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 = 2.1 mn = 0.015

Water flows uniformly 2.1 m deep in a rectangular brickwork channel 4 m wide (Manning n = 0.015). The bed slope is S = 0.003. Use Manning’s equation in SI units to find the mean velocity V.

b = 4 my = 2.1 mn = 0.015S = 0.003
V = m/s
2.Easy
b = 2.5 my = 1 mn = 0.03

Water flows uniformly 1 m deep in a rectangular grass-lined earth channel 2.5 m wide (Manning n = 0.03). The bed slope is S = 0.001. Use Manning’s equation in SI units to find the mean velocity V.

b = 2.5 my = 1 mn = 0.03S = 0.001
V = m/s
3.Medium
b = 5.5 my = 0.9 m3 : 1n = 0.022, S = 0.002

A trapezoidal clean earth channel has a bottom width of 5.5 m and side slopes of 3:1 (horizontal:vertical). Water flows uniformly 0.9 m deep. Manning n = 0.022 and the bed slope is S = 0.002. Find the flow rate Q in m³/s.

b = 5.5 my = 0.9 mz = 3n = 0.022S = 0.002
Q = m³/s
4.Medium
b = 3.5 my = 2 m1 : 1n = 0.03, S = 0.0008

A trapezoidal grass-lined earth channel has a bottom width of 3.5 m and side slopes of 1:1 (horizontal:vertical). Water flows uniformly 2 m deep. Manning n = 0.03 and the bed slope is S = 0.0008. Find the flow rate Q in m³/s.

b = 3.5 my = 2 mz = 1n = 0.03S = 0.0008
Q = m³/s
5.Hard
b = 5.5 my = 0.6 mn = 0.014, Q = 4.6 m³/s

A rectangular unfinished concrete channel 5.5 m wide must carry 4.6 m³/s in uniform flow at a depth of 0.6 m. Manning n = 0.014. Find the required bed slope S (in m/m).

Q = 4.6 m³/sb = 5.5 my = 0.6 mn = 0.014
S = m/m
6.Hard
b = 3 my = 1.1 mn = 0.015, Q = 3.6 m³/s

A rectangular brickwork channel 3 m wide must carry 3.6 m³/s in uniform flow at a depth of 1.1 m. Manning n = 0.015. Find the required bed slope S (in m/m).

Q = 3.6 m³/sb = 3 my = 1.1 mn = 0.015
S = m/m

Answer key

  1. 1. V = 3.711 m/s
  2. 2. V = 0.7124 m/s
  3. 3. Q = 11.37 m³/s
  4. 4. Q = 11.72 m³/s
  5. 5. S = 0.0009791 m/m
  6. 6. S = 0.000491 m/m

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