CVE 372 HYDROMECHANICS OPEN CHANNEL FLOW I
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1 CVE 372 HYDROMECHANICS OPEN CHANNEL FLOW I Dr. Bertuğ Akıntuğ Department of Civil Engineering Middle East Technical University Northern Cyprus Campus CVE 372 Hydromechanics 1/50
2 Overview 3.1 General Characteristics of Open Channel Flow Classification of Open Channel Flows Pressure Distribution in Open Channel Flows Velocity Distribution in Open Channel Flows Friction Loss for Noncircular Conduits 3.2 Uniform Flow Resistance in Open Channel Flow Uniform Flow Equations Composite and Compound Sections 3.3 Specific Energy Concept Specific Energy and Alternate Depth Critical Flow Channel Transition and Chocking Problems CVE 372 Hydromechanics 2/50
3 General Characteristics of Open Channel Flow Open channel flow is a flow which has a free surface. CVE 372 Hydromechanics 3/50
4 General Characteristics of Open Channel Flow Comparison of Open Channel Flow and Pipe Flow Open Channel Flow Pipe Flow S o : channel bottom slope S w : slope of water surface S e : slope of energy grade line CVE 372 Hydromechanics 4/50
5 General Characteristics of Open Channel Flow Kinds of Open Channel Flow An open channel is a conduit in which water flows with a free surface. 1. Canal is usually a long and mild-sloped channel built in the ground. Kennet and Avon Canal, England CVE 372 Hydromechanics 5/50
6 General Characteristics of Open Channel Flow Kinds of Open Channel Flow An open channel is a conduit in which water flows with a free surface. 1. Canal is usually a long and mild-sloped channel built in the ground. Royal Canal, Ireland Llangollen Canal, Denbighshire, Wales, UK CVE 372 Hydromechanics 6/50
7 General Characteristics of Open Channel Flow Kinds of Open Channel Flow 2. Flume is a channel usually supported on or above the surface of the ground to carry water across a depression. Bull Run Hydroelectric Project diversion flume White River diversion flume in Washington CVE 372 Hydromechanics 7/50
8 General Characteristics of Open Channel Flow Kinds of Open Channel Flow 3. Chute is a channel having steep slope. 4. Drop is similar to chute, but the change in elevation is affected in a short distance 5. Culvert is a covered channel flowing partly full, which is installed to drain water through highway and railroad embankments. 6. Open-Flow Tunnel is a comparatively long covered channel used to carry water through a hill or any obstruction on the ground. CVE 372 Hydromechanics 8/50
9 General Characteristics of Open Channel Flow Channel Geometry Prismatic Channel: A channel built with unvarying cross-section and constant bottom slope. Non-prizmatic Channel: A channel bult with varying cross-section or bottom slope. The Channel Section is the cross-section of a channel taken normal to the direction of the flow. CVE 372 Hydromechanics 9/50
10 General Characteristics of Open Channel Flow Geometric Elements of Channel Section y: the depth of flow d: the depth of flow section h: the stage T: the top width A: the water area P: the wetted perimeter R (=A/P) the hydraulic radius D (=A/T) the hydraulic depth CVE 372 Hydromechanics 10/50
11 General Characteristics of Open Channel Flow Classification of Open Channel Flows According to the change in flow depth with respect to time and space GVF: Gradually varied flow RVF: Rapidly varied flow CVE 372 Hydromechanics 11/50
12 General Characteristics of Open Channel Flow Classification of Open Channel Flows According to the change in flow depth with respect to time and space CVE 372 Hydromechanics 12/50
13 General Characteristics of Open Channel Flow Classification of Open Channel Flows According to the change in flow depth with respect to time and space GVF: Gradually varied flow RVF: Rapidly varied flow CVE 372 Hydromechanics 13/50
14 General Characteristics of Open Channel Flow Classification of Open Channel Flows According to the change in flow depth with respect to time and space GVF: Gradually varied flow RVF: Rapidly varied flow CVE 372 Hydromechanics 14/50
15 General Characteristics of Open Channel Flow Classification of Open Channel Flows According to the change in discharge with respect to time and space CVE 372 Hydromechanics 15/50
16 General Characteristics of Open Channel Flow Classification of Open Channel Flows State of Flow Effect of Viscosity According to the Reynolds Number, Re= (VR)/ν IF Re < 500 Laminar Flow 500 < Re < 1000 Transitional Flow Re > 1000 Turbulent Flow CVE 372 Hydromechanics 16/50
17 General Characteristics of Open Channel Flow Classification of Open Channel Flows State of Flow Effect of Gravity According to the Froude Number, Fr= V/(gD) 1/2 IF Fr < 1 Subcritical Flow Fr = 1 Critical Flow V V V Fr > 1 Supercritical Flow CVE 372 Hydromechanics 17/50
18 General Characteristics of Open Channel Flow Pressure Distribution in Open Channel Flows r: radius of curvature CVE 372 Hydromechanics 18/50
19 General Characteristics of Open Channel Flow Velocity Distribution in Open Channel Flows CVE 372 Hydromechanics 19/50
20 General Characteristics of Open Channel Flow Velocity Distribution in Open Channel Flows α: energy correction factor β: momentum correction factor CVE 372 Hydromechanics 20/50
21 General Characteristics of Open Channel Flow Velocity Distribution in Open Channel Flows Equation of Continuity CVE 372 Hydromechanics 21/50
22 Overview 3.1 General Characteristics of Open Channel Flow Classification of Open Channel Flows Pressure Distribution in Open Channel Flows Velocity Distribution in Open Channel Flows Friction Loss for Noncircular Conduits 3.2 Uniform Flow Resistance in Open Channel Flow Uniform Flow Equations Composite and Compound Sections 3.3 Specific Energy Concept Specific Energy and Alternate Depth Critical Flow Channel Transition and Chocking Problems CVE 372 Hydromechanics 22/50
23 Uniform Flow Resistance in Open Channel Flow Resistance formula for uniform flow Water depth is constant Discharge is constant Steady flow S o = S w = S e y n : normal (uniform) depth y n : The depth associated with uniform flow. CVE 372 Hydromechanics 23/50
24 Uniform Flow Uniform Flow Equations C: Chezy coefficient. n: Manning s roughness coefficient CVE 372 Hydromechanics 24/50
25 Uniform Flow Uniform Flow Equations CVE 372 Hydromechanics 25/50
26 Uniform Flow Uniform Flow Equations CVE 372 Hydromechanics 26/50
27 Uniform Flow Uniform Flow Equations Factors Affecting Manning s Roughness Coefficient Surface roughness Vegetation Channel irregularity Channel alignment Silting and scouring Obstructions Size and shape of channel Suspended material, bed load. CVE 372 Hydromechanics 27/50
28 Uniform Flow Composite and Compound Sections Composite Section: A channel section, which is composed of different roughness along the wetted perimeter. F: Drag force CVE 372 Hydromechanics 28/50
29 Uniform Flow Composite and Compound Sections Compound Section: A channel section, which the cross section is composed of several distinct subsections. CVE 372 Hydromechanics 29/50
30 Uniform Flow Composite and Compound Sections Example 1: A trapezoidal channel has a base width b = 6 m and side slopes 1H:1V. The channel bottom slope is S o = and the Manning roughness coefficient is n= compute a) the depth of uniform flow if Q = 12.1 m3/s b) the state of flow c) the average wall-shear stress along the wetted perimeter. Solved in the class CVE 372 Hydromechanics 30/50
31 Uniform Flow Composite and Compound Sections Example 2: For the compound channel given below, determine the total discharge and the state of the flow, if S 0 =0.0009, n 1 =0.014, n 2 =0.02, n 3 = m n 1 n1 n m 0.5 m n 2 n 2 n m n 3 n 2 n m 1.0 m 2.0 m 1.0 m 3.0 m 1.0 m 3.0 m Solved in the class CVE 372 Hydromechanics 31/50
32 Uniform Flow Composite and Compound Sections Exercise 1: M CVE 372 Hydromechanics 32/50
33 Overview 3.1 General Characteristics of Open Channel Flow Classification of Open Channel Flows Pressure Distribution in Open Channel Flows Velocity Distribution in Open Channel Flows Friction Loss for Noncircular Conduits 3.2 Uniform Flow Resistance in Open Channel Flow Uniform Flow Equations Composite and Compound Sections 3.3 Specific Energy Concept Specific Energy and Alternate Depth Critical Flow Channel Transition and Choking Problems CVE 372 Hydromechanics 33/50
34 Specific Energy Concept Specific Energy and Alternate Depth 2 2 V Q E = y + = y + 2g 2gA 2 Specific Energy Curve CVE 372 Hydromechanics 34/50
35 Specific Energy Concept Critical Flow 2 2 V Q E = y + = y + 2g 2gA 2 Specific Energy Curve CVE 372 Hydromechanics 35/50
36 Specific Energy Concept Critical Flow q=q/t (discharge per unit width) CVE 372 Hydromechanics 36/50
37 Specific Energy Concept Critical Flow For a given E, Q = [2gA 2 (E-y)] 1/2, Q=Q(y) [ q=q(y) for rectangular channel The plot of Q vs y (q vs y) gives Koch Parabola CVE 372 Hydromechanics 37/50
38 Specific Energy Concept Critical Flow Example 3: A trapezoidal channel is given with b=4 m, n=0.0143, and z=0.5. a) What is the depth and state of the flow to carry Q=15m 3 /s with S 0 = CVE 372 Hydromechanics 38/50
39 Specific Energy Concept Critical Flow Example 4: Discharge in an open channel of arbitrary cross-section is Q=1m 3 /s. Determine: a) The critical depth for a triangular channel having side slopes of 1:1 b) The critical depth for a semicircular channel c) The critical depth for a rectangular channel with b=2 m d) The alternate depth for part c if y=1 m CVE 372 Hydromechanics 39/50
40 Specific Energy Concept Channel Transition and Choking Problems CVE 372 Hydromechanics 40/50
41 Specific Energy Concept Channel Transition and Choking Problems CVE 372 Hydromechanics 41/50
42 Specific Energy Concept Channel Transition and Choking Problems CVE 372 Hydromechanics 42/50
43 Specific Energy Concept Channel Transition and Choking Problems CVE 372 Hydromechanics 43/50
44 Specific Energy Concept Channel Transition and Choking Problems CVE 372 Hydromechanics 44/50
45 Specific Energy Concept Channel Transition and Choking Problems CVE 372 Hydromechanics 45/50
46 Specific Energy Concept Channel Transition and Choking Problems CVE 372 Hydromechanics 46/50
47 Specific Energy Concept Channel Transition and Choking Problems CVE 372 Hydromechanics 47/50
48 Specific Energy Concept Example 5: a) What will be the normal depth corresponding to 11 m 3 /s discharge in a trapezoidal channel for b=7.5 m, m=3, S 0 = , and n= b) Compute the critical depth and the min. specific energy. 1 1 m m b Solved in the class CVE 372 Hydromechanics 48/50
49 Specific Energy Concept Example 6: Water is flowing at a velocity of 4 m/s and a depth of 4 m in a channel of rectangular section of 5 m in width. There is then a smooth upward step of 0.8 m. a) Determine if there is choking. b) If there is choking, determine the decrease in discharge assuming energy at a section 1 remains constant. c) If the discharge is kept to be the same as in (a), what should be the increase in specific energy and depth at section 1. (1) (2) Solved in the class 4 m/s 4.0 m 0.8 m 5.0 m CVE 372 Hydromechanics 49/50
50 Specific Energy Concept Example 7: Water is flowing at a velocity of 4 m/s and a depth of 3 m in a channel of rectangular cross-section 6 m in width. Find the change in depth and absolute water level produced simultaneously by a downward step of 0.4 m and 2 m contraction in width. Solved in the class CVE 372 Hydromechanics 50/50
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