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 = 4.5 my = 0.5 mn = 0.022

Water flows uniformly 0.5 m deep in a rectangular clean earth channel 4.5 m wide (Manning n = 0.022). The bed slope is S = 0.0005. Use Manning’s equation in SI units to find the mean velocity V.

b = 4.5 my = 0.5 mn = 0.022S = 0.0005
V = m/s
2.Easy
b = 3 my = 0.9 mn = 0.025

Water flows uniformly 0.9 m deep in a rectangular gravel channel 3 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 = 3 my = 0.9 mn = 0.025S = 0.0015
V = m/s
3.Medium
D = 750 mmn = 0.013, S = 0.002

A concrete storm sewer with an inside diameter of 750 mm flows half full. Manning n = 0.013 and the slope is S = 0.002. Find the flow rate Q in m³/s.

D = 750 mmn = 0.013S = 0.002
Q = m³/s
4.Medium
b = 1.5 my = 1.1 m3 : 1n = 0.025, S = 0.004

A trapezoidal gravel channel has a bottom width of 1.5 m and side slopes of 3:1 (horizontal:vertical). Water flows uniformly 1.1 m deep. Manning n = 0.025 and the bed slope is S = 0.004. Find the flow rate Q in m³/s.

b = 1.5 my = 1.1 mz = 3n = 0.025S = 0.004
Q = m³/s
5.Hard
b = 2 my = 1.9 m2 : 1n = 0.03, Q = 12 m³/s

A trapezoidal grass-lined earth channel with a bottom width of 2 m and side slopes of 2:1 (horizontal:vertical) must carry 12 m³/s in uniform flow at a depth of 1.9 m. Manning n = 0.03. Find the required bed slope S (in m/m).

Q = 12 m³/sb = 2 my = 1.9 mz = 2n = 0.03
S = m/m
6.Hard
b = 5.5 my = 2.1 m3 : 1n = 0.03, Q = 38 m³/s

A trapezoidal grass-lined earth channel with a bottom width of 5.5 m and side slopes of 3:1 (horizontal:vertical) must carry 38 m³/s in uniform flow at a depth of 2.1 m. Manning n = 0.03. Find the required bed slope S (in m/m).

Q = 38 m³/sb = 5.5 my = 2.1 mz = 3n = 0.03
S = m/m

Answer key

  1. 1. V = 0.5601 m/s
  2. 2. V = 1.056 m/s
  3. 3. Q = 0.2489 m³/s
  4. 4. Q = 9.757 m³/s
  5. 5. S = 0.001 m/m
  6. 6. S = 0.001463 m/m

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