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214/33310–15FE Reference Handbook 10.4 · Civil · Open Channel · Critical Flow
1. Manning’s Equation2. Darcy–Weisbach Head Loss3. Orifice & Weir Discharge4. Hydraulic Radius5. Hazen–Williams Equation6. Specific Energy7. Froude Number8. Rational Method Peak Runoff9. Pump Power and Efficiency10. Cipoletti / Rectangular Weir11. SCS Curve-Number Runoff12. Open-Channel Continuity13. Hydraulic Jump Sequent Depth14. Pumps in Series and Parallel15. Compound (Parallel) Pipes16. Gradually Varied Flow (dy/dx)17. Unit Hydrograph18. Critical Depth (Rectangular)19. Thiem / Dupuit Confined Well20. Culvert Inlet / Orifice Control21. Chézy Equation22. Horton Infiltration23. Detention Basin Storage Routing24. Time of Concentration (Kirpich)

Handbook formula

Critical Depth (Rectangular)

q=Q/b is unit discharge. At critical, E=1.5 yc and Fr=1. Mild slopes: y_n>y_c (sub). Steep: y_n<y_c (super). Hydraulic jump takes super → sub.

(m²/s)
Discharge per unit width
Critical depth

Step-by-step solved example

Q=9 m³/s in a 3 m wide rectangle. yc?

y_cy_n
yc where Fr = 1; jump from super- to subcritical.

  1. 1. q

    q=9/3=3.0 m²/s.

  2. 2. yc

    (9/9.81)^{1/3}=0.917^{1/3}≈0.97 m.

Answer: yc ≈ 0.97 m

10 practice questions

0/10 correct

1.Fr>1 is

2.Emin for a rectangle is

3.A wide channel approximates

4.If Q doubles in a rectangle, yc scales by

5.Triangle/trapezoid yc needs

6.Control at a free overfall is

7.q=4 m²/s, yc nearest

8.Mild slope GVF approaching a steep slope passes

9.c_wave = √(gy) so Fr=V/c

10.g in USCS for yc=(q²/g)^{1/3} is