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 = 6 my = 2.1 mn = 0.012

Water flows uniformly 2.1 m deep in a rectangular finished concrete channel 6 m wide (Manning n = 0.012). The bed drops 1.5 m per kilometre. Use Manning’s equation in SI units to find the mean velocity V.

b = 6 my = 2.1 mn = 0.012drop = 1.5 m/km
V = m/s
2.Easy
b = 5.5 my = 0.9 mn = 0.012

Water flows uniformly 0.9 m deep in a rectangular finished concrete channel 5.5 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 = 5.5 my = 0.9 mn = 0.012S = 0.003
V = m/s
3.Medium
b = 4 my = 1 m1 : 1n = 0.015, S = 0.0005

A trapezoidal brickwork channel has a bottom width of 4 m and side slopes of 1:1 (horizontal:vertical). Water flows uniformly 1 m deep. Manning n = 0.015 and the bed slope is S = 0.0005. Find the flow rate Q in m³/s.

b = 4 my = 1 mz = 1n = 0.015S = 0.0005
Q = m³/s
4.Medium
b = 3.5 my = 2.4 mn = 0.025, S = 0.0008

A rectangular gravel channel is 3.5 m wide. Water flows uniformly 2.4 m deep. Manning n = 0.025 and the bed slope is S = 0.0008. Find the flow rate Q in m³/s.

b = 3.5 my = 2.4 mn = 0.025S = 0.0008
Q = m³/s
5.Hard
b = 5.5 my = 1 m3 : 1n = 0.012, Q = 13 m³/s

A trapezoidal finished concrete channel with a bottom width of 5.5 m and side slopes of 3:1 (horizontal:vertical) must carry 13 m³/s in uniform flow at a depth of 1 m. Manning n = 0.012. Find the required bed slope S (in m/m).

Q = 13 m³/sb = 5.5 my = 1 mz = 3n = 0.012
S = m/m
6.Hard
b = 3 my = 2.2 mn = 0.022, Q = 20 m³/s

A rectangular clean earth channel 3 m wide must carry 20 m³/s in uniform flow at a depth of 2.2 m. Manning n = 0.022. Find the required bed slope S (in m/m).

Q = 20 m³/sb = 3 my = 2.2 mn = 0.022
S = m/m

Answer key

  1. 1. V = 3.716 m/s
  2. 2. V = 3.523 m/s
  3. 3. Q = 6.055 m³/s
  4. 4. Q = 9.58 m³/s
  5. 5. S = 0.0005231 m/m
  6. 6. S = 0.005177 m/m

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