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 = 4.5 my = 2.1 mn = 0.022

Water flows uniformly 2.1 m deep in a rectangular clean earth channel 4.5 m wide (Manning n = 0.022). The bed slope is S = 0.005. Use Manning’s equation in SI units to find the mean velocity V.

b = 4.5 my = 2.1 mn = 0.022S = 0.005
V = m/s
2.Easy
b = 2.5 my = 1 mn = 0.03

Water flows uniformly 1 m deep in a rectangular grass-lined earth channel 2.5 m wide (Manning n = 0.03). The bed drops 1 m per kilometre. Use Manning’s equation in SI units to find the mean velocity V.

b = 2.5 my = 1 mn = 0.03drop = 1 m/km
V = m/s
3.Medium
b = 2 my = 1.4 m2 : 1n = 0.012, S = 0.002

A trapezoidal finished concrete channel has a bottom width of 2 m and side slopes of 2:1 (horizontal:vertical). Water flows uniformly 1.4 m deep. Manning n = 0.012 and the bed slope is S = 0.002. Find the flow rate Q in m³/s.

b = 2 my = 1.4 mz = 2n = 0.012S = 0.002
Q = m³/s
4.Medium
b = 4.5 my = 1 m3 : 1n = 0.025, S = 0.004

A trapezoidal gravel channel has a bottom width of 4.5 m and side slopes of 3:1 (horizontal:vertical). Water flows uniformly 1 m deep. Manning n = 0.025 and the bed slope is S = 0.004. Find the flow rate Q in m³/s.

b = 4.5 my = 1 mz = 3n = 0.025S = 0.004
Q = m³/s
5.Hard
b = 4 my = 1.9 m3 : 1n = 0.025, Q = 23 m³/s

A trapezoidal gravel channel with a bottom width of 4 m and side slopes of 3:1 (horizontal:vertical) must carry 23 m³/s in uniform flow at a depth of 1.9 m. Manning n = 0.025. Find the required bed slope S (in m/m).

Q = 23 m³/sb = 4 my = 1.9 mz = 3n = 0.025
S = m/m
6.Hard
D = 250 mmn = 0.013, V = 0.6 m/s

A concrete sewer with an inside diameter of 250 mm (Manning n = 0.013) must reach a self-cleansing velocity of 0.6 m/s when flowing just full. Find the minimum slope S (in m/m).

D = 250 mmn = 0.013V = 0.6 m/s
S = m/m

Answer key

  1. 1. V = 3.396 m/s
  2. 2. V = 0.7124 m/s
  3. 3. Q = 21.82 m³/s
  4. 4. Q = 14.86 m³/s
  5. 5. S = 0.0008073 m/m
  6. 6. S = 0.002453 m/m

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