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 my = 2.2 mn = 0.025

Water flows uniformly 2.2 m deep in a rectangular gravel channel 5 m wide (Manning n = 0.025). The bed slope is S = 0.0015. Use Manning’s equation in SI units to find the mean velocity V.

b = 5 my = 2.2 mn = 0.025S = 0.0015
V = m/s
2.Easy
b = 1.5 my = 1.7 mn = 0.03

Water flows uniformly 1.7 m deep in a rectangular grass-lined earth channel 1.5 m wide (Manning n = 0.03). The bed slope is S = 0.002. Use Manning’s equation in SI units to find the mean velocity V.

b = 1.5 my = 1.7 mn = 0.03S = 0.002
V = m/s
3.Medium
D = 900 mmn = 0.013, S = 0.003

A concrete storm sewer with an inside diameter of 900 mm flows half full. Manning n = 0.013 and the slope is S = 0.003. Find the flow rate Q in m³/s.

D = 900 mmn = 0.013S = 0.003
Q = m³/s
4.Medium
D = 1200 mmn = 0.013, S = 0.0008

A concrete storm sewer with an inside diameter of 1200 mm flows just full (as an open channel, not under pressure). Manning n = 0.013 and the slope is S = 0.0008. Find the flow rate Q in m³/s.

D = 1200 mmn = 0.013S = 0.0008
Q = m³/s
5.Hard
b = 3 my = 1.4 m3 : 1n = 0.022, Q = 18 m³/s

A trapezoidal clean earth channel with a bottom width of 3 m and side slopes of 3:1 (horizontal:vertical) must carry 18 m³/s in uniform flow at a depth of 1.4 m. Manning n = 0.022. Find the required bed slope S (in m/m).

Q = 18 m³/sb = 3 my = 1.4 mz = 3n = 0.022
S = m/m
6.Hard
b = 3 my = 1.5 m1.5 : 1n = 0.025, Q = 19 m³/s

A trapezoidal gravel channel with a bottom width of 3 m and side slopes of 1.5:1 (horizontal:vertical) must carry 19 m³/s in uniform flow at a depth of 1.5 m. Manning n = 0.025. Find the required bed slope S (in m/m).

Q = 19 m³/sb = 3 my = 1.5 mz = 1.5n = 0.025
S = m/m

Answer key

  1. 1. V = 1.72 m/s
  2. 2. V = 0.9645 m/s
  3. 3. Q = 0.4958 m³/s
  4. 4. Q = 1.103 m³/s
  5. 5. S = 0.001916 m/m
  6. 6. S = 0.00397 m/m

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