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 = 1.7 mn = 0.015

Water flows uniformly 1.7 m deep in a rectangular brickwork channel 1 m wide (Manning n = 0.015). The bed slope is S = 0.005. Use Manning’s equation in SI units to find the mean velocity V.

b = 1 my = 1.7 mn = 0.015S = 0.005
V = m/s
2.Easy
b = 5.5 my = 1.5 mn = 0.015

Water flows uniformly 1.5 m deep in a rectangular brickwork channel 5.5 m wide (Manning n = 0.015). The bed drops 4 m per kilometre. Use Manning’s equation in SI units to find the mean velocity V.

b = 5.5 my = 1.5 mn = 0.015drop = 4 m/km
V = m/s
3.Medium
b = 3 my = 1.9 mn = 0.022, S = 0.0005

A rectangular clean earth channel is 3 m wide. Water flows uniformly 1.9 m deep. Manning n = 0.022 and the bed slope is S = 0.0005. Find the flow rate Q in m³/s.

b = 3 my = 1.9 mn = 0.022S = 0.0005
Q = m³/s
4.Medium
D = 1200 mmn = 0.013, S = 0.005

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 = 0.005. Find the flow rate Q in m³/s.

D = 1200 mmn = 0.013S = 0.005
Q = m³/s
5.Hard
D = 600 mmn = 0.013, V = 0.6 m/s

A concrete sewer with an inside diameter of 600 mm (Manning n = 0.013) must reach a self-cleansing velocity of 0.6 m/s when flowing just full. Find the minimum slope S (in m/m).

D = 600 mmn = 0.013V = 0.6 m/s
S = m/m
6.Hard
b = 3.5 my = 1.5 mn = 0.025, Q = 7.1 m³/s

A rectangular gravel channel 3.5 m wide must carry 7.1 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 = 7.1 m³/sb = 3.5 my = 1.5 mn = 0.025
S = m/m

Answer key

  1. 1. V = 2.501 m/s
  2. 2. V = 4.133 m/s
  3. 3. Q = 5.15 m³/s
  4. 4. Q = 2.757 m³/s
  5. 5. S = 0.0007634 m/m
  6. 6. S = 0.00152 m/m

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