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 = 5 my = 1.1 mn = 0.025

Water flows uniformly 1.1 m deep in a rectangular gravel channel 5 m wide (Manning n = 0.025). The bed drops 2 m per kilometre. Use Manning’s equation in SI units to find the mean velocity V.

b = 5 my = 1.1 mn = 0.025drop = 2 m/km
V = m/s
2.Easy
b = 1 my = 2.2 mn = 0.025

Water flows uniformly 2.2 m deep in a rectangular gravel channel 1 m wide (Manning n = 0.025). The bed drops 4 m per kilometre. Use Manning’s equation in SI units to find the mean velocity V.

b = 1 my = 2.2 mn = 0.025drop = 4 m/km
V = m/s
3.Medium
D = 900 mmn = 0.013, S = 0.0005

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

D = 900 mmn = 0.013S = 0.0005
Q = m³/s
4.Medium
b = 4.5 my = 2 mn = 0.022, S = 0.003

A rectangular clean earth channel is 4.5 m wide. Water flows uniformly 2 m deep. Manning n = 0.022 and the bed slope is S = 0.003. Find the flow rate Q in m³/s.

b = 4.5 my = 2 mn = 0.022S = 0.003
Q = m³/s
5.Hard
b = 2 my = 1.8 m2 : 1n = 0.025, Q = 11 m³/s

A trapezoidal gravel channel with a bottom width of 2 m and side slopes of 2:1 (horizontal:vertical) must carry 11 m³/s in uniform flow at a depth of 1.8 m. Manning n = 0.025. Find the required bed slope S (in m/m).

Q = 11 m³/sb = 2 my = 1.8 mz = 2n = 0.025
S = m/m
6.Hard
b = 4 my = 2.4 m2 : 1n = 0.022, Q = 35 m³/s

A trapezoidal clean earth channel with a bottom width of 4 m and side slopes of 2:1 (horizontal:vertical) must carry 35 m³/s in uniform flow at a depth of 2.4 m. Manning n = 0.022. Find the required bed slope S (in m/m).

Q = 35 m³/sb = 4 my = 2.4 mz = 2n = 0.022
S = m/m

Answer key

  1. 1. V = 1.495 m/s
  2. 2. V = 1.39 m/s
  3. 3. Q = 0.4048 m³/s
  4. 4. Q = 23.28 m³/s
  5. 5. S = 0.0007413 m/m
  6. 6. S = 0.0008224 m/m

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