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 = 1.5 mn = 0.025

Water flows uniformly 1.5 m deep in a rectangular gravel channel 2.5 m wide (Manning n = 0.025). The bed slope is S = 0.003. Use Manning’s equation in SI units to find the mean velocity V.

b = 2.5 my = 1.5 mn = 0.025S = 0.003
V = m/s
2.Easy
b = 6 my = 0.6 mn = 0.015

Water flows uniformly 0.6 m deep in a rectangular brickwork channel 6 m wide (Manning n = 0.015). The bed slope is S = 0.001. Use Manning’s equation in SI units to find the mean velocity V.

b = 6 my = 0.6 mn = 0.015S = 0.001
V = m/s
3.Medium
b = 1.5 my = 1.2 mn = 0.012, S = 0.003

A rectangular finished concrete channel is 1.5 m wide. Water flows uniformly 1.2 m deep. Manning n = 0.012 and the bed slope is S = 0.003. Find the flow rate Q in m³/s.

b = 1.5 my = 1.2 mn = 0.012S = 0.003
Q = m³/s
4.Medium
b = 6 my = 2.4 m1 : 1n = 0.012, S = 0.002

A trapezoidal finished concrete channel has a bottom width of 6 m and side slopes of 1:1 (horizontal:vertical). Water flows uniformly 2.4 m deep. Manning n = 0.012 and the bed slope is S = 0.002. Find the flow rate Q in m³/s.

b = 6 my = 2.4 mz = 1n = 0.012S = 0.002
Q = m³/s
5.Hard
b = 5 my = 2.2 mn = 0.03, Q = 18 m³/s

A rectangular grass-lined earth channel 5 m wide must carry 18 m³/s in uniform flow at a depth of 2.2 m. Manning n = 0.03. Find the required bed slope S (in m/m).

Q = 18 m³/sb = 5 my = 2.2 mn = 0.03
S = m/m
6.Hard
b = 4 my = 2 mn = 0.03, Q = 12 m³/s

A rectangular grass-lined earth channel 4 m wide must carry 12 m³/s in uniform flow at a depth of 2 m. Manning n = 0.03. Find the required bed slope S (in m/m).

Q = 12 m³/sb = 4 my = 2 mn = 0.03
S = m/m

Answer key

  1. 1. V = 1.697 m/s
  2. 2. V = 1.328 m/s
  3. 3. Q = 4.907 m³/s
  4. 4. Q = 101.8 m³/s
  5. 5. S = 0.001954 m/m
  6. 6. S = 0.002025 m/m

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