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 = 4.5 my = 1.7 mn = 0.014

Water flows uniformly 1.7 m deep in a rectangular unfinished concrete channel 4.5 m wide (Manning n = 0.014). The bed drops 1 m per kilometre. Use Manning’s equation in SI units to find the mean velocity V.

b = 4.5 my = 1.7 mn = 0.014drop = 1 m/km
V = m/s
2.Easy
b = 4 my = 1 mn = 0.014

Water flows uniformly 1 m deep in a rectangular unfinished concrete channel 4 m wide (Manning n = 0.014). The bed drops 2 m per kilometre. Use Manning’s equation in SI units to find the mean velocity V.

b = 4 my = 1 mn = 0.014drop = 2 m/km
V = m/s
3.Medium
D = 450 mmn = 0.013, S = 0.001

A concrete storm sewer with an inside diameter of 450 mm flows half full. Manning n = 0.013 and the slope is S = 0.001. Find the flow rate Q in m³/s.

D = 450 mmn = 0.013S = 0.001
Q = m³/s
4.Medium
D = 900 mmn = 0.013, S = 0.003

A concrete storm sewer with an inside diameter of 900 mm flows just full (as an open channel, not under pressure). 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
5.Hard
b = 5 my = 0.8 mn = 0.03, Q = 2.1 m³/s

A rectangular grass-lined earth channel 5 m wide must carry 2.1 m³/s in uniform flow at a depth of 0.8 m. Manning n = 0.03. Find the required bed slope S (in m/m).

Q = 2.1 m³/sb = 5 my = 0.8 mn = 0.03
S = m/m
6.Hard
b = 2.5 my = 1.2 mn = 0.022, Q = 2.8 m³/s

A rectangular clean earth channel 2.5 m wide must carry 2.8 m³/s in uniform flow at a depth of 1.2 m. Manning n = 0.022. Find the required bed slope S (in m/m).

Q = 2.8 m³/sb = 2.5 my = 1.2 mn = 0.022
S = m/m

Answer key

  1. 1. V = 2.211 m/s
  2. 2. V = 2.438 m/s
  3. 3. Q = 0.04508 m³/s
  4. 4. Q = 0.9915 m³/s
  5. 5. S = 0.0004837 m/m
  6. 6. S = 0.000811 m/m

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