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 = 6 my = 0.5 mn = 0.015

Water flows uniformly 0.5 m deep in a rectangular brickwork channel 6 m wide (Manning n = 0.015). The bed slope is S = 0.003. Use Manning’s equation in SI units to find the mean velocity V.

b = 6 my = 0.5 mn = 0.015S = 0.003
V = m/s
2.Easy
b = 1 my = 0.9 mn = 0.025

Water flows uniformly 0.9 m deep in a rectangular gravel channel 1 m wide (Manning n = 0.025). The bed slope is S = 0.0015. Use Manning’s equation in SI units to find the mean velocity V.

b = 1 my = 0.9 mn = 0.025S = 0.0015
V = m/s
3.Medium
b = 1 my = 1.6 mn = 0.025, S = 0.002

A rectangular gravel channel is 1 m wide. Water flows uniformly 1.6 m deep. Manning n = 0.025 and the bed slope is S = 0.002. Find the flow rate Q in m³/s.

b = 1 my = 1.6 mn = 0.025S = 0.002
Q = m³/s
4.Medium
b = 2 my = 0.5 mn = 0.03, S = 0.0005

A rectangular grass-lined earth channel is 2 m wide. Water flows uniformly 0.5 m deep. Manning n = 0.03 and the bed slope is S = 0.0005. Find the flow rate Q in m³/s.

b = 2 my = 0.5 mn = 0.03S = 0.0005
Q = m³/s
5.Hard
b = 2.5 my = 1.2 m1 : 1n = 0.022, Q = 11 m³/s

A trapezoidal clean earth channel with a bottom width of 2.5 m and side slopes of 1:1 (horizontal:vertical) must carry 11 m³/s in uniform flow at a depth of 1.2 m. Manning n = 0.022. Find the required bed slope S (in m/m).

Q = 11 m³/sb = 2.5 my = 1.2 mz = 1n = 0.022
S = m/m
6.Hard
D = 375 mmn = 0.013, V = 0.6 m/s

A concrete sewer with an inside diameter of 375 mm (Manning n = 0.013) must reach a self-cleansing velocity of 0.6 m/s when flowing just full. Find the minimum slope S (in m/m).

D = 375 mmn = 0.013V = 0.6 m/s
S = m/m

Answer key

  1. 1. V = 2.076 m/s
  2. 2. V = 0.7269 m/s
  3. 3. Q = 1.504 m³/s
  4. 4. Q = 0.3583 m³/s
  5. 5. S = 0.004334 m/m
  6. 6. S = 0.001429 m/m

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