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 = 5 my = 0.7 mn = 0.022

Water flows uniformly 0.7 m deep in a rectangular clean earth channel 5 m wide (Manning n = 0.022). The bed slope is S = 0.0008. Use Manning’s equation in SI units to find the mean velocity V.

b = 5 my = 0.7 mn = 0.022S = 0.0008
V = m/s
2.Easy
b = 6 my = 2.3 mn = 0.025

Water flows uniformly 2.3 m deep in a rectangular gravel channel 6 m wide (Manning n = 0.025). The bed slope is S = 0.001. Use Manning’s equation in SI units to find the mean velocity V.

b = 6 my = 2.3 mn = 0.025S = 0.001
V = m/s
3.Medium
D = 1200 mmn = 0.013, S = 0.0008

A concrete storm sewer with an inside diameter of 1200 mm flows half full. Manning n = 0.013 and the slope is S = 0.0008. Find the flow rate Q in m³/s.

D = 1200 mmn = 0.013S = 0.0008
Q = m³/s
4.Medium
b = 3.5 my = 2 m3 : 1n = 0.03, S = 0.004

A trapezoidal grass-lined earth channel has a bottom width of 3.5 m and side slopes of 3:1 (horizontal:vertical). Water flows uniformly 2 m deep. Manning n = 0.03 and the bed slope is S = 0.004. Find the flow rate Q in m³/s.

b = 3.5 my = 2 mz = 3n = 0.03S = 0.004
Q = m³/s
5.Hard
b = 6 my = 0.7 mn = 0.03, Q = 6.1 m³/s

A rectangular grass-lined earth channel 6 m wide must carry 6.1 m³/s in uniform flow at a depth of 0.7 m. Manning n = 0.03. Find the required bed slope S (in m/m).

Q = 6.1 m³/sb = 6 my = 0.7 mn = 0.03
S = m/m
6.Hard
b = 1.5 my = 2.1 mn = 0.012, Q = 11 m³/s

A rectangular finished concrete channel 1.5 m wide must carry 11 m³/s in uniform flow at a depth of 2.1 m. Manning n = 0.012. Find the required bed slope S (in m/m).

Q = 11 m³/sb = 1.5 my = 2.1 mn = 0.012
S = m/m

Answer key

  1. 1. V = 0.8598 m/s
  2. 2. V = 1.508 m/s
  3. 3. Q = 0.5514 m³/s
  4. 4. Q = 44.64 m³/s
  5. 5. S = 0.00404 m/m
  6. 6. S = 0.003872 m/m

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