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 = 5.5 my = 0.4 mn = 0.014

Water flows uniformly 0.4 m deep in a rectangular unfinished concrete channel 5.5 m wide (Manning n = 0.014). The bed slope is S = 0.002. Use Manning’s equation in SI units to find the mean velocity V.

b = 5.5 my = 0.4 mn = 0.014S = 0.002
V = m/s
2.Easy
b = 5 my = 1.7 mn = 0.03

Water flows uniformly 1.7 m deep in a rectangular grass-lined earth channel 5 m wide (Manning n = 0.03). The bed drops 0.8 m per kilometre. Use Manning’s equation in SI units to find the mean velocity V.

b = 5 my = 1.7 mn = 0.03drop = 0.8 m/km
V = m/s
3.Medium
D = 750 mmn = 0.013, S = 0.0015

A concrete storm sewer with an inside diameter of 750 mm flows half full. Manning n = 0.013 and the slope is S = 0.0015. Find the flow rate Q in m³/s.

D = 750 mmn = 0.013S = 0.0015
Q = m³/s
4.Medium
b = 4 my = 1 mn = 0.03, S = 0.0005

A rectangular grass-lined earth channel is 4 m wide. Water flows uniformly 1 m deep. Manning n = 0.03 and the bed slope is S = 0.0005. Find the flow rate Q in m³/s.

b = 4 my = 1 mn = 0.03S = 0.0005
Q = m³/s
5.Hard
b = 1.5 my = 0.7 m3 : 1n = 0.012, Q = 3.8 m³/s

A trapezoidal finished concrete channel with a bottom width of 1.5 m and side slopes of 3:1 (horizontal:vertical) must carry 3.8 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 = 3.8 m³/sb = 1.5 my = 0.7 mz = 3n = 0.012
S = m/m
6.Hard
b = 5 my = 2.3 mn = 0.03, Q = 14 m³/s

A rectangular grass-lined earth channel 5 m wide must carry 14 m³/s in uniform flow at a depth of 2.3 m. Manning n = 0.03. Find the required bed slope S (in m/m).

Q = 14 m³/sb = 5 my = 2.3 mn = 0.03
S = m/m

Answer key

  1. 1. V = 1.584 m/s
  2. 2. V = 0.9503 m/s
  3. 3. Q = 0.2156 m³/s
  4. 4. Q = 2.275 m³/s
  5. 5. S = 0.001024 m/m
  6. 6. S = 0.001048 m/m

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