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 = 5 my = 0.4 mn = 0.015

Water flows uniformly 0.4 m deep in a rectangular brickwork channel 5 m wide (Manning n = 0.015). The bed slope is S = 0.002. Use Manning’s equation in SI units to find the mean velocity V.

b = 5 my = 0.4 mn = 0.015S = 0.002
V = m/s
2.Easy
b = 3.5 my = 1.3 mn = 0.012

Water flows uniformly 1.3 m deep in a rectangular finished concrete channel 3.5 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 = 3.5 my = 1.3 mn = 0.012S = 0.005
V = m/s
3.Medium
b = 2.5 my = 0.9 m3 : 1n = 0.03, S = 0.005

A trapezoidal grass-lined earth channel has a bottom width of 2.5 m and side slopes of 3:1 (horizontal:vertical). Water flows uniformly 0.9 m deep. Manning n = 0.03 and the bed slope is S = 0.005. Find the flow rate Q in m³/s.

b = 2.5 my = 0.9 mz = 3n = 0.03S = 0.005
Q = m³/s
4.Medium
b = 3 my = 1 m3 : 1n = 0.015, S = 0.004

A trapezoidal brickwork channel has a bottom width of 3 m and side slopes of 3:1 (horizontal:vertical). Water flows uniformly 1 m deep. Manning n = 0.015 and the bed slope is S = 0.004. Find the flow rate Q in m³/s.

b = 3 my = 1 mz = 3n = 0.015S = 0.004
Q = m³/s
5.Hard
b = 3 my = 2.5 mn = 0.025, Q = 6.4 m³/s

A rectangular gravel channel 3 m wide must carry 6.4 m³/s in uniform flow at a depth of 2.5 m. Manning n = 0.025. Find the required bed slope S (in m/m).

Q = 6.4 m³/sb = 3 my = 2.5 mn = 0.025
S = m/m
6.Hard
b = 4 my = 0.7 mn = 0.025, Q = 2.8 m³/s

A rectangular gravel channel 4 m wide must carry 2.8 m³/s in uniform flow at a depth of 0.7 m. Manning n = 0.025. Find the required bed slope S (in m/m).

Q = 2.8 m³/sb = 4 my = 0.7 mn = 0.025
S = m/m

Answer key

  1. 1. V = 1.466 m/s
  2. 2. V = 4.846 m/s
  3. 3. Q = 7.595 m³/s
  4. 4. Q = 18.86 m³/s
  5. 5. S = 0.000496 m/m
  6. 6. S = 0.0015 m/m

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