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 = 0.8 mn = 0.015

Water flows uniformly 0.8 m deep in a rectangular brickwork channel 6 m wide (Manning n = 0.015). The bed slope is S = 0.0015. Use Manning’s equation in SI units to find the mean velocity V.

b = 6 my = 0.8 mn = 0.015S = 0.0015
V = m/s
2.Easy
b = 6 my = 1.2 mn = 0.012

Water flows uniformly 1.2 m deep in a rectangular finished concrete channel 6 m wide (Manning n = 0.012). The bed slope is S = 0.0015. Use Manning’s equation in SI units to find the mean velocity V.

b = 6 my = 1.2 mn = 0.012S = 0.0015
V = m/s
3.Medium
D = 450 mmn = 0.013, S = 0.0005

A concrete storm sewer with an inside diameter of 450 mm flows just full (as an open channel, not under pressure). Manning n = 0.013 and the slope is S = 0.0005. Find the flow rate Q in m³/s.

D = 450 mmn = 0.013S = 0.0005
Q = m³/s
4.Medium
b = 3.5 my = 2.1 m3 : 1n = 0.014, S = 0.0005

A trapezoidal unfinished concrete channel has a bottom width of 3.5 m and side slopes of 3:1 (horizontal:vertical). Water flows uniformly 2.1 m deep. Manning n = 0.014 and the bed slope is S = 0.0005. Find the flow rate Q in m³/s.

b = 3.5 my = 2.1 mz = 3n = 0.014S = 0.0005
Q = m³/s
5.Hard
D = 300 mmn = 0.013, V = 1.2 m/s

A concrete sewer with an inside diameter of 300 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 = 300 mmn = 0.013V = 1.2 m/s
S = m/m
6.Hard
b = 4 my = 0.9 m1.5 : 1n = 0.014, Q = 17 m³/s

A trapezoidal unfinished concrete channel with a bottom width of 4 m and side slopes of 1.5:1 (horizontal:vertical) must carry 17 m³/s in uniform flow at a depth of 0.9 m. Manning n = 0.014. Find the required bed slope S (in m/m).

Q = 17 m³/sb = 4 my = 0.9 mz = 1.5n = 0.014
S = m/m

Answer key

  1. 1. V = 1.901 m/s
  2. 2. V = 2.912 m/s
  3. 3. Q = 0.06375 m³/s
  4. 4. Q = 37.66 m³/s
  5. 5. S = 0.007694 m/m
  6. 6. S = 0.004213 m/m

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