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 = 0.4 mn = 0.012

Water flows uniformly 0.4 m deep in a rectangular finished concrete channel 3.5 m wide (Manning n = 0.012). The bed drops 1.5 m per kilometre. Use Manning’s equation in SI units to find the mean velocity V.

b = 3.5 my = 0.4 mn = 0.012drop = 1.5 m/km
V = m/s
2.Easy
b = 3.5 my = 1.1 mn = 0.015

Water flows uniformly 1.1 m deep in a rectangular brickwork channel 3.5 m wide (Manning n = 0.015). The bed slope is S = 0.002. Use Manning’s equation in SI units to find the mean velocity V.

b = 3.5 my = 1.1 mn = 0.015S = 0.002
V = m/s
3.Medium
b = 5 my = 2.1 m1.5 : 1n = 0.012, S = 0.001

A trapezoidal finished concrete channel has a bottom width of 5 m and side slopes of 1.5:1 (horizontal:vertical). Water flows uniformly 2.1 m deep. Manning n = 0.012 and the bed slope is S = 0.001. Find the flow rate Q in m³/s.

b = 5 my = 2.1 mz = 1.5n = 0.012S = 0.001
Q = m³/s
4.Medium
D = 900 mmn = 0.013, S = 0.0015

A concrete storm sewer with an inside diameter of 900 mm flows just full (as an open channel, not under pressure). Manning n = 0.013 and the slope is S = 0.0015. Find the flow rate Q in m³/s.

D = 900 mmn = 0.013S = 0.0015
Q = m³/s
5.Hard
b = 3.5 my = 0.5 m2 : 1n = 0.022, Q = 3 m³/s

A trapezoidal clean earth channel with a bottom width of 3.5 m and side slopes of 2:1 (horizontal:vertical) must carry 3 m³/s in uniform flow at a depth of 0.5 m. Manning n = 0.022. Find the required bed slope S (in m/m).

Q = 3 m³/sb = 3.5 my = 0.5 mz = 2n = 0.022
S = m/m
6.Hard
b = 2 my = 0.6 mn = 0.014, Q = 1 m³/s

A rectangular unfinished concrete channel 2 m wide must carry 1 m³/s in uniform flow at a depth of 0.6 m. Manning n = 0.014. Find the required bed slope S (in m/m).

Q = 1 m³/sb = 2 my = 0.6 mn = 0.014
S = m/m

Answer key

  1. 1. V = 1.527 m/s
  2. 2. V = 2.295 m/s
  3. 3. Q = 55.4 m³/s
  4. 4. Q = 0.7011 m³/s
  5. 5. S = 0.002997 m/m
  6. 6. S = 0.0005033 m/m

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