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 = 1.2 mn = 0.012

Water flows uniformly 1.2 m deep in a rectangular finished concrete channel 5.5 m wide (Manning n = 0.012). The bed drops 2 m per kilometre. Use Manning’s equation in SI units to find the mean velocity V.

b = 5.5 my = 1.2 mn = 0.012drop = 2 m/km
V = m/s
2.Easy
b = 3.5 my = 1.3 mn = 0.015

Water flows uniformly 1.3 m deep in a rectangular brickwork channel 3.5 m wide (Manning n = 0.015). The bed slope is S = 0.004. Use Manning’s equation in SI units to find the mean velocity V.

b = 3.5 my = 1.3 mn = 0.015S = 0.004
V = m/s
3.Medium
D = 1200 mmn = 0.013, S = 0.0005

A concrete storm sewer with an inside diameter of 1200 mm flows half full. Manning n = 0.013 and the slope is S = 0.0005. Find the flow rate Q in m³/s.

D = 1200 mmn = 0.013S = 0.0005
Q = m³/s
4.Medium
b = 2.5 my = 0.6 mn = 0.015, S = 0.0015

A rectangular brickwork channel is 2.5 m wide. Water flows uniformly 0.6 m deep. Manning n = 0.015 and the bed slope is S = 0.0015. Find the flow rate Q in m³/s.

b = 2.5 my = 0.6 mn = 0.015S = 0.0015
Q = m³/s
5.Hard
b = 4 my = 2.5 mn = 0.012, Q = 20 m³/s

A rectangular finished concrete channel 4 m wide must carry 20 m³/s in uniform flow at a depth of 2.5 m. Manning n = 0.012. Find the required bed slope S (in m/m).

Q = 20 m³/sb = 4 my = 2.5 mn = 0.012
S = m/m
6.Hard
b = 4 my = 1.4 m2 : 1n = 0.014, Q = 18 m³/s

A trapezoidal unfinished concrete channel with a bottom width of 4 m and side slopes of 2:1 (horizontal:vertical) must carry 18 m³/s in uniform flow at a depth of 1.4 m. Manning n = 0.014. Find the required bed slope S (in m/m).

Q = 18 m³/sb = 4 my = 1.4 mz = 2n = 0.014
S = m/m

Answer key

  1. 1. V = 3.306 m/s
  2. 2. V = 3.468 m/s
  3. 3. Q = 0.4359 m³/s
  4. 4. Q = 2.121 m³/s
  5. 5. S = 0.0005005 m/m
  6. 6. S = 0.0007743 m/m

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