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 = 1 my = 0.8 mn = 0.022

Water flows uniformly 0.8 m deep in a rectangular clean earth channel 1 m wide (Manning n = 0.022). The bed drops 0.8 m per kilometre. Use Manning’s equation in SI units to find the mean velocity V.

b = 1 my = 0.8 mn = 0.022drop = 0.8 m/km
V = m/s
2.Easy
b = 5.5 my = 1.3 mn = 0.025

Water flows uniformly 1.3 m deep in a rectangular gravel channel 5.5 m wide (Manning n = 0.025). The bed slope is S = 0.004. Use Manning’s equation in SI units to find the mean velocity V.

b = 5.5 my = 1.3 mn = 0.025S = 0.004
V = m/s
3.Medium
b = 2 my = 2.5 m3 : 1n = 0.014, S = 0.0015

A trapezoidal unfinished concrete channel has a bottom width of 2 m and side slopes of 3:1 (horizontal:vertical). Water flows uniformly 2.5 m deep. Manning n = 0.014 and the bed slope is S = 0.0015. Find the flow rate Q in m³/s.

b = 2 my = 2.5 mz = 3n = 0.014S = 0.0015
Q = m³/s
4.Medium
b = 5 my = 1.7 m3 : 1n = 0.025, S = 0.003

A trapezoidal gravel channel has a bottom width of 5 m and side slopes of 3:1 (horizontal:vertical). Water flows uniformly 1.7 m deep. Manning n = 0.025 and the bed slope is S = 0.003. Find the flow rate Q in m³/s.

b = 5 my = 1.7 mz = 3n = 0.025S = 0.003
Q = m³/s
5.Hard
D = 600 mmn = 0.013, V = 0.9 m/s

A concrete sewer with an inside diameter of 600 mm (Manning n = 0.013) must reach a self-cleansing velocity of 0.9 m/s when flowing just full. Find the minimum slope S (in m/m).

D = 600 mmn = 0.013V = 0.9 m/s
S = m/m
6.Hard
D = 600 mmn = 0.013, V = 0.6 m/s

A concrete sewer with an inside diameter of 600 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 = 600 mmn = 0.013V = 0.6 m/s
S = m/m

Answer key

  1. 1. V = 0.586 m/s
  2. 2. V = 2.328 m/s
  3. 3. Q = 79.6 m³/s
  4. 4. Q = 39.84 m³/s
  5. 5. S = 0.001718 m/m
  6. 6. S = 0.0007634 m/m

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