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 = 2.2 mn = 0.012

Water flows uniformly 2.2 m deep in a rectangular finished concrete channel 3.5 m wide (Manning n = 0.012). The bed slope is S = 0.001. Use Manning’s equation in SI units to find the mean velocity V.

b = 3.5 my = 2.2 mn = 0.012S = 0.001
V = m/s
2.Easy
b = 1.5 my = 0.6 mn = 0.015

Water flows uniformly 0.6 m deep in a rectangular brickwork channel 1.5 m wide (Manning n = 0.015). The bed slope is S = 0.0008. Use Manning’s equation in SI units to find the mean velocity V.

b = 1.5 my = 0.6 mn = 0.015S = 0.0008
V = m/s
3.Medium
b = 2 my = 2.5 m3 : 1n = 0.014, S = 0.0015

A trapezoidal unfinished concrete channel has a bottom width of 2 m and side slopes of 3:1 (horizontal:vertical). Water flows uniformly 2.5 m deep. Manning n = 0.014 and the bed slope is S = 0.0015. Find the flow rate Q in m³/s.

b = 2 my = 2.5 mz = 3n = 0.014S = 0.0015
Q = m³/s
4.Medium
b = 3.5 my = 0.5 m2 : 1n = 0.014, S = 0.0015

A trapezoidal unfinished concrete channel has a bottom width of 3.5 m and side slopes of 2:1 (horizontal:vertical). Water flows uniformly 0.5 m deep. Manning n = 0.014 and the bed slope is S = 0.0015. Find the flow rate Q in m³/s.

b = 3.5 my = 0.5 mz = 2n = 0.014S = 0.0015
Q = m³/s
5.Hard
b = 3.5 my = 2.2 m2 : 1n = 0.03, Q = 44 m³/s

A trapezoidal grass-lined earth channel with a bottom width of 3.5 m and side slopes of 2:1 (horizontal:vertical) must carry 44 m³/s in uniform flow at a depth of 2.2 m. Manning n = 0.03. Find the required bed slope S (in m/m).

Q = 44 m³/sb = 3.5 my = 2.2 mz = 2n = 0.03
S = m/m
6.Hard
D = 450 mmn = 0.013, V = 0.9 m/s

A concrete sewer with an inside diameter of 450 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 = 450 mmn = 0.013V = 0.9 m/s
S = m/m

Answer key

  1. 1. V = 2.591 m/s
  2. 2. V = 0.9065 m/s
  3. 3. Q = 79.6 m³/s
  4. 4. Q = 3.335 m³/s
  5. 5. S = 0.004053 m/m
  6. 6. S = 0.002521 m/m

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