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 = 0.6 mn = 0.03

Water flows uniformly 0.6 m deep in a rectangular grass-lined earth channel 2 m wide (Manning n = 0.03). The bed slope is S = 0.003. Use Manning’s equation in SI units to find the mean velocity V.

b = 2 my = 0.6 mn = 0.03S = 0.003
V = m/s
2.Easy
b = 1 my = 1.8 mn = 0.012

Water flows uniformly 1.8 m deep in a rectangular finished concrete channel 1 m wide (Manning n = 0.012). The bed drops 1 m per kilometre. Use Manning’s equation in SI units to find the mean velocity V.

b = 1 my = 1.8 mn = 0.012drop = 1 m/km
V = m/s
3.Medium
b = 2 my = 1.1 m3 : 1n = 0.025, S = 0.002

A trapezoidal gravel channel has a bottom width of 2 m and side slopes of 3:1 (horizontal:vertical). Water flows uniformly 1.1 m deep. Manning n = 0.025 and the bed slope is S = 0.002. Find the flow rate Q in m³/s.

b = 2 my = 1.1 mz = 3n = 0.025S = 0.002
Q = m³/s
4.Medium
b = 3.5 my = 1.3 m1 : 1n = 0.012, S = 0.001

A trapezoidal finished concrete channel has a bottom width of 3.5 m and side slopes of 1:1 (horizontal:vertical). Water flows uniformly 1.3 m deep. Manning n = 0.012 and the bed slope is S = 0.001. Find the flow rate Q in m³/s.

b = 3.5 my = 1.3 mz = 1n = 0.012S = 0.001
Q = m³/s
5.Hard
b = 5 my = 0.7 mn = 0.022, Q = 4.8 m³/s

A rectangular clean earth channel 5 m wide must carry 4.8 m³/s in uniform flow at a depth of 0.7 m. Manning n = 0.022. Find the required bed slope S (in m/m).

Q = 4.8 m³/sb = 5 my = 0.7 mn = 0.022
S = m/m
6.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

Answer key

  1. 1. V = 0.9494 m/s
  2. 2. V = 1.41 m/s
  3. 3. Q = 7.833 m³/s
  4. 4. Q = 14.98 m³/s
  5. 5. S = 0.002036 m/m
  6. 6. S = 0.003112 m/m

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