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 = 0.012

Water flows uniformly 0.5 m deep in a rectangular finished concrete channel 6 m wide (Manning n = 0.012). 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 = 0.012drop = 5 m/km
V = m/s
2.Easy
b = 1.5 my = 2.3 mn = 0.012

Water flows uniformly 2.3 m deep in a rectangular finished concrete channel 1.5 m wide (Manning n = 0.012). The bed drops 4 m per kilometre. Use Manning’s equation in SI units to find the mean velocity V.

b = 1.5 my = 2.3 mn = 0.012drop = 4 m/km
V = m/s
3.Medium
D = 600 mmn = 0.013, S = 0.003

A concrete storm sewer with an inside diameter of 600 mm flows half full. Manning n = 0.013 and the slope is S = 0.003. Find the flow rate Q in m³/s.

D = 600 mmn = 0.013S = 0.003
Q = m³/s
4.Medium
b = 1 my = 1.2 m2 : 1n = 0.012, S = 0.0005

A trapezoidal finished concrete channel has a bottom width of 1 m and side slopes of 2:1 (horizontal:vertical). Water flows uniformly 1.2 m deep. Manning n = 0.012 and the bed slope is S = 0.0005. Find the flow rate Q in m³/s.

b = 1 my = 1.2 mz = 2n = 0.012S = 0.0005
Q = m³/s
5.Hard
b = 5 my = 2.2 m1.5 : 1n = 0.022, Q = 47 m³/s

A trapezoidal clean earth channel with a bottom width of 5 m and side slopes of 1.5:1 (horizontal:vertical) must carry 47 m³/s in uniform flow at a depth of 2.2 m. Manning n = 0.022. Find the required bed slope S (in m/m).

Q = 47 m³/sb = 5 my = 2.2 mz = 1.5n = 0.022
S = m/m
6.Hard
b = 2.5 my = 1.5 mn = 0.022, Q = 4.2 m³/s

A rectangular clean earth channel 2.5 m wide must carry 4.2 m³/s in uniform flow at a depth of 1.5 m. Manning n = 0.022. Find the required bed slope S (in m/m).

Q = 4.2 m³/sb = 2.5 my = 1.5 mn = 0.022
S = m/m

Answer key

  1. 1. V = 3.35 m/s
  2. 2. V = 3.604 m/s
  3. 3. Q = 0.1682 m³/s
  4. 4. Q = 5.651 m³/s
  5. 5. S = 0.002024 m/m
  6. 6. S = 0.001012 m/m

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