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 = 2.5 mn = 0.025

Water flows uniformly 2.5 m deep in a rectangular gravel channel 1 m wide (Manning n = 0.025). The bed slope is S = 0.003. Use Manning’s equation in SI units to find the mean velocity V.

b = 1 my = 2.5 mn = 0.025S = 0.003
V = m/s
2.Easy
b = 1.5 my = 0.8 mn = 0.022

Water flows uniformly 0.8 m deep in a rectangular clean earth channel 1.5 m wide (Manning n = 0.022). The bed drops 1 m per kilometre. Use Manning’s equation in SI units to find the mean velocity V.

b = 1.5 my = 0.8 mn = 0.022drop = 1 m/km
V = m/s
3.Medium
D = 1200 mmn = 0.013, S = 0.0005

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 = 0.0005. Find the flow rate Q in m³/s.

D = 1200 mmn = 0.013S = 0.0005
Q = m³/s
4.Medium
b = 1.5 my = 0.9 m2 : 1n = 0.022, S = 0.0008

A trapezoidal clean earth channel has a bottom width of 1.5 m and side slopes of 2:1 (horizontal:vertical). Water flows uniformly 0.9 m deep. Manning n = 0.022 and the bed slope is S = 0.0008. Find the flow rate Q in m³/s.

b = 1.5 my = 0.9 mz = 2n = 0.022S = 0.0008
Q = m³/s
5.Hard
b = 5 my = 1 m1 : 1n = 0.014, Q = 20 m³/s

A trapezoidal unfinished concrete channel with a bottom width of 5 m and side slopes of 1:1 (horizontal:vertical) must carry 20 m³/s in uniform flow at a depth of 1 m. Manning n = 0.014. Find the required bed slope S (in m/m).

Q = 20 m³/sb = 5 my = 1 mz = 1n = 0.014
S = m/m
6.Hard
D = 200 mmn = 0.013, V = 0.6 m/s

A concrete sewer with an inside diameter of 200 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 = 200 mmn = 0.013V = 0.6 m/s
S = m/m

Answer key

  1. 1. V = 1.222 m/s
  2. 2. V = 0.7635 m/s
  3. 3. Q = 0.8718 m³/s
  4. 4. Q = 2.524 m³/s
  5. 5. S = 0.003105 m/m
  6. 6. S = 0.003303 m/m

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