Triangular weir modelling

Weirs Laws

  1. function [Q] = vnotch(T,h,alfa,Cd,e)
  2. % T : 1 for true V-Notch
  3. % T : 2 pour V-Notch equivalent
  4. % h : upstream level
  5. % Q : discharge
  6. % Initialisation ---------------------------------------------
  7. R2G = sqrt(2*9.81);
  8. if (T==1)
  9. % triangular weir
  10. Q=1.32*tan(alfa/2)*h^2.47;
  11. else
  12. % Equivalent horizontal weir
  13. if (h>0)
  14. L=e*tan(alfa/2);
  15. Q=Cd*R2G*L*h^1.5;
  16. end
  17. if (h>e)
  18. Q=Q+Cd*R2G*2*L*(h-e)^1.5;
  19. end
  20. if (h>2*e)
  21. Q=Q+Cd*R2G*2*L*(h-2*e)^1.5;
  22. end
  23. if (h>3*e)
  24. Q=Q+Cd*R2G*2*L*(h-3*e)^1.5;
  25. end
  26. if (h>4*e)
  27. Q=Q+Cd*R2G*2*L*(h-4*e)^1.5;
  28. end
  29. end

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Comparison of the results obtained by using the two laws on an example

  1. % Parameters --------------------------------------------
  2. pas=0.005;
  3. val=100;
  4. alfa=pi/2;
  5. e=0.1;
  6. Cd=0.38;
  7. % Calculation ------------------------------------------------
  8. for i=1:val
  9. [Q(i,1)]=vnotch(1,i*pas,alfa,Cd,e);
  10. [Q(i,2)]=vnotch(2,i*pas,alfa,Cd,e);
  11. end
  12. % discharge deviation
  13. plot(Q);
  14. % relative deviation in %
  15. plot((Q(:,2)-Q(:,1))/Q(:,1));

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