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 my = 0.8 mn = 0.022

Water flows uniformly 0.8 m deep in a rectangular clean earth channel 3 m wide (Manning n = 0.022). The bed slope is S = 0.0015. Use Manning’s equation in SI units to find the mean velocity V.

b = 3 my = 0.8 mn = 0.022S = 0.0015
V = m/s
2.Easy
b = 4 my = 1.6 mn = 0.03

Water flows uniformly 1.6 m deep in a rectangular grass-lined earth channel 4 m wide (Manning n = 0.03). The bed slope is S = 0.002. Use Manning’s equation in SI units to find the mean velocity V.

b = 4 my = 1.6 mn = 0.03S = 0.002
V = m/s
3.Medium
D = 600 mmn = 0.013, S = 0.005

A concrete storm sewer with an inside diameter of 600 mm flows just full (as an open channel, not under pressure). Manning n = 0.013 and the slope is S = 0.005. Find the flow rate Q in m³/s.

D = 600 mmn = 0.013S = 0.005
Q = m³/s
4.Medium
b = 1 my = 0.5 mn = 0.012, S = 0.0005

A rectangular finished concrete channel is 1 m wide. Water flows uniformly 0.5 m deep. Manning n = 0.012 and the bed slope is S = 0.0005. Find the flow rate Q in m³/s.

b = 1 my = 0.5 mn = 0.012S = 0.0005
Q = m³/s
5.Hard
b = 6 my = 1.8 m2 : 1n = 0.022, Q = 20 m³/s

A trapezoidal clean earth channel with a bottom width of 6 m and side slopes of 2:1 (horizontal:vertical) must carry 20 m³/s in uniform flow at a depth of 1.8 m. Manning n = 0.022. Find the required bed slope S (in m/m).

Q = 20 m³/sb = 6 my = 1.8 mz = 2n = 0.022
S = m/m
6.Hard
D = 600 mmn = 0.013, V = 1 m/s

A concrete sewer with an inside diameter of 600 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 = 600 mmn = 0.013V = 1 m/s
S = m/m

Answer key

  1. 1. V = 1.141 m/s
  2. 2. V = 1.378 m/s
  3. 3. Q = 0.4342 m³/s
  4. 4. Q = 0.3697 m³/s
  5. 5. S = 0.000492 m/m
  6. 6. S = 0.00212 m/m

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