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 = 2 my = 0.8 mn = 0.012

Water flows uniformly 0.8 m deep in a rectangular finished concrete channel 2 m wide (Manning n = 0.012). The bed drops 0.5 m per kilometre. Use Manning’s equation in SI units to find the mean velocity V.

b = 2 my = 0.8 mn = 0.012drop = 0.5 m/km
V = m/s
2.Easy
b = 2 my = 2.4 mn = 0.022

Water flows uniformly 2.4 m deep in a rectangular clean earth channel 2 m wide (Manning n = 0.022). The bed drops 4 m per kilometre. Use Manning’s equation in SI units to find the mean velocity V.

b = 2 my = 2.4 mn = 0.022drop = 4 m/km
V = m/s
3.Medium
D = 1200 mmn = 0.013, S = 0.003

A concrete storm sewer with an inside diameter of 1200 mm flows half full. Manning n = 0.013 and the slope is S = 0.003. Find the flow rate Q in m³/s.

D = 1200 mmn = 0.013S = 0.003
Q = m³/s
4.Medium
b = 5.5 my = 2.5 m3 : 1n = 0.03, S = 0.0015

A trapezoidal grass-lined earth channel has a bottom width of 5.5 m and side slopes of 3:1 (horizontal:vertical). Water flows uniformly 2.5 m deep. Manning n = 0.03 and the bed slope is S = 0.0015. Find the flow rate Q in m³/s.

b = 5.5 my = 2.5 mz = 3n = 0.03S = 0.0015
Q = m³/s
5.Hard
D = 450 mmn = 0.013, V = 1 m/s

A concrete sewer with an inside diameter of 450 mm (Manning n = 0.013) must reach a self-cleansing velocity of 1 m/s when flowing just full. Find the minimum slope S (in m/m).

D = 450 mmn = 0.013V = 1 m/s
S = m/m
6.Hard
D = 250 mmn = 0.013, V = 1 m/s

A concrete sewer with an inside diameter of 250 mm (Manning n = 0.013) must reach a self-cleansing velocity of 1 m/s when flowing just full. Find the minimum slope S (in m/m).

D = 250 mmn = 0.013V = 1 m/s
S = m/m

Answer key

  1. 1. V = 1.085 m/s
  2. 2. V = 2.279 m/s
  3. 3. Q = 1.068 m³/s
  4. 4. Q = 55.59 m³/s
  5. 5. S = 0.003112 m/m
  6. 6. S = 0.006814 m/m

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