I think these formulas will be very much helpful for those candidates who are preparing for competitive examinations.

1. 𝑡=𝑦𝑓log𝑒(𝑄𝑄−𝑓𝐴)

2. 𝐴𝑚𝑎𝑥=𝑄𝑓

3. 𝑆𝐴𝑅=𝑁𝑎+√𝐶𝑎+++𝑀𝑔++2

4. Δ=8.64𝐵𝐷

5. 𝐴=𝑄𝐷

6. 𝜂𝑐=𝑊𝑎𝑡𝑒𝑟 𝑑𝑒𝑙𝑖𝑣𝑒𝑟𝑒𝑑𝑊𝑎𝑡𝑒𝑟 𝑠𝑢𝑝𝑝𝑙𝑖𝑒𝑑

7. 𝜂𝑎=𝑊𝑎𝑡𝑒𝑟 𝑠𝑡𝑜𝑟𝑒𝑑 𝑖𝑛 𝑟𝑜𝑜𝑡 𝑧𝑜𝑛𝑒𝑊𝑎𝑡𝑒𝑟 𝑑𝑒𝑙𝑖𝑣𝑒𝑟𝑒𝑑

8. 𝜂𝑠=𝑊𝑎𝑡𝑒𝑟 𝑠𝑡𝑜𝑟𝑒𝑑 𝑖𝑛 𝑟𝑜𝑜𝑡 𝑧𝑜𝑛𝑒𝑊𝑎𝑡𝑒𝑟 𝑛𝑒𝑒𝑑𝑒𝑑 𝑖𝑛 𝑟𝑜𝑜𝑡 𝑧𝑜𝑛𝑒

9. 𝜂𝑑=1−𝑑𝐷, 𝐷=𝑚𝑒𝑎𝑛 𝑜𝑓 𝑑𝑒𝑝𝑡ℎ𝑠 and 𝑑=𝑚𝑒𝑎𝑛 𝑜𝑓 𝑎𝑏𝑠𝑜𝑙𝑢𝑡𝑒 𝑣𝑎𝑙𝑢𝑒𝑠 𝑜𝑓 𝑑𝑒𝑣𝑖a𝑡𝑖𝑜𝑛𝑠

10. 𝐶𝐼𝑅=𝐶𝑢−𝑅𝑒

11. 𝑁𝐼𝑅=𝐶𝐼𝑅+𝑤𝑎𝑡𝑒𝑟 𝑙𝑜𝑠𝑡 𝑎𝑠 𝑝𝑒𝑟𝑐𝑜𝑙𝑎𝑡𝑖𝑜𝑛

12. 𝐶𝑢=𝑘𝑝40(1.8𝑡+32)

13. 𝑑𝑒𝑝𝑡ℎ 𝑜𝑓 𝑤𝑎𝑡𝑒𝑟 𝑡𝑜 𝑏𝑒 𝑎𝑝𝑝𝑙𝑖𝑒𝑑=𝛾𝑑𝛾𝑤 𝑑(𝐹−𝑂𝑀𝐶)

14. 𝜏𝑜=𝛾𝑤𝑅𝑆

15. 𝑛=124𝑑16, 𝑑 is in meters

16. 𝑣0=0.55 𝑚 𝑦0.64

17. 𝑣=[1𝑛+(23+0.00155𝑆)1+(23+0.00155𝑆)𝑛√𝑅]√𝑅𝑆

18. 𝑣=(𝑄𝑓2140)16

19. 𝑅=52(𝑣2𝑓)

20. 𝑃=4.75√𝑄

21. 𝑆=𝑓533340𝑄16

22. 𝐷𝑠=1.35(𝑞2𝑓)13

23. 𝑣=10.8𝑅23𝑆13

24. 𝐴=𝑦2(𝜃+cot𝜃),𝑃=2𝑦(𝜃+cot𝜃) for Lined Triangular section.

25. 𝐴=𝐵𝑦+𝑦2(𝜃+cot𝜃),𝑃=𝐵+2𝑦(𝜃+cot𝜃) for Lined Trapezoidal section.

26. Launching apron scour depth, 𝐷=𝑥𝑅−𝑤𝑎𝑡𝑒𝑟 𝑑𝑒𝑝𝑡ℎ 𝑎𝑏𝑜𝑣𝑒 𝑏𝑒𝑑, 𝑅=0.47(𝑄𝑓)13

27. Length of launching apron =√5 𝐷

28. 𝑡=ℎ′𝐺 , where ℎ′=𝑜𝑟𝑑𝑖𝑛𝑎𝑡𝑒 𝑜𝑓 𝐻𝐺𝐿 𝑎𝑏𝑜𝑣𝑒 𝑏𝑜𝑡𝑡𝑜𝑚 𝑜𝑓 𝑡ℎ𝑒 𝑓𝑙𝑜𝑜𝑟

29. 𝑡=ℎ𝐺−1 , where ℎ=𝑜𝑟𝑑𝑖𝑛𝑎𝑡𝑒 𝑜𝑓 𝐻𝐺𝐿 𝑎𝑏𝑜𝑣𝑒 𝑡ℎ𝑒 𝑡𝑜𝑝 𝑜𝑓 𝑡ℎ𝑒 𝑓𝑙𝑜𝑜𝑟

30. 𝐶=19 √𝐷𝑏′ [𝑑+𝐷𝑏], 𝑑=𝑑𝑒𝑝𝑡ℎ 𝑜𝑓 𝑝𝑖𝑙𝑒 𝑎𝑛𝑑 𝐷=𝐷𝑒𝑝𝑡ℎ 𝑜𝑓 𝑛𝑒𝑖𝑔ℎ𝑏𝑜𝑢𝑟𝑖𝑛𝑔 𝑝𝑖𝑙𝑒 𝑏𝑒𝑙𝑜𝑤 𝑡ℎ𝑒 𝑝𝑜𝑖𝑛𝑡.

31. 𝐺𝐸=𝐻𝑑 1𝜋√𝜆 , 𝜆=1+√1+𝛼22 and 𝛼=𝑏𝑑

32. ∅𝐷=1𝜋cos−1(𝜆−2𝜆) and ∅𝐸=1𝜋cos−1(𝜆−1𝜆)

33. ∅𝐶=1𝜋cos−1(𝜆2+1𝜆1),∅𝐷=1𝜋cos−1(𝜆2𝜆1) and ∅𝐸=1𝜋cos−1(𝜆2−1𝜆1) , 𝜆1=√1+𝛼12+√1+𝛼222 and 𝜆2=√1+𝛼12−√1+𝛼222 , 𝛼1=𝑏1𝑑 𝑎𝑛𝑑 𝛼2=𝑏2𝑑

34. Non-modular modules: Drowned pipe outlet, masonry sluice and wooden shoots.

35. Semi modules or flexible modules: Pipe outlet, venturi flume or Kennedy’, open flume and orifice semi module.

36. Rigid modules: Gibb’s module, Kanna’s rigid module and foote module.

37. Flexibility 𝐹=𝑑𝑞/𝑞𝑑𝑄/𝑄=𝑚𝑛.𝑦𝐻 , 𝑞=discharge in outlet and 𝑄= discharge in channel, 𝑚=outlet index and 𝑛=channel index. 𝐻=working head of outlet and 𝑦= depth of water in channel.

Irrigation engineering and water resources valuable formulas
Irrigation engineering and water resources valuable formulas

38. Proportionality: 𝐹=1 𝑎𝑛𝑑 𝑚𝑛=𝐻𝑦

39. Setting =𝐻𝑦

40. 𝑚𝑛>𝐻𝑦 , hyper proportional outlet.

41. 𝑚𝑛<𝐻𝑦 , sub proportional outlet.

42. Sensitivity, 𝑆=𝑑𝑞/𝑞𝑑𝑦/𝑦=𝑛𝑑𝑞/𝑞𝑑𝑄/𝑄=𝑛 𝐹

43. Aqueduct: Canal over drainage with clear gap.

44. Syphon Aqueduct: Canal over drainage with syphonic action.

45. Super passage: Drain over canal with clear gap.

46. Canal Syphon: Drain over canal with syphonic action.

47. Principal stress in dam

𝜎=𝑝𝑣sec2𝛼−𝑝′tan2𝛼

where 𝑝𝑣=𝑚𝑎𝑥𝑖𝑚𝑢𝑚 𝑣𝑒𝑟𝑡𝑖𝑐𝑎𝑙 𝑠𝑡𝑟𝑒𝑠𝑠 and 𝑝′= water pressure of tail water and 𝛼=𝑎𝑛𝑔𝑙𝑒 𝑜𝑓 𝑑𝑎𝑚 𝑓𝑎𝑐𝑒 𝑤𝑖𝑡ℎ 𝑣𝑒𝑟𝑡𝑖𝑐𝑎𝑙

48. 𝐵=𝐻√𝑆𝑐−𝐶 

49. 𝐻=𝑓𝛾𝑤(𝑆𝑐−𝐶+1) and 𝐻𝑚𝑎𝑥=𝑓𝛾𝑤(𝑆𝑐+1)

50. 𝑥1.85=2 𝐻𝑑0.85𝑦