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 = 1.2 mn = 0.015

Water flows uniformly 1.2 m deep in a rectangular brickwork channel 5 m wide (Manning n = 0.015). The bed slope is S = 0.0008. Use Manning’s equation in SI units to find the mean velocity V.

b = 5 my = 1.2 mn = 0.015S = 0.0008
V = m/s
2.Easy
b = 4.5 my = 2.3 mn = 0.03

Water flows uniformly 2.3 m deep in a rectangular grass-lined earth channel 4.5 m wide (Manning n = 0.03). The bed slope is S = 0.004. Use Manning’s equation in SI units to find the mean velocity V.

b = 4.5 my = 2.3 mn = 0.03S = 0.004
V = m/s
3.Medium
b = 4.5 my = 1.9 m1 : 1n = 0.022, S = 0.0005

A trapezoidal clean earth channel has a bottom width of 4.5 m and side slopes of 1:1 (horizontal:vertical). Water flows uniformly 1.9 m deep. Manning n = 0.022 and the bed slope is S = 0.0005. Find the flow rate Q in m³/s.

b = 4.5 my = 1.9 mz = 1n = 0.022S = 0.0005
Q = m³/s
4.Medium
b = 3 my = 1.3 m3 : 1n = 0.022, S = 0.004

A trapezoidal clean earth channel has a bottom width of 3 m and side slopes of 3:1 (horizontal:vertical). Water flows uniformly 1.3 m deep. Manning n = 0.022 and the bed slope is S = 0.004. Find the flow rate Q in m³/s.

b = 3 my = 1.3 mz = 3n = 0.022S = 0.004
Q = m³/s
5.Hard
b = 1 my = 0.9 mn = 0.014, Q = 0.67 m³/s

A rectangular unfinished concrete channel 1 m wide must carry 0.67 m³/s in uniform flow at a depth of 0.9 m. Manning n = 0.014. Find the required bed slope S (in m/m).

Q = 0.67 m³/sb = 1 my = 0.9 mn = 0.014
S = m/m
6.Hard
b = 5.5 my = 1.4 m3 : 1n = 0.025, Q = 17 m³/s

A trapezoidal gravel channel with a bottom width of 5.5 m and side slopes of 3:1 (horizontal:vertical) must carry 17 m³/s in uniform flow at a depth of 1.4 m. Manning n = 0.025. Find the required bed slope S (in m/m).

Q = 17 m³/sb = 5.5 my = 1.4 mz = 3n = 0.025
S = m/m

Answer key

  1. 1. V = 1.64 m/s
  2. 2. V = 2.297 m/s
  3. 3. Q = 14.2 m³/s
  4. 4. Q = 22.21 m³/s
  5. 5. S = 0.0004933 m/m
  6. 6. S = 0.001055 m/m

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