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 my = 1.3 mn = 0.012

Water flows uniformly 1.3 m deep in a rectangular finished concrete channel 4 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 = 4 my = 1.3 mn = 0.012S = 0.005
V = m/s
2.Easy
b = 1.5 my = 2.5 mn = 0.025

Water flows uniformly 2.5 m deep in a rectangular gravel channel 1.5 m wide (Manning n = 0.025). The bed slope is S = 0.004. Use Manning’s equation in SI units to find the mean velocity V.

b = 1.5 my = 2.5 mn = 0.025S = 0.004
V = m/s
3.Medium
D = 300 mmn = 0.013, S = 0.0015

A concrete storm sewer with an inside diameter of 300 mm flows half full. Manning n = 0.013 and the slope is S = 0.0015. Find the flow rate Q in m³/s.

D = 300 mmn = 0.013S = 0.0015
Q = m³/s
4.Medium
b = 3.5 my = 1.7 mn = 0.014, S = 0.0008

A rectangular unfinished concrete channel is 3.5 m wide. Water flows uniformly 1.7 m deep. Manning n = 0.014 and the bed slope is S = 0.0008. Find the flow rate Q in m³/s.

b = 3.5 my = 1.7 mn = 0.014S = 0.0008
Q = m³/s
5.Hard
b = 1.5 my = 2.1 mn = 0.012, Q = 9.7 m³/s

A rectangular finished concrete channel 1.5 m wide must carry 9.7 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 = 9.7 m³/sb = 1.5 my = 2.1 mn = 0.012
S = m/m
6.Hard
b = 2 my = 1.8 mn = 0.014, Q = 14 m³/s

A rectangular unfinished concrete channel 2 m wide must carry 14 m³/s in uniform flow at a depth of 1.8 m. Manning n = 0.014. Find the required bed slope S (in m/m).

Q = 14 m³/sb = 2 my = 1.8 mn = 0.014
S = m/m

Answer key

  1. 1. V = 5.027 m/s
  2. 2. V = 1.753 m/s
  3. 3. Q = 0.01873 m³/s
  4. 4. Q = 10.89 m³/s
  5. 5. S = 0.003011 m/m
  6. 6. S = 0.005343 m/m

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