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 = 2.4 mn = 0.025

Water flows uniformly 2.4 m deep in a rectangular gravel channel 2 m wide (Manning n = 0.025). The bed slope is S = 0.002. Use Manning’s equation in SI units to find the mean velocity V.

b = 2 my = 2.4 mn = 0.025S = 0.002
V = m/s
2.Easy
b = 3 my = 0.6 mn = 0.015

Water flows uniformly 0.6 m deep in a rectangular brickwork channel 3 m wide (Manning n = 0.015). The bed drops 2 m per kilometre. Use Manning’s equation in SI units to find the mean velocity V.

b = 3 my = 0.6 mn = 0.015drop = 2 m/km
V = m/s
3.Medium
b = 6 my = 1.1 mn = 0.03, S = 0.0008

A rectangular grass-lined earth channel is 6 m wide. Water flows uniformly 1.1 m deep. Manning n = 0.03 and the bed slope is S = 0.0008. Find the flow rate Q in m³/s.

b = 6 my = 1.1 mn = 0.03S = 0.0008
Q = m³/s
4.Medium
b = 2 my = 1 m2 : 1n = 0.015, S = 0.0015

A trapezoidal brickwork channel has a bottom width of 2 m and side slopes of 2:1 (horizontal:vertical). Water flows uniformly 1 m deep. Manning n = 0.015 and the bed slope is S = 0.0015. Find the flow rate Q in m³/s.

b = 2 my = 1 mz = 2n = 0.015S = 0.0015
Q = m³/s
5.Hard
b = 1 my = 1.2 m1 : 1n = 0.025, Q = 1.7 m³/s

A trapezoidal gravel channel with a bottom width of 1 m and side slopes of 1:1 (horizontal:vertical) must carry 1.7 m³/s in uniform flow at a depth of 1.2 m. Manning n = 0.025. Find the required bed slope S (in m/m).

Q = 1.7 m³/sb = 1 my = 1.2 mz = 1n = 0.025
S = m/m
6.Hard
b = 4 my = 1.6 m1 : 1n = 0.025, Q = 20 m³/s

A trapezoidal gravel channel with a bottom width of 4 m and side slopes of 1:1 (horizontal:vertical) must carry 20 m³/s in uniform flow at a depth of 1.6 m. Manning n = 0.025. Find the required bed slope S (in m/m).

Q = 20 m³/sb = 4 my = 1.6 mz = 1n = 0.025
S = m/m

Answer key

  1. 1. V = 1.418 m/s
  2. 2. V = 1.695 m/s
  3. 3. Q = 5.384 m³/s
  4. 4. Q = 7.494 m³/s
  5. 5. S = 0.0005112 m/m
  6. 6. S = 0.002914 m/m

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