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 = 3.5 my = 1.2 mn = 0.03

Water flows uniformly 1.2 m deep in a rectangular grass-lined earth channel 3.5 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 = 3.5 my = 1.2 mn = 0.03S = 0.001
V = m/s
2.Easy
b = 3.5 my = 1.5 mn = 0.022

Water flows uniformly 1.5 m deep in a rectangular clean earth channel 3.5 m wide (Manning n = 0.022). The bed drops 0.8 m per kilometre. Use Manning’s equation in SI units to find the mean velocity V.

b = 3.5 my = 1.5 mn = 0.022drop = 0.8 m/km
V = m/s
3.Medium
b = 6 my = 1.4 mn = 0.022, S = 0.002

A rectangular clean earth channel is 6 m wide. Water flows uniformly 1.4 m deep. Manning n = 0.022 and the bed slope is S = 0.002. Find the flow rate Q in m³/s.

b = 6 my = 1.4 mn = 0.022S = 0.002
Q = m³/s
4.Medium
b = 1 my = 0.6 m1 : 1n = 0.022, S = 0.005

A trapezoidal clean earth channel has a bottom width of 1 m and side slopes of 1:1 (horizontal:vertical). Water flows uniformly 0.6 m deep. Manning n = 0.022 and the bed slope is S = 0.005. Find the flow rate Q in m³/s.

b = 1 my = 0.6 mz = 1n = 0.022S = 0.005
Q = m³/s
5.Hard
b = 1.5 my = 2.5 m1.5 : 1n = 0.022, Q = 27 m³/s

A trapezoidal clean earth channel with a bottom width of 1.5 m and side slopes of 1.5:1 (horizontal:vertical) must carry 27 m³/s in uniform flow at a depth of 2.5 m. Manning n = 0.022. Find the required bed slope S (in m/m).

Q = 27 m³/sb = 1.5 my = 2.5 mz = 1.5n = 0.022
S = m/m
6.Hard
b = 1 my = 0.9 mn = 0.025, Q = 0.38 m³/s

A rectangular gravel channel 1 m wide must carry 0.38 m³/s in uniform flow at a depth of 0.9 m. Manning n = 0.025. Find the required bed slope S (in m/m).

Q = 0.38 m³/sb = 1 my = 0.9 mn = 0.025
S = m/m

Answer key

  1. 1. V = 0.8404 m/s
  2. 2. V = 1.115 m/s
  3. 3. Q = 16.55 m³/s
  4. 4. Q = 1.55 m³/s
  5. 5. S = 0.001524 m/m
  6. 6. S = 0.000506 m/m

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