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 = 3.5 my = 0.7 mn = 0.03

Water flows uniformly 0.7 m deep in a rectangular grass-lined earth channel 3.5 m wide (Manning n = 0.03). The bed drops 5 m per kilometre. Use Manning’s equation in SI units to find the mean velocity V.

b = 3.5 my = 0.7 mn = 0.03drop = 5 m/km
V = m/s
2.Easy
b = 6 my = 1.7 mn = 0.025

Water flows uniformly 1.7 m deep in a rectangular gravel channel 6 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 = 6 my = 1.7 mn = 0.025S = 0.0015
V = m/s
3.Medium
b = 4.5 my = 1 m1 : 1n = 0.012, S = 0.0008

A trapezoidal finished concrete channel has a bottom width of 4.5 m and side slopes of 1:1 (horizontal:vertical). Water flows uniformly 1 m deep. Manning n = 0.012 and the bed slope is S = 0.0008. Find the flow rate Q in m³/s.

b = 4.5 my = 1 mz = 1n = 0.012S = 0.0008
Q = m³/s
4.Medium
D = 750 mmn = 0.013, S = 0.001

A concrete storm sewer with an inside diameter of 750 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 = 750 mmn = 0.013S = 0.001
Q = m³/s
5.Hard
b = 4.5 my = 0.9 m1.5 : 1n = 0.015, Q = 17 m³/s

A trapezoidal brickwork channel with a bottom width of 4.5 m and side slopes of 1.5:1 (horizontal:vertical) must carry 17 m³/s in uniform flow at a depth of 0.9 m. Manning n = 0.015. Find the required bed slope S (in m/m).

Q = 17 m³/sb = 4.5 my = 0.9 mz = 1.5n = 0.015
S = m/m
6.Hard
D = 200 mmn = 0.013, V = 1.2 m/s

A concrete sewer with an inside diameter of 200 mm (Manning n = 0.013) must reach a self-cleansing velocity of 1.2 m/s when flowing just full. Find the minimum slope S (in m/m).

D = 200 mmn = 0.013V = 1.2 m/s
S = m/m

Answer key

  1. 1. V = 1.485 m/s
  2. 2. V = 1.636 m/s
  3. 3. Q = 10.71 m³/s
  4. 4. Q = 0.352 m³/s
  5. 5. S = 0.003924 m/m
  6. 6. S = 0.01321 m/m

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