Open-channel flow (Manning) worksheet with answers

Free printable Open-channel flow (Manning) worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
b = 1.5 my = 1.6 mn = 0.025

Water flows uniformly 1.6 m deep in a rectangular gravel channel 1.5 m wide (Manning n = 0.025). The bed slope is S = 0.001. Use Manning’s equation in SI units to find the mean velocity V.

b = 1.5 my = 1.6 mn = 0.025S = 0.001
V = m/s
2.Easy
b = 4 my = 1.7 mn = 0.014

Water flows uniformly 1.7 m deep in a rectangular unfinished concrete channel 4 m wide (Manning n = 0.014). The bed drops 4 m per kilometre. Use Manning’s equation in SI units to find the mean velocity V.

b = 4 my = 1.7 mn = 0.014drop = 4 m/km
V = m/s
3.Medium
D = 900 mmn = 0.013, S = 0.0005

A concrete storm sewer with an inside diameter of 900 mm flows half full. Manning n = 0.013 and the slope is S = 0.0005. Find the flow rate Q in m³/s.

D = 900 mmn = 0.013S = 0.0005
Q = m³/s
4.Medium
D = 450 mmn = 0.013, S = 0.003

A concrete storm sewer with an inside diameter of 450 mm flows half full. Manning n = 0.013 and the slope is S = 0.003. Find the flow rate Q in m³/s.

D = 450 mmn = 0.013S = 0.003
Q = m³/s
5.Hard
b = 1.5 my = 2.2 m1.5 : 1n = 0.015, Q = 17 m³/s

A trapezoidal brickwork channel with a bottom width of 1.5 m and side slopes of 1.5:1 (horizontal:vertical) must carry 17 m³/s in uniform flow at a depth of 2.2 m. Manning n = 0.015. Find the required bed slope S (in m/m).

Q = 17 m³/sb = 1.5 my = 2.2 mz = 1.5n = 0.015
S = m/m
6.Hard
b = 1.5 my = 2 m2 : 1n = 0.022, Q = 23 m³/s

A trapezoidal clean earth channel with a bottom width of 1.5 m and side slopes of 2:1 (horizontal:vertical) must carry 23 m³/s in uniform flow at a depth of 2 m. Manning n = 0.022. Find the required bed slope S (in m/m).

Q = 23 m³/sb = 1.5 my = 2 mz = 2n = 0.022
S = m/m

Answer key

  1. 1. V = 0.8081 m/s
  2. 2. V = 4.27 m/s
  3. 3. Q = 0.2024 m³/s
  4. 4. Q = 0.07808 m³/s
  5. 5. S = 0.0005016 m/m
  6. 6. S = 0.001975 m/m

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