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 = 2 mn = 0.015

Water flows uniformly 2 m deep in a rectangular brickwork channel 3.5 m wide (Manning n = 0.015). The bed drops 5 m per kilometre. Use Manning’s equation in SI units to find the mean velocity V.

b = 3.5 my = 2 mn = 0.015drop = 5 m/km
V = m/s
2.Easy
b = 1 my = 2.5 mn = 0.015

Water flows uniformly 2.5 m deep in a rectangular brickwork channel 1 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 = 1 my = 2.5 mn = 0.015drop = 4 m/km
V = m/s
3.Medium
b = 5 my = 1.6 m3 : 1n = 0.014, S = 0.001

A trapezoidal unfinished concrete channel has a bottom width of 5 m and side slopes of 3:1 (horizontal:vertical). Water flows uniformly 1.6 m deep. Manning n = 0.014 and the bed slope is S = 0.001. Find the flow rate Q in m³/s.

b = 5 my = 1.6 mz = 3n = 0.014S = 0.001
Q = m³/s
4.Medium
D = 900 mmn = 0.013, S = 0.0015

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 = 0.0015. Find the flow rate Q in m³/s.

D = 900 mmn = 0.013S = 0.0015
Q = m³/s
5.Hard
b = 2 my = 1.3 m3 : 1n = 0.025, Q = 18 m³/s

A trapezoidal gravel channel with a bottom width of 2 m and side slopes of 3:1 (horizontal:vertical) must carry 18 m³/s in uniform flow at a depth of 1.3 m. Manning n = 0.025. Find the required bed slope S (in m/m).

Q = 18 m³/sb = 2 my = 1.3 mz = 3n = 0.025
S = m/m
6.Hard
b = 4 my = 1.5 mn = 0.03, Q = 4 m³/s

A rectangular grass-lined earth channel 4 m wide must carry 4 m³/s in uniform flow at a depth of 1.5 m. Manning n = 0.03. Find the required bed slope S (in m/m).

Q = 4 m³/sb = 4 my = 1.5 mn = 0.03
S = m/m

Answer key

  1. 1. V = 4.502 m/s
  2. 2. V = 2.352 m/s
  3. 3. Q = 36.29 m³/s
  4. 4. Q = 0.7011 m³/s
  5. 5. S = 0.005048 m/m
  6. 6. S = 0.0004913 m/m

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