The program ONLINE_TRACTIVE_FORCE calculates the normal depth and bottom width of a prismatic open channel of rectangular or trapezoidal cross section, based on the tractive force method as described in Chow (1959). Only noncohesive material (sand and gravel) can be specified on sides and bottom.

  1. The program consists of seven (7) pages. Page 1 is the index. Page 2 is the input page. The remaining pages (Pages 3 through 7) are the output pages.

  2. Coarse noncohesive material has diameter d25 > 5 mm (0.2 in). Fine noncohesive material has diameter d50 ≤ 5 mm (0.2 in).

  3. Two cases are possible for the material on sides and bottom:

    • The same coarse noncohesive material specified on both sides and bottom (data type 2), and

    • A coarse noncohesive material specified for the sides (data type 2), and a fine noncohesive material for the bottom (data type 3).

  4. The programs accepts either SI (metric) units, or U.S. Customary units. All calculations are performed in U.S. Customary units, with the appropriate input/output conversions.

  5. The program calculates normal depth by iteration, using Newton's approximation. For side control, normal depth is calculated in Page 4. When conditions are such that there is bottom control, normal depth is calculated in Page 7. For safety reasons, the maximum number of iterations is limited to 999.

  6. The results are given in Page 6 for the case of side control, and in Page 7 for bottom control.

  7. Input variables outside of the following ranges will trigger error messages and stop execution.

    Discharge Q:   Q > 0;      Side slope z [z H : 1 V]:   1 ≤ z ≤ 2 ;      Manning's n:   0.008 ≤ n ≤ 0.250;

    Bottom slope So:   0.00001 ≤ So ≤ 0.1;

    Sides particle size d25:   0.2 < d25 ≤ 4 in (U.S. Customary units);    5 < d25 ≤ 100 mm (SI units).

  8. The bottom particle size d50 is restricted in the range   0.1 ≤ d50 ≤ 5 mm. However, you can specify d50 = 0 [or leave it blank] as an exception, to signal to the program that the material is the same in sides and bottom (default value). A bottom particle size too small, in the range 0 < d50 < 0.1 mm, will be reset to d50 = 0.1 mm.

  9. The side angle φ = tan-1(1/z) is limited to values less than or equal to the angle of repose θ, a function of d25. If this is the case, correct by increasing z (a milder side slope) or increasing θ (a stronger material).

  10. In addition to the upper limit on the side angle φ (see item 9), the tractive force ratio K (Page 2) is limited to values greater than or equal to 0.05. If this is the case, correct by increasing z or increasing θ.