Critical flow through an Open channel
- 1. IWM 321: Hydraulic Engineering Chapter 3: Critical Flow Ajoy Kumar Saha Assistant Professor Dept of Irrigation and water management Faculty of Agricultural Engineering and Technology Sylhet Agricultural University, Bangladesh 1
- 2. Outline of this course • Critical Flow criteria • Section factor • Hydraulic exponent and their • Critical flow computation • Control of flow 2
- 3. Critical Flow criteria: Conditions and Characters • Specific energy is a minimum for a given discharge • Discharge is a maximum for a given specific discharge • Specific force is a minimum for a given discharge • Velocity head is equal to half the hydraulic depth in a channel of small slope 3
- 4. Critical Flow criteria: Conditions and Characters • Froude number is equal to unity, and • Velocity of flow in a channel is equal to celerity of small gravity waves in shallow water channel caused by local disturbance 4
- 5. General feature of Critical Flow • Flow at or near the critical state is unstable • Cause: minor change of sp. Energy causes major change in depth of flow • Water surface appears unstable and wavy • If the designed depth is near to the critical depth, it is recommended that - shape or slope of the channel should altered 5
- 6. Important terms: • Critical section Critical state of flow have referred mainly to a particular section of a channel • Critical flow If the critical state of flow exists throughout the entire length of the channel, the flow in the channel is called critical flow - Uniform flow is occurred in critical flow condition 6
- 7. Important terms: • Critical slope , Sc A slope which allow uniform and critical depth for given discharge • Mild or subcritical slope A slope of a channel less than the critical slope which causes slower flow of subcritical state for a given discharge • Steep or supercritical slope A slope of a channel greater than the critical slope which causes faster flow of supercritical state for a given discharge 7
- 8. Section Factor for critical flow, Z • The section factor for critical flow computation of a channel is the product of the water area and the square root of hydraulic depth Z = A D where, Z= Section factor A = Water Area D = Hydraulic depth But remember condition of critical flow, V2/2g = D/2 Put V=Q/A and find Z = Q/g 8
- 9. Section Factor for critical flow, Z But remember condition of critical flow, V2/2g = D/2 Now putting V = Q/A we get, Z = Q/g .................................(1) If the energy coefficient is not consider to be unity Z = Q/g/ ................................(2) 9
- 10. Section Factor for critical flow, Z Equation 1 and 2 are very use full for critical flow analysis • If critical Q given, we can calculate Z, later yc • Or if we have given yc , we can calculate Z, later easily we can calculate Qc 10
- 11. Hydraulic Exponent for Critical-flow Computation Since the section factor is a function of the depth of flow y, and it may be assume that Z = Cy M ............................................. (3) Where C is the coefficent and M is a parameter called hydraulic exponent for the critical flow 11
- 12. Hydraulic Exponent for Critical-flow Computation So, If we put all the values for the trapezoidal section we will get This equation indicates that the M is a function of z(y/b) 12
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- 15. Computation of Critical-flow 1. Algebraic method - For simple geometric channel section 2. Graphical method - For complicated or natural channel section 3. Method of Design chart - The design chart for determining the critical depth can be used with great expediency 15
- 16. Computation of Critical-flow: Algebraic method Example 4.2 Compute the critical depth and velocity of the trapezoidal channel (figure A) carrying a discharge of 400 cfs. 16
- 17. Computation of Critical-flow: Algebraic method 17
- 18. Computation of Critical-flow: Graphical method Example 4.3 A 36 in. concrete circular culvert carries a discharge of 20 cfs. Determine the critical depth. Solution: Construct a curve of y vs. Z like as following figure. 18
- 19. Computation of Critical-flow: Graphical method Again, we can easily calculate the value of Z, Because Q is given, So Z = Q/g This Z value is calculate for critical flow Corresponding, Z value we can get another yc using previous graph or plot 19
- 20. Computation of Critical-flow: Method of Design chart Example 4.4 (Same data as Example 4.2) Compute the critical depth and velocity of the trapezoidal channel (figure A) carrying a discharge of 400 cfs. Solution: We can calculate Z = Q/g = 400/32.22 = 70.5 Here, b = 20 ft Now Z /b2.5 = 0.0394 Using chart (go next slide) for above values.... 20
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- 22. Computation of Critical-flow: Graphical method Using chart for above values.... y/b = 0.108 Or y = 2.16 ft, that mean critical depth, yc = 2.16 ft. 22
- 23. What is control of flow? • Establish a definitive flow condition in channel • Specifically build a relation between stage and discharge of the flow • The flow of a channel could be controlled by a control section 23 Control of flow
- 24. Control section: • A certain section of a channel where control of flow is achieved • It restricts the transmission of the effect of changes in flow condition either u/s or d/s • It is a suitable site for guaging station • It helps to develop a rating curve (depth-discharge relation curve) 24 Control of flow
- 25. Control section: • At critical state, the stage-discharge curve theoretically possible • Independent of channel roughness and other uncontrolled circumstances. 25 Control of flow
- 27. Control of flow What is control of flow? • Establish a definitive flow condition in channel • Specifically build a relation between stage and discharge of the flow Control section in a channel: • A certain section of a channel where control of flow is achieved • It restricts the transmission of the effect of changes in flow condition either u/s or d/s • It is a suitable site for gaging station • It helps to develop a rating curve (depth-discharge relation curve) 27
- 28. Control of flow Mild or subcritical slope 28
- 29. Control of flow Critical flow 29
- 30. Control of flow Super Critical flow 30
Editor's Notes
- #2: Ajoy Kumar Saha Lecturer, Irrigation and water management