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 = 2.5 my = 1.1 mn = 0.014

Water flows uniformly 1.1 m deep in a rectangular unfinished concrete channel 2.5 m wide (Manning n = 0.014). The bed slope is S = 0.004. Use Manning’s equation in SI units to find the mean velocity V.

b = 2.5 my = 1.1 mn = 0.014S = 0.004
V = m/s
2.Easy
b = 2.5 my = 1.5 mn = 0.012

Water flows uniformly 1.5 m deep in a rectangular finished concrete channel 2.5 m wide (Manning n = 0.012). The bed slope is S = 0.005. Use Manning’s equation in SI units to find the mean velocity V.

b = 2.5 my = 1.5 mn = 0.012S = 0.005
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 just full (as an open channel, not under pressure). 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 = 0.6 mn = 0.012, S = 0.0015

A rectangular finished concrete channel is 3.5 m wide. Water flows uniformly 0.6 m deep. Manning n = 0.012 and the bed slope is S = 0.0015. Find the flow rate Q in m³/s.

b = 3.5 my = 0.6 mn = 0.012S = 0.0015
Q = m³/s
5.Hard
b = 4 my = 0.7 m1.5 : 1n = 0.012, Q = 11 m³/s

A trapezoidal finished concrete channel with a bottom width of 4 m and side slopes of 1.5:1 (horizontal:vertical) must carry 11 m³/s in uniform flow at a depth of 0.7 m. Manning n = 0.012. Find the required bed slope S (in m/m).

Q = 11 m³/sb = 4 my = 0.7 mz = 1.5n = 0.012
S = m/m
6.Hard
b = 4 my = 1.9 mn = 0.03, Q = 7 m³/s

A rectangular grass-lined earth channel 4 m wide must carry 7 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 = 7 m³/sb = 4 my = 1.9 mn = 0.03
S = m/m

Answer key

  1. 1. V = 3.16 m/s
  2. 2. V = 4.565 m/s
  3. 3. Q = 1.103 m³/s
  4. 4. Q = 3.961 m³/s
  5. 5. S = 0.003156 m/m
  6. 6. S = 0.0007904 m/m

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