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 = 3 my = 1.2 mn = 0.022

Water flows uniformly 1.2 m deep in a rectangular clean earth channel 3 m wide (Manning n = 0.022). The bed drops 0.5 m per kilometre. Use Manning’s equation in SI units to find the mean velocity V.

b = 3 my = 1.2 mn = 0.022drop = 0.5 m/km
V = m/s
2.Easy
b = 4 my = 0.8 mn = 0.022

Water flows uniformly 0.8 m deep in a rectangular clean earth channel 4 m wide (Manning n = 0.022). The bed slope is S = 0.0005. Use Manning’s equation in SI units to find the mean velocity V.

b = 4 my = 0.8 mn = 0.022S = 0.0005
V = m/s
3.Medium
b = 2 my = 1.1 m2 : 1n = 0.025, S = 0.0008

A trapezoidal gravel channel has a bottom width of 2 m and side slopes of 2:1 (horizontal:vertical). Water flows uniformly 1.1 m deep. Manning n = 0.025 and the bed slope is S = 0.0008. Find the flow rate Q in m³/s.

b = 2 my = 1.1 mz = 2n = 0.025S = 0.0008
Q = m³/s
4.Medium
b = 2 my = 1.8 m1 : 1n = 0.015, S = 0.0005

A trapezoidal brickwork channel has a bottom width of 2 m and side slopes of 1:1 (horizontal:vertical). Water flows uniformly 1.8 m deep. Manning n = 0.015 and the bed slope is S = 0.0005. Find the flow rate Q in m³/s.

b = 2 my = 1.8 mz = 1n = 0.015S = 0.0005
Q = m³/s
5.Hard
b = 6 my = 0.5 m1.5 : 1n = 0.012, Q = 8.8 m³/s

A trapezoidal finished concrete channel with a bottom width of 6 m and side slopes of 1.5:1 (horizontal:vertical) must carry 8.8 m³/s in uniform flow at a depth of 0.5 m. Manning n = 0.012. Find the required bed slope S (in m/m).

Q = 8.8 m³/sb = 6 my = 0.5 mz = 1.5n = 0.012
S = m/m
6.Hard
D = 300 mmn = 0.013, V = 0.75 m/s

A concrete sewer with an inside diameter of 300 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 = 300 mmn = 0.013V = 0.75 m/s
S = m/m

Answer key

  1. 1. V = 0.7757 m/s
  2. 2. V = 0.6999 m/s
  3. 3. Q = 3.993 m³/s
  4. 4. Q = 9.954 m³/s
  5. 5. S = 0.002993 m/m
  6. 6. S = 0.003006 m/m

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