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 my = 0.5 mn = 0.03

Water flows uniformly 0.5 m deep in a rectangular grass-lined earth channel 1 m wide (Manning n = 0.03). The bed slope is S = 0.004. Use Manning’s equation in SI units to find the mean velocity V.

b = 1 my = 0.5 mn = 0.03S = 0.004
V = m/s
2.Easy
b = 1 my = 2.4 mn = 0.012

Water flows uniformly 2.4 m deep in a rectangular finished concrete channel 1 m wide (Manning n = 0.012). The bed slope is S = 0.003. Use Manning’s equation in SI units to find the mean velocity V.

b = 1 my = 2.4 mn = 0.012S = 0.003
V = m/s
3.Medium
D = 900 mmn = 0.013, S = 0.002

A concrete storm sewer with an inside diameter of 900 mm flows half full. Manning n = 0.013 and the slope is S = 0.002. Find the flow rate Q in m³/s.

D = 900 mmn = 0.013S = 0.002
Q = m³/s
4.Medium
D = 300 mmn = 0.013, S = 0.001

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 = 0.001. Find the flow rate Q in m³/s.

D = 300 mmn = 0.013S = 0.001
Q = m³/s
5.Hard
D = 250 mmn = 0.013, V = 0.9 m/s

A concrete sewer with an inside diameter of 250 mm (Manning n = 0.013) must reach a self-cleansing velocity of 0.9 m/s when flowing just full. Find the minimum slope S (in m/m).

D = 250 mmn = 0.013V = 0.9 m/s
S = m/m
6.Hard
D = 200 mmn = 0.013, V = 0.75 m/s

A concrete sewer with an inside diameter of 200 mm (Manning n = 0.013) must reach a self-cleansing velocity of 0.75 m/s when flowing just full. Find the minimum slope S (in m/m).

D = 200 mmn = 0.013V = 0.75 m/s
S = m/m

Answer key

  1. 1. V = 0.8366 m/s
  2. 2. V = 2.535 m/s
  3. 3. Q = 0.4048 m³/s
  4. 4. Q = 0.03058 m³/s
  5. 5. S = 0.005519 m/m
  6. 6. S = 0.005161 m/m

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