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 my = 1.9 mn = 0.015

Water flows uniformly 1.9 m deep in a rectangular brickwork channel 4 m wide (Manning n = 0.015). The bed slope is S = 0.0015. Use Manning’s equation in SI units to find the mean velocity V.

b = 4 my = 1.9 mn = 0.015S = 0.0015
V = m/s
2.Easy
b = 5 my = 1.8 mn = 0.025

Water flows uniformly 1.8 m deep in a rectangular gravel channel 5 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 = 5 my = 1.8 mn = 0.025S = 0.005
V = m/s
3.Medium
b = 4 my = 1.9 m1 : 1n = 0.012, S = 0.001

A trapezoidal finished concrete channel has a bottom width of 4 m and side slopes of 1:1 (horizontal:vertical). Water flows uniformly 1.9 m deep. Manning n = 0.012 and the bed slope is S = 0.001. Find the flow rate Q in m³/s.

b = 4 my = 1.9 mz = 1n = 0.012S = 0.001
Q = m³/s
4.Medium
b = 5.5 my = 0.8 mn = 0.025, S = 0.0005

A rectangular gravel channel is 5.5 m wide. Water flows uniformly 0.8 m deep. Manning n = 0.025 and the bed slope is S = 0.0005. Find the flow rate Q in m³/s.

b = 5.5 my = 0.8 mn = 0.025S = 0.0005
Q = m³/s
5.Hard
b = 2.5 my = 1.9 mn = 0.03, Q = 3.7 m³/s

A rectangular grass-lined earth channel 2.5 m wide must carry 3.7 m³/s in uniform flow at a depth of 1.9 m. Manning n = 0.03. Find the required bed slope S (in m/m).

Q = 3.7 m³/sb = 2.5 my = 1.9 mn = 0.03
S = m/m
6.Hard
b = 4 my = 0.6 m1.5 : 1n = 0.012, Q = 4.7 m³/s

A trapezoidal finished concrete channel with a bottom width of 4 m and side slopes of 1.5:1 (horizontal:vertical) must carry 4.7 m³/s in uniform flow at a depth of 0.6 m. Manning n = 0.012. Find the required bed slope S (in m/m).

Q = 4.7 m³/sb = 4 my = 0.6 mz = 1.5n = 0.012
S = m/m

Answer key

  1. 1. V = 2.538 m/s
  2. 2. V = 2.915 m/s
  3. 3. Q = 33.28 m³/s
  4. 4. Q = 2.861 m³/s
  5. 5. S = 0.0007958 m/m
  6. 6. S = 0.0009874 m/m

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