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 = 5.5 my = 1.2 mn = 0.014

Water flows uniformly 1.2 m deep in a rectangular unfinished concrete channel 5.5 m wide (Manning n = 0.014). The bed slope is S = 0.004. Use Manning’s equation in SI units to find the mean velocity V.

b = 5.5 my = 1.2 mn = 0.014S = 0.004
V = m/s
2.Easy
b = 5 my = 0.9 mn = 0.025

Water flows uniformly 0.9 m deep in a rectangular gravel channel 5 m wide (Manning n = 0.025). The bed drops 0.8 m per kilometre. Use Manning’s equation in SI units to find the mean velocity V.

b = 5 my = 0.9 mn = 0.025drop = 0.8 m/km
V = m/s
3.Medium
b = 1 my = 1.7 m3 : 1n = 0.025, S = 0.005

A trapezoidal gravel channel has a bottom width of 1 m and side slopes of 3:1 (horizontal:vertical). Water flows uniformly 1.7 m deep. Manning n = 0.025 and the bed slope is S = 0.005. Find the flow rate Q in m³/s.

b = 1 my = 1.7 mz = 3n = 0.025S = 0.005
Q = m³/s
4.Medium
D = 300 mmn = 0.013, S = 0.002

A concrete storm sewer with an inside diameter of 300 mm flows just full (as an open channel, not under pressure). Manning n = 0.013 and the slope is S = 0.002. Find the flow rate Q in m³/s.

D = 300 mmn = 0.013S = 0.002
Q = m³/s
5.Hard
b = 1.5 my = 2.2 m1 : 1n = 0.025, Q = 15 m³/s

A trapezoidal gravel channel with a bottom width of 1.5 m and side slopes of 1:1 (horizontal:vertical) must carry 15 m³/s in uniform flow at a depth of 2.2 m. Manning n = 0.025. Find the required bed slope S (in m/m).

Q = 15 m³/sb = 1.5 my = 2.2 mz = 1n = 0.025
S = m/m
6.Hard
b = 2.5 my = 1.1 mn = 0.03, Q = 2.5 m³/s

A rectangular grass-lined earth channel 2.5 m wide must carry 2.5 m³/s in uniform flow at a depth of 1.1 m. Manning n = 0.03. Find the required bed slope S (in m/m).

Q = 2.5 m³/sb = 2.5 my = 1.1 mn = 0.03
S = m/m

Answer key

  1. 1. V = 4.007 m/s
  2. 2. V = 0.8592 m/s
  3. 3. Q = 26.98 m³/s
  4. 4. Q = 0.04325 m³/s
  5. 5. S = 0.001978 m/m
  6. 6. S = 0.00152 m/m

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