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 = 1 my = 1 mn = 0.014

Water flows uniformly 1 m deep in a rectangular unfinished concrete channel 1 m wide (Manning n = 0.014). The bed slope is S = 0.0005. Use Manning’s equation in SI units to find the mean velocity V.

b = 1 my = 1 mn = 0.014S = 0.0005
V = m/s
2.Easy
b = 2 my = 2.3 mn = 0.012

Water flows uniformly 2.3 m deep in a rectangular finished concrete channel 2 m wide (Manning n = 0.012). The bed slope is S = 0.004. Use Manning’s equation in SI units to find the mean velocity V.

b = 2 my = 2.3 mn = 0.012S = 0.004
V = m/s
3.Medium
b = 3 my = 2.4 mn = 0.012, S = 0.005

A rectangular finished concrete channel is 3 m wide. Water flows uniformly 2.4 m deep. Manning n = 0.012 and the bed slope is S = 0.005. Find the flow rate Q in m³/s.

b = 3 my = 2.4 mn = 0.012S = 0.005
Q = m³/s
4.Medium
D = 300 mmn = 0.013, S = 0.0015

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 = 0.0015. Find the flow rate Q in m³/s.

D = 300 mmn = 0.013S = 0.0015
Q = m³/s
5.Hard
b = 6 my = 1.6 mn = 0.015, Q = 21 m³/s

A rectangular brickwork channel 6 m wide must carry 21 m³/s in uniform flow at a depth of 1.6 m. Manning n = 0.015. Find the required bed slope S (in m/m).

Q = 21 m³/sb = 6 my = 1.6 mn = 0.015
S = m/m
6.Hard
D = 600 mmn = 0.013, V = 0.75 m/s

A concrete sewer with an inside diameter of 600 mm (Manning n = 0.013) must reach a self-cleansing velocity of 0.75 m/s when flowing just full. Find the minimum slope S (in m/m).

D = 600 mmn = 0.013V = 0.75 m/s
S = m/m

Answer key

  1. 1. V = 0.7678 m/s
  2. 2. V = 4.143 m/s
  3. 3. Q = 40.22 m³/s
  4. 4. Q = 0.03745 m³/s
  5. 5. S = 0.001017 m/m
  6. 6. S = 0.001193 m/m

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