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 = 3.5 my = 1.5 mn = 0.014

Water flows uniformly 1.5 m deep in a rectangular unfinished concrete channel 3.5 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 = 3.5 my = 1.5 mn = 0.014S = 0.004
V = m/s
2.Easy
b = 4.5 my = 2.1 mn = 0.03

Water flows uniformly 2.1 m deep in a rectangular grass-lined earth channel 4.5 m wide (Manning n = 0.03). The bed slope is S = 0.001. Use Manning’s equation in SI units to find the mean velocity V.

b = 4.5 my = 2.1 mn = 0.03S = 0.001
V = m/s
3.Medium
b = 3 my = 1.5 mn = 0.012, S = 0.001

A rectangular finished concrete channel is 3 m wide. Water flows uniformly 1.5 m deep. Manning n = 0.012 and the bed slope is S = 0.001. Find the flow rate Q in m³/s.

b = 3 my = 1.5 mn = 0.012S = 0.001
Q = m³/s
4.Medium
b = 2.5 my = 0.7 mn = 0.014, S = 0.0008

A rectangular unfinished concrete channel is 2.5 m wide. Water flows uniformly 0.7 m deep. Manning n = 0.014 and the bed slope is S = 0.0008. Find the flow rate Q in m³/s.

b = 2.5 my = 0.7 mn = 0.014S = 0.0008
Q = m³/s
5.Hard
b = 5 my = 0.5 m1 : 1n = 0.03, Q = 2.9 m³/s

A trapezoidal grass-lined earth channel with a bottom width of 5 m and side slopes of 1:1 (horizontal:vertical) must carry 2.9 m³/s in uniform flow at a depth of 0.5 m. Manning n = 0.03. Find the required bed slope S (in m/m).

Q = 2.9 m³/sb = 5 my = 0.5 mz = 1n = 0.03
S = m/m
6.Hard
b = 3.5 my = 2.3 mn = 0.025, Q = 7.2 m³/s

A rectangular gravel channel 3.5 m wide must carry 7.2 m³/s in uniform flow at a depth of 2.3 m. Manning n = 0.025. Find the required bed slope S (in m/m).

Q = 7.2 m³/sb = 3.5 my = 2.3 mn = 0.025
S = m/m

Answer key

  1. 1. V = 3.918 m/s
  2. 2. V = 1.114 m/s
  3. 3. Q = 9.789 m³/s
  4. 4. Q = 2.072 m³/s
  5. 5. S = 0.003096 m/m
  6. 6. S = 0.0005041 m/m

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