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 = 0.6 mn = 0.025

Water flows uniformly 0.6 m deep in a rectangular gravel channel 3.5 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 = 3.5 my = 0.6 mn = 0.025S = 0.003
V = m/s
2.Easy
b = 3 my = 1.7 mn = 0.014

Water flows uniformly 1.7 m deep in a rectangular unfinished concrete channel 3 m wide (Manning n = 0.014). The bed slope is S = 0.005. Use Manning’s equation in SI units to find the mean velocity V.

b = 3 my = 1.7 mn = 0.014S = 0.005
V = m/s
3.Medium
D = 1200 mmn = 0.013, S = 0.0008

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 = 0.0008. Find the flow rate Q in m³/s.

D = 1200 mmn = 0.013S = 0.0008
Q = m³/s
4.Medium
D = 600 mmn = 0.013, S = 0.0015

A concrete storm sewer with an inside diameter of 600 mm flows half full. Manning n = 0.013 and the slope is S = 0.0015. Find the flow rate Q in m³/s.

D = 600 mmn = 0.013S = 0.0015
Q = m³/s
5.Hard
b = 2.5 my = 1.3 m3 : 1n = 0.015, Q = 15 m³/s

A trapezoidal brickwork channel with a bottom width of 2.5 m and side slopes of 3:1 (horizontal:vertical) must carry 15 m³/s in uniform flow at a depth of 1.3 m. Manning n = 0.015. Find the required bed slope S (in m/m).

Q = 15 m³/sb = 2.5 my = 1.3 mz = 3n = 0.015
S = m/m
6.Hard
b = 6 my = 2.5 mn = 0.022, Q = 32 m³/s

A rectangular clean earth channel 6 m wide must carry 32 m³/s in uniform flow at a depth of 2.5 m. Manning n = 0.022. Find the required bed slope S (in m/m).

Q = 32 m³/sb = 6 my = 2.5 mn = 0.022
S = m/m

Answer key

  1. 1. V = 1.28 m/s
  2. 2. V = 4.341 m/s
  3. 3. Q = 1.103 m³/s
  4. 4. Q = 0.1189 m³/s
  5. 5. S = 0.001026 m/m
  6. 6. S = 0.001457 m/m

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