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 = 2.5 my = 1.6 mn = 0.022

Water flows uniformly 1.6 m deep in a rectangular clean earth channel 2.5 m wide (Manning n = 0.022). The bed slope is S = 0.003. Use Manning’s equation in SI units to find the mean velocity V.

b = 2.5 my = 1.6 mn = 0.022S = 0.003
V = m/s
2.Easy
b = 2 my = 0.9 mn = 0.015

Water flows uniformly 0.9 m deep in a rectangular brickwork channel 2 m wide (Manning n = 0.015). The bed slope is S = 0.0008. Use Manning’s equation in SI units to find the mean velocity V.

b = 2 my = 0.9 mn = 0.015S = 0.0008
V = m/s
3.Medium
b = 1.5 my = 0.5 m3 : 1n = 0.022, S = 0.0015

A trapezoidal clean earth channel has a bottom width of 1.5 m and side slopes of 3:1 (horizontal:vertical). Water flows uniformly 0.5 m deep. Manning n = 0.022 and the bed slope is S = 0.0015. Find the flow rate Q in m³/s.

b = 1.5 my = 0.5 mz = 3n = 0.022S = 0.0015
Q = m³/s
4.Medium
b = 1 my = 1.7 m2 : 1n = 0.015, S = 0.005

A trapezoidal brickwork channel has a bottom width of 1 m and side slopes of 2:1 (horizontal:vertical). Water flows uniformly 1.7 m deep. Manning n = 0.015 and the bed slope is S = 0.005. Find the flow rate Q in m³/s.

b = 1 my = 1.7 mz = 2n = 0.015S = 0.005
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
D = 375 mmn = 0.013, V = 1.2 m/s

A concrete sewer with an inside diameter of 375 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 = 375 mmn = 0.013V = 1.2 m/s
S = m/m

Answer key

  1. 1. V = 1.966 m/s
  2. 2. V = 1.146 m/s
  3. 3. Q = 1.24 m³/s
  4. 4. Q = 32.12 m³/s
  5. 5. S = 0.001718 m/m
  6. 6. S = 0.005714 m/m

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