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 = 3.5 my = 1.8 mn = 0.025

Water flows uniformly 1.8 m deep in a rectangular gravel channel 3.5 m wide (Manning n = 0.025). The bed slope is S = 0.0005. Use Manning’s equation in SI units to find the mean velocity V.

b = 3.5 my = 1.8 mn = 0.025S = 0.0005
V = m/s
2.Easy
b = 5 my = 0.8 mn = 0.012

Water flows uniformly 0.8 m deep in a rectangular finished concrete channel 5 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 = 5 my = 0.8 mn = 0.012drop = 0.5 m/km
V = m/s
3.Medium
b = 1.5 my = 1.8 m3 : 1n = 0.014, S = 0.003

A trapezoidal unfinished concrete channel has a bottom width of 1.5 m and side slopes of 3:1 (horizontal:vertical). Water flows uniformly 1.8 m deep. Manning n = 0.014 and the bed slope is S = 0.003. Find the flow rate Q in m³/s.

b = 1.5 my = 1.8 mz = 3n = 0.014S = 0.003
Q = m³/s
4.Medium
b = 5 my = 0.9 m1 : 1n = 0.022, S = 0.002

A trapezoidal clean earth channel has a bottom width of 5 m and side slopes of 1:1 (horizontal:vertical). Water flows uniformly 0.9 m deep. Manning n = 0.022 and the bed slope is S = 0.002. Find the flow rate Q in m³/s.

b = 5 my = 0.9 mz = 1n = 0.022S = 0.002
Q = m³/s
5.Hard
D = 300 mmn = 0.013, V = 1 m/s

A concrete sewer with an inside diameter of 300 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 = 300 mmn = 0.013V = 1 m/s
S = m/m
6.Hard
D = 375 mmn = 0.013, V = 0.9 m/s

A concrete sewer with an inside diameter of 375 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 = 375 mmn = 0.013V = 0.9 m/s
S = m/m

Answer key

  1. 1. V = 0.8259 m/s
  2. 2. V = 1.334 m/s
  3. 3. Q = 47.42 m³/s
  4. 4. Q = 8.54 m³/s
  5. 5. S = 0.005343 m/m
  6. 6. S = 0.003214 m/m

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