depth.

[030] FIGURE 24: Hydraulic Jump for 8 m dam downstream.

[031] FIGURE 25: Hydraulic Jump for 9.5 m dam downstream.

[032] FIGURE 26: Water surface profile of proposed canal.

[033] FIGURE 27: Plan and elevation of proposed tail race canal.

[034] FIGURE 28: Water surface profile of proposed tail race canal.

[035] FIGURE 29: Plan and elevation of proposed power generation system.

DESCRIPTION OF ONE OR MORE PREFERRED EMBODIMENT

036. In open channel water conveyance systems, gravity is the driving force that moves the water while frictional forces along the wetted perimeter of the channel oppose the motion. A slight downward slope (generally less than 10 degrees) is sufficient to overcome the opposing frictional forces. The bottom or sides of a flow channel may be either unlined or lined with suitable materials, and when lined flow retarding frictional forces are reduced. The overall flow velocity in these types of open channels is usually designed to be relatively small to prevent turbulent flow conditions in the channel or to prevent scouring along the wetted perimeter of the channel. Ambient flow velocities in open fluid flow channels are generally less than 2 m per second.

Page No. 2 Consequently, since the available power from a channel is proportional to Discharge and Head (Q & H). Normally in irrigation subcritical channel, a huge water or discharge (Q) available but it is very rare or not possible to find Head (H) or potential energy required for power generation, because the irrigation channel are mild slope channels. I have found that this problem may be addressed by establishing the potential energy or Head (H) by modifying the channel cross section at designated location along the length of the channel where a novel mild slope hydropower system is to be deployed. Any such modification to channel section must not adversely affect the basic function of the channel, i.e., to convey water for irrigation or drinking purposes, and this invention produces power from otherwise mild slope subcritical channels and without any undesirable effects on the primary purpose of the flow channel.

A contraction in a channels cross section generally referred to as throat, will result in a increase in flow velocity through the throat. This phenomenon is analogous to the venture effect in pipe flow, notwithstanding significant differences between pipe flow and open channel flow is driven by pressure where as the open channel flow is caused by gravity.

Ambient flow velocities in open channels are generally in subcritical range and head required for power generation is almost nil. Flow velocities must be accelerated in the waterways beyond a lower threshold limit at those designated location to establish kinetic energy and through hydraulic jump convert kinetic energy in to potential energy or head at downstream of jump where the water is diverted in to intake of the mild slope hydro power system are to be installed.

For open channels with small slopes, uniform or gradually varied flows, and negligible energy losses, the flow hydraulics are governed by the Bernoulli equation which express conservation of energy along the length of the channel:

Y _{1 }+V _{1 } ^{2 }/2g =Y _{2 }+V _{2 } ^{2 }/2g (1).

Where Y is the depth of flow, V is the flow velocity, g is the acceleration due to gravity, and subscripts 1 and 2 refers to section 1 (Upstream) and section 2 (Downstream ).

By definition, the specific energy E of an open channel flow relative to the bottom of the channel is the sum of the two terms on either side of the Bernoulli equation 1 above:

E= Y+V ^{2 }/2g (2) A plot of equation 2, generally called the specific energy curve, is shown in figurel, with the flow depth Y along the vertical axis and specific energy, E, along the horizontal axis.

As shown in figure 1, for a given values of specific energy, there are two possible flow depths in a channel. At higher or deeper depth, the velocities are smaller ( subcritical value) and at the lower value of depth, the flow velocity is higher (super-critical value). The transition from sub- critical to super-critical velocity happens at the smallest value of specific energy.

In open channels that are primarily used for water conveyance purpose, the velocities are generally in the sub-critical range. In other words, the larger value of two possible flow depths for a given value of specific energy is applicable and the flow velocity is relatively very small. As the channel cross section narrows, the flow depth decreases while the flow velocity increases. At the critical depth, the flow velocity changes from sub-critical to super-critical.

Page No. 3 In open channel flow the hydraulic jump occurs when a super-critical stream meets sub-critical Stream of sufficient depth. The super-critical stream jumps up to meet alternative depth. While doing so it generates considerable disturbances in the form of large scale eddies and a reverse flow roller with the result that the jump falls short of its alternative depth.

Figure 2 shows the hydraulic jump interpreted by specific-energy and specific -force curves and Figure 3 is a schematic sketch of typical hydraulic jump in a horizontal channel. Section 1, where the incoming super -critical stream undergoes an abrupt rise in the depth forming the commencement of jump, is called the toe of jump. Section 2 which lies beyond the roller and with an essentially level water surface are called the end of the jump and distance between section 1 and 2 is the length of jump, Lj. The initial depth of the super-critical stream is Yj and Y _{2 } is the final depth, after the jump, of the sub-critical stream. The two depths Yi and Y _{2 } at end of the jump are sequent depths.

Due to high turbulence and shear action of the roller, there is considerable loss of energy in the jump between section 1 and 2. In view of the high energy loss, the nature of which is difficult to estimate, the energy equation cannot be applied to section 1 and 2 to relate the various flow parameters. In such situation, the use of momentum equation is advocated. In fact, the hydraulic jump is typical example where a judicious use of the momentum equation yields meaningful results.

In hydraulic jump the momentum equation used for calculate sequent depth Y _{2 } and energy loss can be written as follows:

Sequent Depth Y _{2 }= Y,/2 [ (1+8F, ^{2 })-!] (3)

Energy loss ΔΕ = (Y _{2 }-Yi) ^{3 }/4Y _{2 }Y _{: } (4).

Where Yi is initial depth of jump, Y _{2 } is Sequent depth to Yi of jump and Fi is Froude number of initial depth Y, .

Equation 2, 3 and 4 may be used to calculate the flow velocities along a channel gradually varying width, sequent depth of hydraulic jump and energy loss of hydraulic jump respectively. For illustrative purpose, Table 1 summarizes these calculation of flow velocity and other relevant parameters of channel with gradually contraction and hydraulic jump in channel width from 32 m to 8 m at entrance of jump and constant discharge Q value of 285 Cumecs.

Page No. 4 11 000198

TABLE 1: SUMMARY OF FLOW VELOCITY AND DEPTH OF RECTANGLE CHANNEL

WITH BED WIDTH CONTRACTION ON CHUTE AND HYDRAULIC JUMP

0 Table 1 also shows the values of the Froude number, F, defined blow, for various flow

velocities.

F = V/ (gD) (5)

In equation 5, D is the hydraulic depth, and for a rectangular channel D will be equal to the flow depth Y. for trapezoidal channel, D is defined as (b+zY)/Y(b+2zY). Where b is the channel width at the base and z is the inverse of the slope of the side of the channel. The Froude number is less than 1 for sub-critical flows, greater than 1 for super-critical flows, and equal to 1 at the critical flow velocity.

1 Where the flow depth Y is used, it can be shown that the denominator in equation 5 for the

Froude Number is the celerity of an elementary gravity wave in shallow water.

C = ^ (gY) (6)

Then, equation 5 can be rewritten as

F = V/c (7)

Page No. 5 11 000198

With the Froude Number now defined as in equation , the following observation can be made:

1. Where F<1, the flow in a particular channel is sub-critical. Gravitational forces will be

dominant over the inertial forces, and the velocity of flow is less than the celerity of an elementary gravity wave. Thus, such a wave can propagate upstream against the flow .

As a result, the upstream areas are affected by what happens in the downstream areas, and narrowing of the channel in the downstream may affect the flow depth upstream. 2. Where F>1, the flow in a channel is super-critical. Now inertial forces are

dominant over the gravitational forces, and the velocity of flow is greater than the celerity of an elementary gravity wave. Thus, such a wave cannot propagate upstream against the flow. As a result, the upstream areas are not affected by what happens in the downstream areas, and narrowing of the channel in the downstream will not affect the flow depth upstream.

The hydraulic jump was first investigated experimentally by the Italian engineer Bidone, in 1818. It is an intriguing and interesting phenomenon that has caught the imagination of many research works. The literature on this topic is vast and ever-expanding. The main reason for such continued interest in this topic is its immense practical utility in hydraulic engineering and allied fields. Practical application of the hydraulics jump are many: It is used

(1) To dissipate energy in water flowing over dams, weirs, and other hydraulic structure and

thus prevent scouring downstream from the structures ;

(2) To recover head or raise the water level on the downstream side of the channel thus

maintain high water level in the channel for irrigation or other water distribution purpose ;

(3) To increase weight on an apron and thus reduce uplift pressure under a masonry structure

by rising the water depth on the apron ;

(4) To increase the discharge of sluice by holding back tail water, since the effective head will be reduced if the tail water is allowed to drown the jump.

A hydraulic jump primarily serves as energy dissipater to dissipate excess energy in most applications, so for the hydraulic jump never used for creation of head in subcritical flow channel for power generation. In this invention, I found that the application 2 and 4 of hydraulic jump, mentioned on above paragraph 055 can be used to create head for power generation. In this invention application 2 can be used to rise the water level or head or potential energy at channel downstream of jump and the application 4 can be used to holding back tail water, that caused by obstruction, which is required to rise the water level to increase potential energy or head above the normal depth of the channel at suitable location required for power generation.

For supercritical flow in a horizontal channel, the energy of flow is dissipated through frictional resistance along the channel, resulting in decrease in velocity and an increase in depth in the direction of flow. A hydraulic jump will form in the channel if the Froude number F, of the flow, the flow depth Yi, and downstream depth Y _{2 } satisfy the equation 3 and equation can be rewritten as:

Y _{2 }/Y, =½[ (l +8Fi ^{2 }) -l ] (8) this equation may be represented by the curve in figure 4. This curve verified satisfactorily with many experimental data and will be found very useful in the analysis and design for hydraulic jumps.

Page No. 6 Hydraulic jump on horizontal floor are of several types. According to the studies of U.S. Bureau of reclamation , these types can be conveniently classified according to the Froude number Fj of the incoming flow as follows and also shown in Figure 5.

For Fj = 1, the flow is critical, and hence no jump can form

(a) For F] = lto 1.7, The jump may be called an undular Jump.

(b) For Fi = 1.7 to 2.5, The jump may be called a weak Jump.

(c) For Fj = 2.5 to 4.5, The jump may be called an oscillating Jump.

(d) For Fi = 4.5 to 9.0, The jump may be called a steady jump.

(e) For F _{! } = 9.0 and larger, The jump may be called a strong jump.

Similar to hydraulic jump on horizontal floor, jump in sloping channels having appreciable slope, it is essential to consider the weight of water in the jump; in horizontal channel the effect of this weight is negligible. Thus, the momentum formulas for jump on horizontal floor cannot be applied straightforwardly to jump on sloping floor. The momentum principle can be used to derive an equation analogous to equation 3, and sequent depth ration in sloping floor jump can be written as follows:

Where Y _{2 } is Sequent depth corresponding to Yi in a horizontal floor jump, Y _{s } is sequent depth of sloping floor jump and tanS is the bed slope of the sloping floor channel.

Length of Jump:

The length of jump may be defined as the horizontal distance between the toe of the jump to section where the water surface becomes essentially level after reaching the maximum depth and shown in figure 3. The expression for length of the jump on horizontal and sloping floor channel can be written as:

Length of the jump in horizontal floor Lj = 6.9(Y _{2 }-Yi) (10)

Length of the jump on sloping floor , Lj = Y _{2 }(6.1 + 4 tane) — -(11)

Height of the Jump h = Y _{2 }-Yi — -- --(12)

Location of Jump

The depth downstream of hydraulic structure, such as an overflow spillway, a chute, or a sluice, controlled by the downstream channel or local control is known as tail water depth. Tail water level plays a significant role in the formation of jump at a particular location. There are three alternative patterns that allows a hydraulic jump to form downstream of hydraulic structure and shown in figure 6.

Page No. 7 1 000198

Case 1: As shown figure 6, this pattern in which the tail water depth Y _{2 }' is equal to the depth Y _{2 } sequent to Y[. In this case the value of F,, Y and Y _{2 }' (= Y _{2 }) will satisfy equation 8, and jump will occur on a solid apron immediately ahead of the depth Yi.

Case 2: Represents the pattern in which the tail water depth Y _{2 }' is less than Y _{2 } sequent to Yi.

This means that the tail water depth in case 1 is decreased. As a result, the jump will recede to far downstream from structure to a point where equation 8 is again satisfied.

Jumps with sequent depth Y _{2 } equal to or less than Y _{2 }' as in case 1 and case2 are known as free jumps.

Case 3: Represents the pattern in which tail water depth Y _{2 }* is greater than Y _{2 } sequent to Y,.

This means that the tail water depth in case 1 is increased. As a result, the jump will be forced upstream and may finally be drowned out at the structure, becoming a submerged jump.

A hydraulic jump formed whenever the momentum equation 8 is satisfied between the supercritical and subcritical parts of stream. This theoretical condition is generally used locate the position of jump. For a closer estimate of the jump position, however, the length of the jump should be considered. The figure 7 illustrate the location of a jump.

Figure 7 shows a rectangle sluice in a mild channel. The profile AB and CD can easily identified as of M3 and M2 type. The algorithm for the location of the location of the jump by graphical and numerical computation procedure is as follows:

1. Starting from point A, compute the GVF profile M3 i.e. AB. Point B is the critical depth.

2. Calculate sequent depth profile A' B, this curve is obtained by using appropriate form of the

general momentum equation 3. For a channel of very small slope if depth G = YI, depth at E = Y _{2 } = Y,/2 [ (1+8F, ^{2 })-1].

3. Starting from point D compute the M2 profile, curve CD.

4. The intersection of the curve D F C with A' F B i.e. the point F shift the point on M2

profile in the downstream direction by respective Lj values, obtained point F and curve C F.

5. The toe of the jump, point G, is located by drawing a horizontal line from F to cut A' B at E

and then a vertical line from E to cut the curve A B at G.

As an exemplary embodiment of the present invention, the design of the present invention can assume a trapezoidal canal of length 2000 m, width of about 16.45 m, bed slope of 1:7500, Manning's N is 0.018, side slope of 2:1, discharge rate of 285 cumecs, an velocity of 1.618 m s. The entire 2000 m length canal will be suitably modified and divided in to 5 reaches.

Reachl is 400 m length, the existing canal design is to be retained. Reach 2 is 20 m length , it is diverge transition from trapezoidal to rectangle to create sill height of 3.5 m above the existing bed level without choking the upstream depth. The bed slope of the existing canal will be modified in to adverse or upward slope of ratio 1: 5.65, diverge the bed width from 16.45 m to 32 m and converge the top width from 40 m trapezoidal to 32 m rectangle by standard transition method considering = 12.5° Reach 3 is 60 m length, the sill is continued with the bed slope of the reach is 1:200 and the normal depth Y _{n }= 1.7 m is maintained throughout the reach. Reach 4, the chute with transition is a Acceleration zone length of 70 m with bed width varying from 32 m to 8 m and bed slope 3.5:70. In this reach the first 55 m length is converging rectangle standard transition from 32 to 8 m bed width by angle of θ = 12.5° the rest 15 m length is rectangle throat, accelerate the velocities to supercritical, take hydraulic jump due to break in the bed at end of the reach, rises the water level or convert kinetic energy available

Page No. 8 before the jump in to potential energy after hydraulic jump losses at downstream of jump. Any further increase in tail water depth i.e. in reach 5 of the channel required for power generation, hydraulic jump holding the back tail water (if tail water depth less than or equal to sequent depth (Y _{2 }) of jump). Reach 5, total length of 1450, or more depending up on availability of free board length in the canal. In this reach also same original existing canal design will be retained i.e. Y„ = 6.1, bed slope 1:7500 and at end of the reach will construct a 10 m gated weir to pool the water above the normal depth( Y„) of the original canal and divert the water in to power generation.

TABLE 2: PROPOSED CANAL DESIGN SUMMARY

065 The bed width, bed slope and other parameters of modified canal design is tabulated in table 2, and elevation and plan of the existing and modified channel section is shown in figure 8 .

066 Once the potential head created, from the above mechanism divert the water to power house located on the canal banks by head race or intake approach channel of length 50 m with bed slope of 1:7500 for power generation. When the water exit from power house after power generation it required to leave back to irrigation channel by tail race channel of length 100 m with bed slope of 1:4500. At end of tail race channel a chute of 100 m length with bed slope of 1.94:100 is placed between irrigation and tail race channel. The proposed design of Head race or intake approach channel, Tail race channel and Tail race chute is shown in table 3.

Page No. 9

Chute

TABLE 3: PROPOSED HEAD RACE AND TAIL RACE CANAL AND TAIL RACE CHUTE DESIGN SUMMARY

In this invention the pre acceleration zone i.e. reach 3 and chute zone i.e. reach 4, plays a important role to obtain potential energy at downstream of hydraulic jump. To obtain potential energy (Y _{2 }) 9.665 m for power generation, subcritical velocities would accelerate to supercritical velocity to create kinetic energy at acceleration ( chute ) zone. The potential energy after losses of hydraulic jump Y _{2 } at reach 5 can be calculated by equation 8. For different width, kinetic energy of canal at rapidly varied flow section at reach 4 is tabulated in table 5.

068 An exemplary embodiment of the construction details of canal system or design according to the present invention is shown in figure 12. The figure 8,9,10and 1 1 represents the classification of flow profile for gradually varied flow, plan and elevation of existing canal, trapezoidal cross section of the canal and water surface profile of length 2000 m of existing canal respectively. The expected initial and steady condition water surface profile at each reach and other hydraulic parameters of modified canal are described in detail.

069 In the plan view of fig 12, the flow direction from left to right is labeled and shown by an arrow the left end of the figure. The flow begins at an entrance end reach 1 and concludes at an opposite exit end reach 5. Various length and designation are indicated for the several sections that make up the canal system or design and are noted along the bottom most line in the figure. They are reachl , reach2, reach3, reach4,and reach5 respectively.

070 With reference to the elevation view of fig 12, there are number of angled bottom floor structures that together with obstruction walls make up the canal system or design. The entrance

Page No. 10 end begins with reachl, where the existing or original canal cross section is retained, and the canal parameters of reach 1 is as shown in first row of table 2. Since Y„ > Y _{c } with free flow condition an M2 profile as expected is obtained, calculate and plot the M2 profile with depth 6.1 m at 0 m chainage to 400 m chainage. Figure 13 presents the flow profile in reach 1.

Rreach 2 begins with change in bed slope, where the existing or original canal cross section is modified, i.e. the bed of the canal changes from 1:7500 to adverse slope of ratio 1:5.65 at chainage 400m and continues up to chainage 420 m for a length of 20 m, and sill height of 3.5 m created . the canal parameters of reach 2 is as shown in second row of table 2. Since because of the sill height there may be chance of choking the upstream depth but with our canal design parameters at this reach the backwater or choking of upstream depth is very nominal and it is within the free board area. The Discharge and Head rating table for 3.5 m sill height is calculated reach 2 and upstream depth in reachl V/S Discharge is tabulated in table 4 below. The plot of profile as shown in fig 14.

TABLE 4: DISCHARGE AND HEAD RATING TABLE AT REACH 2

With an sill height 3.5 m provided at chainage 420 m and because of diverge transition and bed slope of 1:200 in this reach and since Yn < Yc the profile can be expected. The plot of S2 profile as shown in figure 15.

Reach 3 starts at tip of the 3.5 m sill height at end of reach 2 to continue 60 m downstream of canal. The canal parameters of reach 3 is as shown in third row of table 2. A transition in the bed width from 16.45 m to 32 m has been provided (refer to standard transition pattern) and it is used for pre-acceleration zone of subcritical velocity. Figure 16 gives the initial flow profile from reach 1 to 3.

Page No. 11 0198

074 The reach 4 is mainly used for final acceleration after reach 3, the canal parameters of this reach

is tabulated in fourth row of table 2. In this reach the acceleration to supercritical flow and Since y _{c } > y„ an S2 profile of water is seen as expected. The velocity in this section rapidly increases.

The maximum velocity attained would be around 15.838 m/s. Figure 17 represents the S2 profile in reach 4.

075 Based on above results the water surface profiles for all the reaches have been plotted. Figures

12 to 24 presents the water surface profiles in different reaches for the proposed design of the canal. Figure 18 presents the occurrence of flow profiles from reach 1 to 3. Figure 19 represents the final flow profile from reach 1 to 3. The table 5 below shows the summary of kinetic energy and potential energy before and after jump respectively for various bed width.

TABLE 5: SUMMARY OF POTENTIAL ENERGY AFTER HYDRALIC JUMP FOR VARIOUS KINETIC ENERGY BEFORE JUMP

076 The results summarized in table 5 are for hydraulic jump on horizontal floor canal. So the

sequent depth on sloping floor is calculated by equation 9

-^ = [l .0071 ^{3 2386ωηβ }] , Here tan6 = 0.0001333

Y _{2 }

Y _{s } = Y _{2 } x 1.0071 _{x e } < ^{3 }- ^{2386 * 0 }' ^{000,33 }>

Y _{s }= Y _{2 } x 1.0071 x 1.0004 = 9.72 = Y _{2 }

Page No. 12 i.e., the sequent depth for this sloping floor case would be 0.006 times the sequent depth calculated on horizontal floor. Hence for all calculations of hydraulic jump in this invention, the hydraulic jump on horizontal floor is holds good. The relationship between flow depth and kinetic energy before the jump for modification of existing canal from 32 m to 8 m at reach 4 and sequent depth or potential energy and flow velocity after jump at reach 5 shown in table 5. Where the flow depths decreases at higher velocities resulting from reach 3. The reach 4 i.e. chute further accelerates the flow in to the supercritical stage where the Froude number F _{t } reaches a value of 3.371 at end of the reach 4. Beyond this point, due to break in bed slope, the hydraulic jump will form and convert supercritical flow velocity into potential energy at reach 5, The flow velocity has dropped off to subcritical stage and the Froude number is less than 1. Consequently, at reach 3 with bed width from 32 m and bed slope of 1:200 permits the flow velocity to be accelerated from the ambient 1.618 m/s to 5.234 m/s (shown in table 2), at starting of reach 4 i.e. at chute with 8 m bed width further accelerated to 15.838 m s at the tail end of the chute. Of course, the increase in velocity is at the expense of the flow depths which decreases from 6.1 m normal depth of original canal to 2.249 m corresponding to above values of velocity. It is found that at chute with bed width of 8 m, kinetic energy of 15.838 m and Froude Number F _{1= 3J71 }, it is possible to get potential energy (after losses) of 9.655 m. at reach 5 and which will be used for power generation. The practical application of hydraulic jump mentioned in the section 055 above, the application 2 and 4 are applicable for present invention. The view of water surface profile as shown in figure 26, it understand that reach 4 and reach 5 is separated by a phenomenon called hydraulic jump, due to break in grade between reach 4 and 5. The hydraulic jump rises the water surface and maintain the higher water elevation at downstream of hydraulic structure i.e. chute, the height of the water depth or water elevation of jump is depends on the tail water depth (Y,), shown in figure 6 and explained in three cases in the section 062 above. The maximum height of the water depth in present invention is Y _{2 } = 9.655 m. This is meant for application 2 of hydraulic jump. In Present invention the hydraulic jump also act like buffer between reach 4 and 5, i.e. any increase in height of downstream water depth or water elevation (at reach 5) is not reflect or affect to the upstream of the canal (reach 4). The limit of increase in height of water depth or water elevation at reach 5 is depends on sequent depth height i.e. Y _{2 }= 9.655 m. Present invention the maximum height of increase in water depth at end of reach 5 by gated weir is Y, = 9.5 m, so Y _{2 } > Y|. the hydraulic jump holds the back tail water increased by weir above the normal depth and this back tail water is not affect upstream depth at reach 4. This meant for application 4 of hydraulic jump.

The length of jump, location of jump and height of jump are important parameter affecting the size of the stilling basin. The tail water depth at reach 5 plays a important role in formation of jump in particular location. The equation Hand 12 are holds good for calculate length and height of jump and the graphical method described in section 063 above is used for find the location of jump on reach 5. The table 6 below shows the length, location, and height of jump for various tail water condition, found by graphical method shown in fig 20, 21 and 22 .

Page No. 13 Reach 5 with Q = 285 m ^{3 }/s, Manning N =0.018,

Bed width B = 8 m, bed slope S _{0 }= 1:7500, Normal Depth

Y _{c }=5.058

TABLE 6: HYDRAULIC JUMP FOR DIFFERENT CASES

080 From the table 6, it is observed that at reach 5 in case A, tail water depth Y, = 6 < Y _{2 } = 9.655, as explained in case 2 of section 062 above, the location of jump is found at 305 m downstream from the chute. The figure 23 shows the jump on reach 5 for free flow condition .

In case B of above table, the tail water depth Y, = 8, i.e. with obstruction of 2 m above normal depth at end of reach 5. So Tail water depth Y _{t } = 6 < Y _{2 } = 9.655, because of the increase in tail water depth, the jump will be forced upstream toward chute and shifted location of jump from 305 m to 125 m from the chute. This case shown in figure 24 .

In case C of above table, the tail water depth Y, = 9.5, i.e. with obstruction of 3.5 m above normal depth at end of reach 5. So Tail water depth Y, = 9.5 < Y _{2 } = 9.655, because further increase in tail water depth, the jump will be further forced upstream towards chute and shifted location of jump from 125 m to 2.5 m from chute. This case shown in figure 25.

081 In the above section 080, it is found that in all the 3 cases the jump will be free jump, so that downstream depth should not affect to upstream depth and the 3.5 m head or potential energy can be achieved at reach 5 for power generation.

082 Once the potential energy is achieved at reach 5, power generation is possible by diverting water to power house by head race or intake approach channel. The total power extracted in hydropower is depends on the difference in the elevation of the water surface at head race channel to the elevation of the water surface at tail race channel.

083 In the above section 082, it is found that by lowering the elevation of depth at tail race channel, it is possible to increase the head required for power generation. The present invention adopted this mechanism to improve the head at tail race by lowering the normal depth instantly. The design parameters of tail race canal, Tail race sill, Tail race pre acceleration and tail race chute are tabulated in row 2 , row 3, row4 and row5 of table 3 respectively.

084 An exemplary embodiment of the construction details of tail race canal system or design according to the present invention is shown in figure 27. The figure 28 represents the flow profile for gradually varied flow or water surface profile of length 250 m of tail race canal . The expected initial and steady condition water surface profile at each reach and other hydraulic parameters of tail race canal are described in detail.

Page No. 14 085 In the plan view of fig 27, the flow direction from left to right is labeled and shown by an arrow the left end of the figure. The water after power generation and outlet of turbine draft tube the flow begins at an entrance end of tail race canal and concludes at an opposite exit end .

086 With reference to the elevation view of fig 27, there are number of angled bottom floor structures that together with diverge walls and chute make up the canal system or design. The first 100 m length of entrance end of tail race canal, the canal cross section and the canal parameters is as shown in second row of table 3. Since Y„ > Y _{c } with free flow condition an M2 profile as expected is obtained and shown figure 27.

087 The bed of the tail race canal changes from 1 :4500 to adverse slope of ratio 2:9.24 at chainage 100m and continues up to chainage 109.5 m for a length of 9.5 m, and sill height of 2 m created. The canal parameters of this reach is as shown in third row of table 3. Since because of the sill height there may be chance of chocking the upstream depth, but with our canal design parameters at this reach the backwater or chocking of upstream depth is very nominal and maintains -the tail race depth for power generation is un affected. Discharge and Head rating table for 2 m sill height is calculated and upstream depth in tail race canal V/S Discharge is tabulated in table 7 below. The plot of profile as shown in fig 28.

TABLE 7: DISCHARGE AND HEAD RATING TABLE AT TAIL RACE

In the next chainage canal starts at tip of the 2 m sill height and to continue up to 60 m downstream of canal. The canal parameters of reach are as shown in fourth row of table 3. Because of the diverging bed width and bed slope of 1:1000 and since Y _{n } > Y _{c } the M2 profile is expected and obtained. Transition in the bed width from 38 m to 42 m has been provided (refer to standard transition pattern) and it is used for pre-acceleration zone of subcritical velocity.

Page No. IS 089 The next reach is mainly used for final acceleration, the canal parameters of this reach is tabulated in fifth row of table 3. In this reach the acceleration to supercritical flow and Since > y _{n, } ^{an } S2 profile of water is seen as expected. The velocity in this section rapidly increases. The maximum velocity attained would be around 10.682 m/s. Figure 27 represents the S2 profile in this reach .

090 From the above table 7 it is observed that the depth at tail race is 4.3 m compared to 6.1 m normal depth of existing irrigation canal. So it possible to create 1.7 mhead at tail race channel. With this mechanism and mechanism as explained earlier adopted to create 3.5 m head by modifying the irrigation canal before water diverting to power house, it is possible to create a total head of 5.2 m for mild slope hydropower generation.

The lowering the depth at tail race channel will disturb the existing irrigation system, so it is required to recover the depth before leaving to irrigation canal from the tail race channel. This is achieved by adopting chute in between tail race and irrigation canal. The table below shows calculation of values required for recovering the depth at irrigation canal.

TABLE 8: SUMMARY OF RESULTS TO RECOVER DEPTH AT IRRIGATION CANAL.

092 The normal depth required for irrigation system is 6.1 m, and from the table 8 above observed that the sequent depth for 12 m bed width is Y2= 6.142 m, hence it is possible to recover the depth at irrigation channel from the concept of hydraulic jump explained earlier, the recovered depth at irrigation canal should not affect the tail race channel depth as shown in figure 28, so with all this mechanism in present invention, it is possible to create head of 5.2 m .

093 The dimensions of canal according to the present invention, and other important dimension are set forth in the table 2 and 3. As was noted previously, and as is demonstrated, the various dimensions and sizes of canal can vary. Likewise, it should be understood that the dimensions of the present canal can be varied to fit particular site condition ( for example, channel width, cross section, flow depth, and ambient flow velocity, as well as other such factors).

094 Concept of Power generation in mild slope channel.

The figure 29 shows the complete system of mild slope hydropower generation concept. Once the potential energy or head is achieved at reach 5, divert the water in to power house and the generation of power is achieved by following:

Page No. 16 a. Take full reservoir level equal to maximum water level in canal.

b. Take a small pipe on one side of canal through a intake structure .

c. Locate the power house on banks of canal.

d. Take the pipe inside the power house till turbine guide vanes

e. Now using FRL and TWL of Power House, power generation is possible.

f. When turbine trips the gates will automatically open and water will flow over the weir. g. Gate will be of automatically falling shutters type.

h. Typical flow diagram for the typical case study is shown in Fig.29.

095 In hydro power scheme the power can be determined from the following equation:

i* = Q x I ! x g x j

P = power in KW, Q = discharge in m ^{3 }/s, H = Head in meter, g = gravity (9.81), η = system efficiency.

096 While the range of power that might be generated by use the present invention can be in the range of about 100 KW to about 25 MW, depending up on discharge availability in the canal, where the 5.2 m head, 285 cumecs of discharge and assuming a 85% efficiency hydro power system the power generated by system is:

P = 12,357 KW.

097 The foregoing has described power generation from mild slope hydro power generation that includes subcritical flow accelerate to supercritical kinetic energy and convert in to potential energy in which power generation can be efficiently carried out. While the invention has been described in connection with what is presently considered to be the most practical and preferred embodiment , it is to be understood that the invention is not to be limited to the disclosed embodiment , but on the contrary, is intended to cover various modifications and equivalent arrangements included within the spirit and scope of the appended claims.

Page No. 17

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