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 my = 2 mn = 0.03

Water flows uniformly 2 m deep in a rectangular grass-lined earth channel 2 m wide (Manning n = 0.03). The bed slope is S = 0.005. Use Manning’s equation in SI units to find the mean velocity V.

b = 2 my = 2 mn = 0.03S = 0.005
V = m/s
2.Easy
b = 5 my = 2.4 mn = 0.014

Water flows uniformly 2.4 m deep in a rectangular unfinished concrete channel 5 m wide (Manning n = 0.014). The bed drops 3 m per kilometre. Use Manning’s equation in SI units to find the mean velocity V.

b = 5 my = 2.4 mn = 0.014drop = 3 m/km
V = m/s
3.Medium
b = 5 my = 0.7 m1 : 1n = 0.015, S = 0.004

A trapezoidal brickwork channel has a bottom width of 5 m and side slopes of 1:1 (horizontal:vertical). Water flows uniformly 0.7 m deep. Manning n = 0.015 and the bed slope is S = 0.004. Find the flow rate Q in m³/s.

b = 5 my = 0.7 mz = 1n = 0.015S = 0.004
Q = m³/s
4.Medium
b = 6 my = 2.2 m3 : 1n = 0.015, S = 0.0008

A trapezoidal brickwork channel has a bottom width of 6 m and side slopes of 3:1 (horizontal:vertical). Water flows uniformly 2.2 m deep. Manning n = 0.015 and the bed slope is S = 0.0008. Find the flow rate Q in m³/s.

b = 6 my = 2.2 mz = 3n = 0.015S = 0.0008
Q = m³/s
5.Hard
b = 5.5 my = 2.5 m1 : 1n = 0.022, Q = 48 m³/s

A trapezoidal clean earth channel with a bottom width of 5.5 m and side slopes of 1:1 (horizontal:vertical) must carry 48 m³/s in uniform flow at a depth of 2.5 m. Manning n = 0.022. Find the required bed slope S (in m/m).

Q = 48 m³/sb = 5.5 my = 2.5 mz = 1n = 0.022
S = m/m
6.Hard
D = 250 mmn = 0.013, V = 0.75 m/s

A concrete sewer with an inside diameter of 250 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 = 250 mmn = 0.013V = 0.75 m/s
S = m/m

Answer key

  1. 1. V = 1.799 m/s
  2. 2. V = 4.478 m/s
  3. 3. Q = 11.59 m³/s
  4. 4. Q = 65.16 m³/s
  5. 5. S = 0.001501 m/m
  6. 6. S = 0.003833 m/m

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