Critical flow through an Open channel

Critical flow conditions, characteristics, section factor............

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 , S c 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, V 2 /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, V 2 /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 y c Or if we have given y c , we can calculate Z, later easily we can calculate Q c 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 = C y 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 Algebraic method - For simple geometric channel section Graphical method - For complicated or natural channel section 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: M ethod 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 /b 2.5 = 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

26. 26 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