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 = 2.5 my = 1.9 mn = 0.022

Water flows uniformly 1.9 m deep in a rectangular clean earth channel 2.5 m wide (Manning n = 0.022). The bed slope is S = 0.005. Use Manning’s equation in SI units to find the mean velocity V.

b = 2.5 my = 1.9 mn = 0.022S = 0.005
V = m/s
2.Easy
b = 4.5 my = 1.5 mn = 0.012

Water flows uniformly 1.5 m deep in a rectangular finished concrete channel 4.5 m wide (Manning n = 0.012). The bed slope is S = 0.005. Use Manning’s equation in SI units to find the mean velocity V.

b = 4.5 my = 1.5 mn = 0.012S = 0.005
V = m/s
3.Medium
D = 300 mmn = 0.013, S = 0.005

A concrete storm sewer with an inside diameter of 300 mm flows just full (as an open channel, not under pressure). Manning n = 0.013 and the slope is S = 0.005. Find the flow rate Q in m³/s.

D = 300 mmn = 0.013S = 0.005
Q = m³/s
4.Medium
D = 450 mmn = 0.013, S = 0.0005

A concrete storm sewer with an inside diameter of 450 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 = 450 mmn = 0.013S = 0.0005
Q = m³/s
5.Hard
b = 5.5 my = 2.5 mn = 0.022, Q = 21 m³/s

A rectangular clean earth channel 5.5 m wide must carry 21 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 = 21 m³/sb = 5.5 my = 2.5 mn = 0.022
S = m/m
6.Hard
b = 6 my = 1.3 m1.5 : 1n = 0.03, Q = 11 m³/s

A trapezoidal grass-lined earth channel with a bottom width of 6 m and side slopes of 1.5:1 (horizontal:vertical) must carry 11 m³/s in uniform flow at a depth of 1.3 m. Manning n = 0.03. Find the required bed slope S (in m/m).

Q = 11 m³/sb = 6 my = 1.3 mz = 1.5n = 0.03
S = m/m

Answer key

  1. 1. V = 2.663 m/s
  2. 2. V = 5.493 m/s
  3. 3. Q = 0.06838 m³/s
  4. 4. Q = 0.06375 m³/s
  5. 5. S = 0.000788 m/m
  6. 6. S = 0.001066 m/m

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