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 = 2.5 my = 2.5 mn = 0.015

Water flows uniformly 2.5 m deep in a rectangular brickwork channel 2.5 m wide (Manning n = 0.015). The bed drops 5 m per kilometre. Use Manning’s equation in SI units to find the mean velocity V.

b = 2.5 my = 2.5 mn = 0.015drop = 5 m/km
V = m/s
2.Easy
b = 2.5 my = 2.4 mn = 0.012

Water flows uniformly 2.4 m deep in a rectangular finished concrete channel 2.5 m wide (Manning n = 0.012). The bed drops 3 m per kilometre. Use Manning’s equation in SI units to find the mean velocity V.

b = 2.5 my = 2.4 mn = 0.012drop = 3 m/km
V = m/s
3.Medium
b = 4 my = 0.7 m1 : 1n = 0.025, S = 0.001

A trapezoidal gravel channel has a bottom width of 4 m and side slopes of 1:1 (horizontal:vertical). Water flows uniformly 0.7 m deep. Manning n = 0.025 and the bed slope is S = 0.001. Find the flow rate Q in m³/s.

b = 4 my = 0.7 mz = 1n = 0.025S = 0.001
Q = m³/s
4.Medium
b = 3 my = 2.5 mn = 0.015, S = 0.005

A rectangular brickwork channel is 3 m wide. Water flows uniformly 2.5 m deep. Manning n = 0.015 and the bed slope is S = 0.005. Find the flow rate Q in m³/s.

b = 3 my = 2.5 mn = 0.015S = 0.005
Q = m³/s
5.Hard
b = 6 my = 0.6 m3 : 1n = 0.03, Q = 2.1 m³/s

A trapezoidal grass-lined earth channel with a bottom width of 6 m and side slopes of 3:1 (horizontal:vertical) must carry 2.1 m³/s in uniform flow at a depth of 0.6 m. Manning n = 0.03. Find the required bed slope S (in m/m).

Q = 2.1 m³/sb = 6 my = 0.6 mz = 3n = 0.03
S = m/m
6.Hard
D = 200 mmn = 0.013, V = 0.6 m/s

A concrete sewer with an inside diameter of 200 mm (Manning n = 0.013) must reach a self-cleansing velocity of 0.6 m/s when flowing just full. Find the minimum slope S (in m/m).

D = 200 mmn = 0.013V = 0.6 m/s
S = m/m

Answer key

  1. 1. V = 4.175 m/s
  2. 2. V = 4.005 m/s
  3. 3. Q = 2.794 m³/s
  4. 4. Q = 33.87 m³/s
  5. 5. S = 0.0004851 m/m
  6. 6. S = 0.003303 m/m

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