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 = 2.5 my = 1.7 mn = 0.022

Water flows uniformly 1.7 m deep in a rectangular clean earth channel 2.5 m wide (Manning n = 0.022). The bed drops 3 m per kilometre. Use Manning’s equation in SI units to find the mean velocity V.

b = 2.5 my = 1.7 mn = 0.022drop = 3 m/km
V = m/s
2.Easy
b = 1.5 my = 2.3 mn = 0.015

Water flows uniformly 2.3 m deep in a rectangular brickwork channel 1.5 m wide (Manning n = 0.015). The bed slope is S = 0.002. Use Manning’s equation in SI units to find the mean velocity V.

b = 1.5 my = 2.3 mn = 0.015S = 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 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
4.Medium
b = 3 my = 2 mn = 0.03, S = 0.0008

A rectangular grass-lined earth channel is 3 m wide. Water flows uniformly 2 m deep. Manning n = 0.03 and the bed slope is S = 0.0008. Find the flow rate Q in m³/s.

b = 3 my = 2 mn = 0.03S = 0.0008
Q = m³/s
5.Hard
b = 1.5 my = 1.6 mn = 0.03, Q = 1.4 m³/s

A rectangular grass-lined earth channel 1.5 m wide must carry 1.4 m³/s in uniform flow at a depth of 1.6 m. Manning n = 0.03. Find the required bed slope S (in m/m).

Q = 1.4 m³/sb = 1.5 my = 1.6 mn = 0.03
S = m/m
6.Hard
b = 5.5 my = 0.8 mn = 0.022, Q = 6.5 m³/s

A rectangular clean earth channel 5.5 m wide must carry 6.5 m³/s in uniform flow at a depth of 0.8 m. Manning n = 0.022. Find the required bed slope S (in m/m).

Q = 6.5 m³/sb = 5.5 my = 0.8 mn = 0.022
S = m/m

Answer key

  1. 1. V = 2.001 m/s
  2. 2. V = 2.039 m/s
  3. 3. Q = 0.9915 m³/s
  4. 4. Q = 5.104 m³/s
  5. 5. S = 0.0007503 m/m
  6. 6. S = 0.001999 m/m

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