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 my = 1.7 mn = 0.022

Water flows uniformly 1.7 m deep in a rectangular clean earth channel 3 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 = 3 my = 1.7 mn = 0.022drop = 5 m/km
V = m/s
2.Easy
b = 2.5 my = 1.6 mn = 0.012

Water flows uniformly 1.6 m deep in a rectangular finished concrete channel 2.5 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 = 2.5 my = 1.6 mn = 0.012drop = 1.5 m/km
V = m/s
3.Medium
b = 3.5 my = 2.2 mn = 0.014, S = 0.0008

A rectangular unfinished concrete channel is 3.5 m wide. Water flows uniformly 2.2 m deep. Manning n = 0.014 and the bed slope is S = 0.0008. Find the flow rate Q in m³/s.

b = 3.5 my = 2.2 mn = 0.014S = 0.0008
Q = m³/s
4.Medium
b = 3 my = 1.4 m3 : 1n = 0.014, S = 0.002

A trapezoidal unfinished concrete channel has a bottom width of 3 m and side slopes of 3:1 (horizontal:vertical). Water flows uniformly 1.4 m deep. Manning n = 0.014 and the bed slope is S = 0.002. Find the flow rate Q in m³/s.

b = 3 my = 1.4 mz = 3n = 0.014S = 0.002
Q = m³/s
5.Hard
D = 250 mmn = 0.013, V = 0.9 m/s

A concrete sewer with an inside diameter of 250 mm (Manning n = 0.013) must reach a self-cleansing velocity of 0.9 m/s when flowing just full. Find the minimum slope S (in m/m).

D = 250 mmn = 0.013V = 0.9 m/s
S = m/m
6.Hard
b = 1 my = 0.9 m1 : 1n = 0.03, Q = 1.9 m³/s

A trapezoidal grass-lined earth channel with a bottom width of 1 m and side slopes of 1:1 (horizontal:vertical) must carry 1.9 m³/s in uniform flow at a depth of 0.9 m. Manning n = 0.03. Find the required bed slope S (in m/m).

Q = 1.9 m³/sb = 1 my = 0.9 mz = 1n = 0.03
S = m/m

Answer key

  1. 1. V = 2.763 m/s
  2. 2. V = 2.549 m/s
  3. 3. Q = 15.29 m³/s
  4. 4. Q = 28.9 m³/s
  5. 5. S = 0.005519 m/m
  6. 6. S = 0.002938 m/m

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