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 = 2.3 mn = 0.014

Water flows uniformly 2.3 m deep in a rectangular unfinished concrete channel 2 m wide (Manning n = 0.014). The bed slope is S = 0.004. Use Manning’s equation in SI units to find the mean velocity V.

b = 2 my = 2.3 mn = 0.014S = 0.004
V = m/s
2.Easy
b = 1 my = 1.6 mn = 0.015

Water flows uniformly 1.6 m deep in a rectangular brickwork channel 1 m wide (Manning n = 0.015). The bed drops 5 m per kilometre. Use Manning’s equation in SI units to find the mean velocity V.

b = 1 my = 1.6 mn = 0.015drop = 5 m/km
V = m/s
3.Medium
b = 1 my = 0.6 mn = 0.012, S = 0.005

A rectangular finished concrete channel is 1 m wide. Water flows uniformly 0.6 m deep. Manning n = 0.012 and the bed slope is S = 0.005. Find the flow rate Q in m³/s.

b = 1 my = 0.6 mn = 0.012S = 0.005
Q = m³/s
4.Medium
b = 5 my = 1.7 mn = 0.025, S = 0.0008

A rectangular gravel channel is 5 m wide. Water flows uniformly 1.7 m deep. Manning n = 0.025 and the bed slope is S = 0.0008. Find the flow rate Q in m³/s.

b = 5 my = 1.7 mn = 0.025S = 0.0008
Q = m³/s
5.Hard
D = 450 mmn = 0.013, V = 0.75 m/s

A concrete sewer with an inside diameter of 450 mm (Manning n = 0.013) must reach a self-cleansing velocity of 0.75 m/s when flowing just full. Find the minimum slope S (in m/m).

D = 450 mmn = 0.013V = 0.75 m/s
S = m/m
6.Hard
D = 600 mmn = 0.013, V = 1.2 m/s

A concrete sewer with an inside diameter of 600 mm (Manning n = 0.013) must reach a self-cleansing velocity of 1.2 m/s when flowing just full. Find the minimum slope S (in m/m).

D = 600 mmn = 0.013V = 1.2 m/s
S = m/m

Answer key

  1. 1. V = 3.551 m/s
  2. 2. V = 2.477 m/s
  3. 3. Q = 1.487 m³/s
  4. 4. Q = 9.693 m³/s
  5. 5. S = 0.00175 m/m
  6. 6. S = 0.003053 m/m

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