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 my = 1.5 mn = 0.012

Water flows uniformly 1.5 m deep in a rectangular finished concrete channel 5 m wide (Manning n = 0.012). The bed drops 0.8 m per kilometre. Use Manning’s equation in SI units to find the mean velocity V.

b = 5 my = 1.5 mn = 0.012drop = 0.8 m/km
V = m/s
2.Easy
b = 6 my = 2.1 mn = 0.015

Water flows uniformly 2.1 m deep in a rectangular brickwork channel 6 m wide (Manning n = 0.015). The bed slope is S = 0.001. Use Manning’s equation in SI units to find the mean velocity V.

b = 6 my = 2.1 mn = 0.015S = 0.001
V = m/s
3.Medium
b = 3.5 my = 0.6 mn = 0.025, S = 0.0005

A rectangular gravel channel is 3.5 m wide. Water flows uniformly 0.6 m deep. Manning n = 0.025 and the bed slope is S = 0.0005. Find the flow rate Q in m³/s.

b = 3.5 my = 0.6 mn = 0.025S = 0.0005
Q = m³/s
4.Medium
b = 1.5 my = 0.7 mn = 0.03, S = 0.001

A rectangular grass-lined earth channel is 1.5 m wide. Water flows uniformly 0.7 m deep. Manning n = 0.03 and the bed slope is S = 0.001. Find the flow rate Q in m³/s.

b = 1.5 my = 0.7 mn = 0.03S = 0.001
Q = m³/s
5.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
6.Hard
b = 5.5 my = 1.4 m2 : 1n = 0.015, Q = 34 m³/s

A trapezoidal brickwork channel with a bottom width of 5.5 m and side slopes of 2:1 (horizontal:vertical) must carry 34 m³/s in uniform flow at a depth of 1.4 m. Manning n = 0.015. Find the required bed slope S (in m/m).

Q = 34 m³/sb = 5.5 my = 1.4 mz = 2n = 0.015
S = m/m

Answer key

  1. 1. V = 2.258 m/s
  2. 2. V = 2.427 m/s
  3. 3. Q = 1.098 m³/s
  4. 4. Q = 0.5622 m³/s
  5. 5. S = 0.001193 m/m
  6. 6. S = 0.001958 m/m

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