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 = 1.5 mn = 0.015

Water flows uniformly 1.5 m deep in a rectangular brickwork channel 3 m wide (Manning n = 0.015). The bed drops 1.5 m per kilometre. Use Manning’s equation in SI units to find the mean velocity V.

b = 3 my = 1.5 mn = 0.015drop = 1.5 m/km
V = m/s
2.Easy
b = 5.5 my = 1.5 mn = 0.025

Water flows uniformly 1.5 m deep in a rectangular gravel channel 5.5 m wide (Manning n = 0.025). The bed drops 0.8 m per kilometre. Use Manning’s equation in SI units to find the mean velocity V.

b = 5.5 my = 1.5 mn = 0.025drop = 0.8 m/km
V = m/s
3.Medium
b = 2.5 my = 1.8 m1.5 : 1n = 0.022, S = 0.003

A trapezoidal clean earth channel has a bottom width of 2.5 m and side slopes of 1.5:1 (horizontal:vertical). Water flows uniformly 1.8 m deep. Manning n = 0.022 and the bed slope is S = 0.003. Find the flow rate Q in m³/s.

b = 2.5 my = 1.8 mz = 1.5n = 0.022S = 0.003
Q = m³/s
4.Medium
b = 1.5 my = 1.1 m1.5 : 1n = 0.03, S = 0.0005

A trapezoidal grass-lined earth channel has a bottom width of 1.5 m and side slopes of 1.5:1 (horizontal:vertical). Water flows uniformly 1.1 m deep. Manning n = 0.03 and the bed slope is S = 0.0005. Find the flow rate Q in m³/s.

b = 1.5 my = 1.1 mz = 1.5n = 0.03S = 0.0005
Q = m³/s
5.Hard
b = 4.5 my = 1.9 m3 : 1n = 0.015, Q = 32 m³/s

A trapezoidal brickwork channel with a bottom width of 4.5 m and side slopes of 3:1 (horizontal:vertical) must carry 32 m³/s in uniform flow at a depth of 1.9 m. Manning n = 0.015. Find the required bed slope S (in m/m).

Q = 32 m³/sb = 4.5 my = 1.9 mz = 3n = 0.015
S = m/m
6.Hard
D = 600 mmn = 0.013, V = 0.75 m/s

A concrete sewer with an inside diameter of 600 mm (Manning n = 0.013) must reach a self-cleansing velocity of 0.75 m/s when flowing just full. Find the minimum slope S (in m/m).

D = 600 mmn = 0.013V = 0.75 m/s
S = m/m

Answer key

  1. 1. V = 2.131 m/s
  2. 2. V = 1.109 m/s
  3. 3. Q = 23.94 m³/s
  4. 4. Q = 1.906 m³/s
  5. 5. S = 0.0004957 m/m
  6. 6. S = 0.001193 m/m

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