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 = 1.7 mn = 0.025

Water flows uniformly 1.7 m deep in a rectangular gravel channel 2.5 m wide (Manning n = 0.025). The bed slope is S = 0.001. Use Manning’s equation in SI units to find the mean velocity V.

b = 2.5 my = 1.7 mn = 0.025S = 0.001
V = m/s
2.Easy
b = 1.5 my = 2 mn = 0.03

Water flows uniformly 2 m deep in a rectangular grass-lined earth channel 1.5 m wide (Manning n = 0.03). The bed slope is S = 0.005. Use Manning’s equation in SI units to find the mean velocity V.

b = 1.5 my = 2 mn = 0.03S = 0.005
V = m/s
3.Medium
b = 5.5 my = 2.3 mn = 0.015, S = 0.001

A rectangular brickwork channel is 5.5 m wide. Water flows uniformly 2.3 m deep. Manning n = 0.015 and the bed slope is S = 0.001. Find the flow rate Q in m³/s.

b = 5.5 my = 2.3 mn = 0.015S = 0.001
Q = m³/s
4.Medium
D = 300 mmn = 0.013, S = 0.0008

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

D = 300 mmn = 0.013S = 0.0008
Q = m³/s
5.Hard
b = 1.5 my = 1.8 mn = 0.012, Q = 6.6 m³/s

A rectangular finished concrete channel 1.5 m wide must carry 6.6 m³/s in uniform flow at a depth of 1.8 m. Manning n = 0.012. Find the required bed slope S (in m/m).

Q = 6.6 m³/sb = 1.5 my = 1.8 mn = 0.012
S = m/m
6.Hard
b = 3 my = 1 mn = 0.03, Q = 5 m³/s

A rectangular grass-lined earth channel 3 m wide must carry 5 m³/s in uniform flow at a depth of 1 m. Manning n = 0.03. Find the required bed slope S (in m/m).

Q = 5 m³/sb = 3 my = 1 mn = 0.03
S = m/m

Answer key

  1. 1. V = 1.016 m/s
  2. 2. V = 1.574 m/s
  3. 3. Q = 30.99 m³/s
  4. 4. Q = 0.02735 m³/s
  5. 5. S = 0.002009 m/m
  6. 6. S = 0.00494 m/m

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