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 = 2.4 mn = 0.014

Water flows uniformly 2.4 m deep in a rectangular unfinished concrete channel 3 m wide (Manning n = 0.014). The bed drops 1 m per kilometre. Use Manning’s equation in SI units to find the mean velocity V.

b = 3 my = 2.4 mn = 0.014drop = 1 m/km
V = m/s
2.Easy
b = 3.5 my = 1 mn = 0.03

Water flows uniformly 1 m deep in a rectangular grass-lined earth channel 3.5 m wide (Manning n = 0.03). The bed slope is S = 0.0008. Use Manning’s equation in SI units to find the mean velocity V.

b = 3.5 my = 1 mn = 0.03S = 0.0008
V = m/s
3.Medium
b = 4.5 my = 2 m2 : 1n = 0.03, S = 0.002

A trapezoidal grass-lined earth channel has a bottom width of 4.5 m and side slopes of 2:1 (horizontal:vertical). Water flows uniformly 2 m deep. Manning n = 0.03 and the bed slope is S = 0.002. Find the flow rate Q in m³/s.

b = 4.5 my = 2 mz = 2n = 0.03S = 0.002
Q = m³/s
4.Medium
b = 3.5 my = 1.1 m2 : 1n = 0.014, S = 0.001

A trapezoidal unfinished concrete channel has a bottom width of 3.5 m and side slopes of 2:1 (horizontal:vertical). Water flows uniformly 1.1 m deep. Manning n = 0.014 and the bed slope is S = 0.001. Find the flow rate Q in m³/s.

b = 3.5 my = 1.1 mz = 2n = 0.014S = 0.001
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
b = 5.5 my = 1.7 mn = 0.025, Q = 8.6 m³/s

A rectangular gravel channel 5.5 m wide must carry 8.6 m³/s in uniform flow at a depth of 1.7 m. Manning n = 0.025. Find the required bed slope S (in m/m).

Q = 8.6 m³/sb = 5.5 my = 1.7 mn = 0.025
S = m/m

Answer key

  1. 1. V = 2.141 m/s
  2. 2. V = 0.6975 m/s
  3. 3. Q = 29.63 m³/s
  4. 4. Q = 11.64 m³/s
  5. 5. S = 0.001718 m/m
  6. 6. S = 0.0004951 m/m

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