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 = 6 my = 0.5 mn = 0.022

Water flows uniformly 0.5 m deep in a rectangular clean earth channel 6 m wide (Manning n = 0.022). The bed drops 5 m per kilometre. Use Manning’s equation in SI units to find the mean velocity V.

b = 6 my = 0.5 mn = 0.022drop = 5 m/km
V = m/s
2.Easy
b = 1.5 my = 2.2 mn = 0.014

Water flows uniformly 2.2 m deep in a rectangular unfinished concrete channel 1.5 m wide (Manning n = 0.014). The bed slope is S = 0.0015. Use Manning’s equation in SI units to find the mean velocity V.

b = 1.5 my = 2.2 mn = 0.014S = 0.0015
V = m/s
3.Medium
b = 4.5 my = 1.7 m3 : 1n = 0.022, S = 0.005

A trapezoidal clean earth channel has a bottom width of 4.5 m and side slopes of 3:1 (horizontal:vertical). Water flows uniformly 1.7 m deep. Manning n = 0.022 and the bed slope is S = 0.005. Find the flow rate Q in m³/s.

b = 4.5 my = 1.7 mz = 3n = 0.022S = 0.005
Q = m³/s
4.Medium
b = 3 my = 2.1 m2 : 1n = 0.03, S = 0.003

A trapezoidal grass-lined earth channel has a bottom width of 3 m and side slopes of 2:1 (horizontal:vertical). Water flows uniformly 2.1 m deep. Manning n = 0.03 and the bed slope is S = 0.003. Find the flow rate Q in m³/s.

b = 3 my = 2.1 mz = 2n = 0.03S = 0.003
Q = m³/s
5.Hard
D = 300 mmn = 0.013, V = 1 m/s

A concrete sewer with an inside diameter of 300 mm (Manning n = 0.013) must reach a self-cleansing velocity of 1 m/s when flowing just full. Find the minimum slope S (in m/m).

D = 300 mmn = 0.013V = 1 m/s
S = m/m
6.Hard
b = 3.5 my = 2.5 mn = 0.03, Q = 8.4 m³/s

A rectangular grass-lined earth channel 3.5 m wide must carry 8.4 m³/s in uniform flow at a depth of 2.5 m. Manning n = 0.03. Find the required bed slope S (in m/m).

Q = 8.4 m³/sb = 3.5 my = 2.5 mn = 0.03
S = m/m

Answer key

  1. 1. V = 1.827 m/s
  2. 2. V = 1.878 m/s
  3. 3. Q = 54.88 m³/s
  4. 4. Q = 31.52 m³/s
  5. 5. S = 0.005343 m/m
  6. 6. S = 0.000798 m/m

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