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 mn = 0.015

Water flows uniformly 1 m deep in a rectangular brickwork channel 3.5 m wide (Manning n = 0.015). The bed slope is S = 0.001. Use Manning’s equation in SI units to find the mean velocity V.

b = 3.5 my = 1 mn = 0.015S = 0.001
V = m/s
2.Easy
b = 5 my = 2.2 mn = 0.025

Water flows uniformly 2.2 m deep in a rectangular gravel channel 5 m wide (Manning n = 0.025). The bed slope is S = 0.002. Use Manning’s equation in SI units to find the mean velocity V.

b = 5 my = 2.2 mn = 0.025S = 0.002
V = m/s
3.Medium
b = 2 my = 1.3 m1.5 : 1n = 0.015, S = 0.004

A trapezoidal brickwork channel has a bottom width of 2 m and side slopes of 1.5:1 (horizontal:vertical). Water flows uniformly 1.3 m deep. Manning n = 0.015 and the bed slope is S = 0.004. Find the flow rate Q in m³/s.

b = 2 my = 1.3 mz = 1.5n = 0.015S = 0.004
Q = m³/s
4.Medium
b = 4.5 my = 2.1 m2 : 1n = 0.015, S = 0.0005

A trapezoidal brickwork channel has a bottom width of 4.5 m and side slopes of 2:1 (horizontal:vertical). Water flows uniformly 2.1 m deep. Manning n = 0.015 and the bed slope is S = 0.0005. Find the flow rate Q in m³/s.

b = 4.5 my = 2.1 mz = 2n = 0.015S = 0.0005
Q = m³/s
5.Hard
D = 200 mmn = 0.013, V = 1 m/s

A concrete sewer with an inside diameter of 200 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 = 200 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 = 1.56 m/s
  2. 2. V = 1.986 m/s
  3. 3. Q = 18.16 m³/s
  4. 4. Q = 32.69 m³/s
  5. 5. S = 0.009175 m/m
  6. 6. S = 0.006814 m/m

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