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 = 4 my = 1.6 mn = 0.022

Water flows uniformly 1.6 m deep in a rectangular clean earth channel 4 m wide (Manning n = 0.022). The bed drops 3 m per kilometre. Use Manning’s equation in SI units to find the mean velocity V.

b = 4 my = 1.6 mn = 0.022drop = 3 m/km
V = m/s
2.Easy
b = 2.5 my = 2.5 mn = 0.022

Water flows uniformly 2.5 m deep in a rectangular clean earth channel 2.5 m wide (Manning n = 0.022). The bed slope is S = 0.002. Use Manning’s equation in SI units to find the mean velocity V.

b = 2.5 my = 2.5 mn = 0.022S = 0.002
V = m/s
3.Medium
D = 600 mmn = 0.013, S = 0.001

A concrete storm sewer with an inside diameter of 600 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 = 600 mmn = 0.013S = 0.001
Q = m³/s
4.Medium
D = 600 mmn = 0.013, S = 0.002

A concrete storm sewer with an inside diameter of 600 mm flows half full. Manning n = 0.013 and the slope is S = 0.002. Find the flow rate Q in m³/s.

D = 600 mmn = 0.013S = 0.002
Q = m³/s
5.Hard
b = 4.5 my = 1.9 mn = 0.015, Q = 23 m³/s

A rectangular brickwork channel 4.5 m wide must carry 23 m³/s in uniform flow at a depth of 1.9 m. Manning n = 0.015. Find the required bed slope S (in m/m).

Q = 23 m³/sb = 4.5 my = 1.9 mn = 0.015
S = m/m
6.Hard
b = 5 my = 2.4 m1 : 1n = 0.025, Q = 51 m³/s

A trapezoidal gravel channel with a bottom width of 5 m and side slopes of 1:1 (horizontal:vertical) must carry 51 m³/s in uniform flow at a depth of 2.4 m. Manning n = 0.025. Find the required bed slope S (in m/m).

Q = 51 m³/sb = 5 my = 2.4 mz = 1n = 0.025
S = m/m

Answer key

  1. 1. V = 2.302 m/s
  2. 2. V = 1.8 m/s
  3. 3. Q = 0.1942 m³/s
  4. 4. Q = 0.1373 m³/s
  5. 5. S = 0.001565 m/m
  6. 6. S = 0.002984 m/m

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