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 my = 2.5 mn = 0.025

Water flows uniformly 2.5 m deep in a rectangular gravel channel 2 m wide (Manning n = 0.025). The bed slope is S = 0.002. Use Manning’s equation in SI units to find the mean velocity V.

b = 2 my = 2.5 mn = 0.025S = 0.002
V = m/s
2.Easy
b = 3 my = 2 mn = 0.012

Water flows uniformly 2 m deep in a rectangular finished concrete channel 3 m wide (Manning n = 0.012). The bed slope is S = 0.003. Use Manning’s equation in SI units to find the mean velocity V.

b = 3 my = 2 mn = 0.012S = 0.003
V = m/s
3.Medium
D = 750 mmn = 0.013, S = 0.003

A concrete storm sewer with an inside diameter of 750 mm flows just full (as an open channel, not under pressure). Manning n = 0.013 and the slope is S = 0.003. Find the flow rate Q in m³/s.

D = 750 mmn = 0.013S = 0.003
Q = m³/s
4.Medium
b = 4.5 my = 1.1 m1 : 1n = 0.025, S = 0.004

A trapezoidal gravel channel has a bottom width of 4.5 m and side slopes of 1:1 (horizontal:vertical). Water flows uniformly 1.1 m deep. Manning n = 0.025 and the bed slope is S = 0.004. Find the flow rate Q in m³/s.

b = 4.5 my = 1.1 mz = 1n = 0.025S = 0.004
Q = m³/s
5.Hard
b = 1.5 my = 2.3 mn = 0.03, Q = 2.5 m³/s

A rectangular grass-lined earth channel 1.5 m wide must carry 2.5 m³/s in uniform flow at a depth of 2.3 m. Manning n = 0.03. Find the required bed slope S (in m/m).

Q = 2.5 m³/sb = 1.5 my = 2.3 mn = 0.03
S = m/m
6.Hard
b = 1 my = 2.5 mn = 0.015, Q = 2.9 m³/s

A rectangular brickwork channel 1 m wide must carry 2.9 m³/s in uniform flow at a depth of 2.5 m. Manning n = 0.015. Find the required bed slope S (in m/m).

Q = 2.9 m³/sb = 1 my = 2.5 mn = 0.015
S = m/m

Answer key

  1. 1. V = 1.429 m/s
  2. 2. V = 4.119 m/s
  3. 3. Q = 0.6098 m³/s
  4. 4. Q = 13.53 m³/s
  5. 5. S = 0.00101 m/m
  6. 6. S = 0.0009729 m/m

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