Paddy and Water Environment

, Volume 12, Issue 1, pp 203–212 | Cite as

Velocity distribution and discharge calculation at a sharp-crested weir



A sharp-crested weir in open channel is a useful device to calculate discharge via head-discharge relationship. However, water stage measurement site and discharge coefficient significantly influence discharge calculation accuracy. Therefore, this study measures and simulates velocity distribution at the weir section using 16-MHz MicroADV and FLOW-3D, respectively. The water depth and surface velocity at the weir section are selected to characterize velocity distribution using gamma probability density function. In this study, accurate discharge is calculated by velocity–area integration method based on velocity distribution derived from measured water depth and surface velocity. The main contributions of this study are to give an exact measurement site, link velocity distribution and discharge, avoid discharge coefficient influence, and improve discharge calculation accuracy.


Sharp-crested weir Velocity distribution Surface velocity Crest Froude number 


  1. Ackers P, White WR, Perkins JA, Harrison AJM (1978) Weirs and flumes for flow measurement. Wiley, New YorkGoogle Scholar
  2. Bagheri S, Heidarpour M (2010) Application of free vortex theory to estimating discharge coefficient for sharp-crested weirs. Biosyst Eng 105:423–427CrossRefGoogle Scholar
  3. Chanson H, Montes JS (1998) Overflow characteristics of circular weirs: effects of inflow conditions. J Irrig Drain Eng 124(3):152–162CrossRefGoogle Scholar
  4. Costa JE, Cheng RT, Haeni FP, Melcher N, Spicer KR, Hayes E, Plant W, Hayes K, Teague C, Barrick D (2006) Use of radars to monitor stream discharge by noncontact methods. Water Resour Res 42:1–14CrossRefGoogle Scholar
  5. Ferrari A (2010) SPH simulation of free surface flow over a sharp-crested weir. Adv Water Resour 33:270–276CrossRefGoogle Scholar
  6. Ghodsian M (2003) Supercritical flow over a rectangular side weir. Can J Civ Eng 30:596–600CrossRefGoogle Scholar
  7. Hirt CW, Nichols BD (1981) Volume of fluid (VOF) method for the dynamics of free boundaries. J Comput Phys 39:201–225CrossRefGoogle Scholar
  8. Hirt CW, Sicilian JM (1985) A porosity technique for the definition of obstacles in rectangular cell meshes. In: Proc. 4th Int. Conf. Ship Hydrodynamics, National Academy of Science, Washington, DCGoogle Scholar
  9. Accessed 20 Nov 2012
  10. Kindsvater CE, Carter R (1957) Discharge characteristics of rectangular thin-plate weirs. J Hydraul Div 83(3):1–36Google Scholar
  11. Lai JS, Tsorng SC, Tan YC, Hwang CY (2008) Measurements and analysis of flow field over sharp-crested weir. Taiwan Water Conservancy 56(1):49–59 (in Chinese)Google Scholar
  12. Lin C, Huang WY, Suen HF, Hsieh SC (2002) Study on the characteristics of velocity field of free overfalls over a vertical drop. In: Proc. Hydraul Meas Exp Methods Conf, Estes Park, CO, USAGoogle Scholar
  13. Muson BR, Young DF, Okiishi TH (1990) Fundamentals of fluid mechanics. Wiley, New YorkGoogle Scholar
  14. Qu J, Ramamurthy AS, Tadayon R, Chen Z (2009) Numerical simulation of sharp-crested weir flows. Can J Civ Eng 36:1530–1534CrossRefGoogle Scholar
  15. Rajaratnam N, Muralidhar D (1971) Pressure and velocity distribution for sharp-crested weirs. J Hydraul Res 9(2):241–248CrossRefGoogle Scholar
  16. Ramamurthy AS, Tim US, Rao MV (1987) Flow over sharp-crested weirs. J Irrig Drain Eng 113(2):163–172CrossRefGoogle Scholar
  17. Rehbock T (1929) Discussion of ‘‘precise weir measurements’’ by Schoder EW and Turner KB Trans ASCE 93: 1143–1162Google Scholar
  18. Rouse H (1936) Discharge characteristics of the free overfall. Civ Eng ASCE 6(4):257–260Google Scholar
  19. Samani AK, Ansari A, Borghei SM (2010) Hydraulic behaviour of flow over an oblique weir. J Hydraul Res 48(5):669–673CrossRefGoogle Scholar
  20. Sargisonl JE, Percy A (2009) Hydraulics of broad-crested weirs with varying side slopes. J Irrig Drain Eng 135(1):115–118CrossRefGoogle Scholar
  21. Subramanya K (1986) Flow in open channels. Tata McGraw-Hill, New DelhiGoogle Scholar
  22. Swamee PK (1988) Generalized rectangular weir equation. J Hydraul Eng 114(8):945–949CrossRefGoogle Scholar
  23. Tadayon R, Ramamurthy AS (2009) Turbulence modeling of flows over circular spillways. J Irrig Drain Eng 135(4):493–498CrossRefGoogle Scholar
  24. U.S. Bureau of Reclamation (1997) Water measurement manual. 3rd (ed.), U.S. Government Printing Office, Washington, DCGoogle Scholar
  25. Versteeg HK, Malalasekera W (1995) An introduction to computational fluid dynamics: the finite volume method. Longman Scientific & Technical, UKGoogle Scholar
  26. Zhang X, Yuan L, Peng R, Chen Z (2010) Hydraulic relations for clinging flow of sharp-crested weir. J Hydraul Eng 136(6):385–390CrossRefGoogle Scholar

Copyright information

© Springer Japan 2013

Authors and Affiliations

  • Shun-Chung Tsung
    • 1
  • Jihn-Sung Lai
    • 2
  • Der-Liang Young
    • 3
  1. 1.Taiwan Typhoon and Flood Research InstituteTaipeiTaiwan
  2. 2.Hydrotech Research Institute, National Taiwan UniversityTaipeiTaiwan
  3. 3.Department of Civil EngineeringNational Taiwan UniversityTaipeiTaiwan

Personalised recommendations