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 = 0.005. Use Manning’s equation in SI units to find the mean velocity V.

b = 5.5 my = 0.4 mn = 0.014S = 0.005
V = m/s
2.Easy
b = 5 my = 1.3 mn = 0.012

Water flows uniformly 1.3 m deep in a rectangular finished concrete channel 5 m wide (Manning n = 0.012). The bed slope is S = 0.002. Use Manning’s equation in SI units to find the mean velocity V.

b = 5 my = 1.3 mn = 0.012S = 0.002
V = m/s
3.Medium
b = 4.5 my = 0.8 m1.5 : 1n = 0.025, S = 0.0008

A trapezoidal gravel channel has a bottom width of 4.5 m and side slopes of 1.5:1 (horizontal:vertical). Water flows uniformly 0.8 m deep. Manning n = 0.025 and the bed slope is S = 0.0008. Find the flow rate Q in m³/s.

b = 4.5 my = 0.8 mz = 1.5n = 0.025S = 0.0008
Q = m³/s
4.Medium
b = 2.5 my = 1.6 mn = 0.014, S = 0.002

A rectangular unfinished concrete channel is 2.5 m wide. Water flows uniformly 1.6 m deep. Manning n = 0.014 and the bed slope is S = 0.002. Find the flow rate Q in m³/s.

b = 2.5 my = 1.6 mn = 0.014S = 0.002
Q = m³/s
5.Hard
b = 1 my = 2.1 m1 : 1n = 0.025, Q = 7.9 m³/s

A trapezoidal gravel channel with a bottom width of 1 m and side slopes of 1:1 (horizontal:vertical) must carry 7.9 m³/s in uniform flow at a depth of 2.1 m. Manning n = 0.025. Find the required bed slope S (in m/m).

Q = 7.9 m³/sb = 1 my = 2.1 mz = 1n = 0.025
S = m/m
6.Hard
b = 1.5 my = 2.4 mn = 0.022, Q = 3.2 m³/s

A rectangular clean earth channel 1.5 m wide must carry 3.2 m³/s in uniform flow at a depth of 2.4 m. Manning n = 0.022. Find the required bed slope S (in m/m).

Q = 3.2 m³/sb = 1.5 my = 2.4 mn = 0.022
S = m/m

Answer key

  1. 1. V = 2.505 m/s
  2. 2. V = 3.358 m/s
  3. 3. Q = 3.741 m³/s
  4. 4. Q = 10.09 m³/s
  5. 5. S = 0.001002 m/m
  6. 6. S = 0.0008065 m/m

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