Module 2- Non Uniform Flow in Open Channels (HHM).pptx

Non-uniform flow features changing velocity and depth along the channel. It includes gradually varied flow (GVF), with slow depth changes, and rapidly varied flow (RVF), with abrupt changes like hydraulic jumps. Key aspects include GVF equations, RVF principles, numerical methods, and practical applications in hydraulic design.

1. Module - 2 Non-uniform Flow in Open Channels

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3. Non-uniform Flow in Open Channels: Non-uniform flow is a flow for which the depth of flow is aried . This varied flow can be either Gradually varied flow (GVF) or Rapidly varied flow (RVF). Such situations occur when control structures are used in the channel or when any obstruction is found in the channel Such situations may also occur at the free discharges and when a sharp change in the channel slope takes place. Dr. Indrajeet Sahu Module-2 (HHM) VCE 3

4. The most important elements, in non-uniform flow, that will be studied in this section are: Classification of channel-bed slopes. Classification of water surface profiles. The dynamic equation of gradually varied flow. Hydraulic jumps as examples of rapidly varied flow . Dr. Indrajeet Sahu Module-2 (HHM) VCE 4

5. Non-uniform Flow in Open Channels Dr. Indrajeet Sahu Module-2 (HHM) VCE 5

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14. Classification of Channel-Bed Slopes The slope of the channel bed can be classified as: Critical Slope: the bottom slope of the channel is equal to the critical slope. In this case S0 = Sc or yn = yc . 2) Mild Slope: the bottom slope of the channel is less than the critical slope. In this case S0 < Sc or yn > yc . 3) Steep Slope: the bottom slope of the channel is greater than the critical slope. In this case S0 > Sc or yn < yc . 4) Horizontal Slope: the bottom slope of the channel is equal to zero (horizontal bed). In this case S0 = 0.0 . 5) Adverse Slope: the bottom slope of the channel rises in the direction of the flow (slope is opposite to direction of flow). In this case S0 = negative . Dr. Indrajeet Sahu Module-2 (HHM) VCE 14

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16. Classification of Flow Profiles (water surface profiles): Dr. Indrajeet Sahu Module-2 (HHM) VCE 16

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19. Classification of Flow Profiles (water surface profiles) Dr. Indrajeet Sahu Module-2 (HHM) VCE 19

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22. Classification of Flow Profiles (water surface profiles): Dr. Indrajeet Sahu Module-2 (HHM) VCE 22

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25. Hydraulic Jump A hydraulic jump occurs when flow changes from a supercritical flow (unstable) to a sub-critical flow (stable). There is a sudden rise in water level at the point where the hydraulic jump occurs. Rollers (eddies) of turbulent water form at this point. These rollers cause dissipation of energy. Dr. Indrajeet Sahu Module-2 (HHM) VCE 25

26. General Expression for Hydraulic Jump: In the analysis of hydraulic jumps, the following assumptions are made: (1) The length of hydraulic jump is small. Consequently, the loss of head due to friction is negligible. (2) The flow is uniform and pressure distribution is due to hydrostatic before and after the jump. (3) The slope of the bed of the channel is very small, so that the component of the weight of the fluid in the direction of the flow is neglected. Dr. Indrajeet Sahu Module-2 (HHM) VCE 26

27. Hydraulic Jump in Rectangular Channels But for Rectangular section Dr. Indrajeet Sahu Module-2 (HHM) VCE 27

28. Hydraulic Jump in Rectangular Channels Dr. Indrajeet Sahu Module-2 (HHM) VCE 28

29. Hydraulic Jump Dr. Indrajeet Sahu Module-2 (HHM) VCE 29

30. Hydraulic Jump Dr. Indrajeet Sahu Module-2 (HHM) VCE 30

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32. Hydraulic Jump in Rectangular Channels Dr. Indrajeet Sahu Module-2 (HHM) VCE 32

33. Dr. Indrajeet Sahu Module-2 (HHM) VCE 33 Example 1 A 3-m wide rectangular channel carries 15 m 3 /s of water at a 0.7 m depth before entering a jump. Compute the downstrem water depth and the critical depth Hydraulic Jump

34. Dr. Indrajeet Sahu Module-2 (HHM) VCE 34 Example 2 d n = Depth can calculated from manning equation d 1 =d n d 2 Hydraulic Jump

35. d 1 =d n d 2 a) b) Hydraulic Jump Dr. Indrajeet Sahu Module-2 (HHM) VCE 35

36. c) d 1 =d n d 2 Hydraulic Jump Dr. Indrajeet Sahu Module-2 (HHM) VCE 36

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38. WATER SURFACE PROFILES CLASSIFICATION Horizontal channel: So = 0 → Q = 0 Adverse channel: So < 0 Q cannot be computed, For the horizontal (S o = 0) and adverse slope ( S o < 0) channels , For the horizontal and adverse slope channels, the uniform flow depth y o does not exist.

39. For a given Q, n, and S o at a channel, y o = Uniform flow depth, y c = Critical flow depth, y = Non-uniform flow depth. The depth y is measured vertically from the channel bottom, the slope of the water surface dy / dx is relative to this channel bottom. the prediction of surface profiles from the analysis of WATER SURFACE PROFILES CLASSIFICATION

40. Classification of Profiles According to dy/dl 1) dy/dx>0; the depth of flow is increasing with the distance. (A rising Curve) 2) dy/dx<0; the depth of flow is decreasing with the distance. (A falling Curve) 3) dy/dx=0. The flow is uniform Sf=So 4) dy/dx = -∞. The water surface forms a right angle with the channel bed. 5) dy/dx=∞/∞. The depth of flow approaches a zero. 6) dy/dx= S o The water surface profile forms a horizontal line. This is special case of the rising water profile dl=dx

41. WATER SURFACE PROFILES CLASSIFICATION Classification of profiles according to dy / dl or (dh/dx) .

42. GRAPHICAL REPRESENTATION OF THE GVF Zone 1: y > y o > y c Zone 2: y o > y > y c Zone 3: y o > y c > y

43. Example : Draw water surface profile for two reaches of the open channel given in Figure below. A gate is located between the two reaches and the second reach ends with a sudden fall. The open channel and gate location. Critical and normal depths. Water surface profile .

44. Example: Draw water surface profile for two reaches of the open channel given in Figure below. A gate is located between the two reaches and the second reach ends with a sudden fall. The open channel and gate location. Water surface profile.

45. Jump Location and Water Surface Profiles If hydraulic jump is formed, two different locations are expected for the jump according to the normal depths y o1 and y o2. y o1 is known Calculate conjugate depth of the jump y’ If y’<y o2 Case I If y’>y o2 Case II

46. Example A wide rectangular channel carries a specific discharge of 4.0 m 2 /s. The channel consists of three long reaches with bed slope of 0.008, 0.0004 and Sc respectively. A gate located at the end of the last reach. Draw water surface profile. Manning’s n=0.016. First calculate y c , y o1 , y o2 , and realize that y c = y o3 . To know whether the jump will occur in the first or second reach, calculate y’ (subcritical depth) of the jump. If y’ < y o2 then the jump will take place in the first reach.

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49. CONTROL SECTIONS Control section is a section where a unique relationships between the discharge and the depth of flow. Gates, weir, and sudden falls and critical depth of are some example of control sections. Subcritical flows have theirs CS at downstream Supercritical flows have theirs CS at upstream Bold squares show the control sections.

50. S f : average friction slope in the reach Manning Formula is sufficient to accurately evaluate the slope of total energy line, S f DIRECT STEP METHOD A nonuniform water surface profile

51. DIRECT STEP METHOD Subcritical Flow The condition at the downstream is known y D , V D and S fD are known Chose an appropriate value for y u Calculate the corresponding V u , S fu and S f Then Calculate DX Supercritical Flow The condition at the upstream is known y u , V u and S fu are known Chose an appropriate value for y D Calculate the corresponding S fD , V D and S f Then Calculate D X

52. Example A trapezoidal concrete-lined channel has a constant bed slope of 0.0015, a bed width of 3 m and side slopes 1:1. A control gate increased the depth immediately upstream to 4.0m when the discharge is 19 m 3 /s. Compute WSP to a depth 5% greater than the uniform flow depth (n=0.017). Two possibilities exist: OR

53. Solution The first task is to calculate the critical and normal depths. Using Manning formula, the depth of uniform flow: y o = 1.75 m Using the critical flow condition, the critical depth: y c = 1.36 m It can be realized that the profile should be M1 since y o > yc That is to say, the possibility is valid in our problem.

54. Dr. Indrajeet Sahu Module-2 (HHM) VCE 54 Computation Method for determination of GVA profile

55. Dr. Indrajeet Sahu Module-2 (HHM) VCE 55 1. Graphical Integration Method

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62. Dr. Indrajeet Sahu Module-2 (HHM) VCE 62 2. Direct Integration Method

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70. Dr. Indrajeet Sahu Module-2 (HHM) VCE 70 3. Step Method

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