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 = 4.5 my = 1 mn = 0.012

Water flows uniformly 1 m deep in a rectangular finished concrete channel 4.5 m wide (Manning n = 0.012). The bed drops 5 m per kilometre. Use Manning’s equation in SI units to find the mean velocity V.

b = 4.5 my = 1 mn = 0.012drop = 5 m/km
V = m/s
2.Easy
b = 1 my = 1 mn = 0.025

Water flows uniformly 1 m deep in a rectangular gravel channel 1 m wide (Manning n = 0.025). The bed slope is S = 0.005. Use Manning’s equation in SI units to find the mean velocity V.

b = 1 my = 1 mn = 0.025S = 0.005
V = m/s
3.Medium
b = 3 my = 1.3 m2 : 1n = 0.015, S = 0.002

A trapezoidal brickwork channel has a bottom width of 3 m and side slopes of 2:1 (horizontal:vertical). Water flows uniformly 1.3 m deep. Manning n = 0.015 and the bed slope is S = 0.002. Find the flow rate Q in m³/s.

b = 3 my = 1.3 mz = 2n = 0.015S = 0.002
Q = m³/s
4.Medium
b = 4.5 my = 1.8 m2 : 1n = 0.015, S = 0.005

A trapezoidal brickwork channel has a bottom width of 4.5 m and side slopes of 2:1 (horizontal:vertical). Water flows uniformly 1.8 m deep. Manning n = 0.015 and the bed slope is S = 0.005. Find the flow rate Q in m³/s.

b = 4.5 my = 1.8 mz = 2n = 0.015S = 0.005
Q = m³/s
5.Hard
b = 2.5 my = 1.6 m1.5 : 1n = 0.015, Q = 11 m³/s

A trapezoidal brickwork channel with a bottom width of 2.5 m and side slopes of 1.5:1 (horizontal:vertical) must carry 11 m³/s in uniform flow at a depth of 1.6 m. Manning n = 0.015. Find the required bed slope S (in m/m).

Q = 11 m³/sb = 2.5 my = 1.6 mz = 1.5n = 0.015
S = m/m
6.Hard
b = 6 my = 1.8 mn = 0.03, Q = 8.7 m³/s

A rectangular grass-lined earth channel 6 m wide must carry 8.7 m³/s in uniform flow at a depth of 1.8 m. Manning n = 0.03. Find the required bed slope S (in m/m).

Q = 8.7 m³/sb = 6 my = 1.8 mn = 0.03
S = m/m

Answer key

  1. 1. V = 4.611 m/s
  2. 2. V = 1.36 m/s
  3. 3. Q = 19.11 m³/s
  4. 4. Q = 75.96 m³/s
  5. 5. S = 0.0004755 m/m
  6. 6. S = 0.0004991 m/m

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