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 = 0.5 mn = 0.015

Water flows uniformly 0.5 m deep in a rectangular brickwork channel 5 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 = 5 my = 0.5 mn = 0.015drop = 2 m/km
V = m/s
2.Easy
b = 2.5 my = 1.8 mn = 0.03

Water flows uniformly 1.8 m deep in a rectangular grass-lined earth channel 2.5 m wide (Manning n = 0.03). The bed slope is S = 0.0015. Use Manning’s equation in SI units to find the mean velocity V.

b = 2.5 my = 1.8 mn = 0.03S = 0.0015
V = m/s
3.Medium
b = 4 my = 1.2 m2 : 1n = 0.014, S = 0.002

A trapezoidal unfinished concrete channel has a bottom width of 4 m and side slopes of 2:1 (horizontal:vertical). Water flows uniformly 1.2 m deep. Manning n = 0.014 and the bed slope is S = 0.002. Find the flow rate Q in m³/s.

b = 4 my = 1.2 mz = 2n = 0.014S = 0.002
Q = m³/s
4.Medium
b = 2.5 my = 2.3 mn = 0.022, S = 0.0005

A rectangular clean earth channel is 2.5 m wide. Water flows uniformly 2.3 m deep. Manning n = 0.022 and the bed slope is S = 0.0005. Find the flow rate Q in m³/s.

b = 2.5 my = 2.3 mn = 0.022S = 0.0005
Q = m³/s
5.Hard
b = 3 my = 1.2 mn = 0.03, Q = 3.5 m³/s

A rectangular grass-lined earth channel 3 m wide must carry 3.5 m³/s in uniform flow at a depth of 1.2 m. Manning n = 0.03. Find the required bed slope S (in m/m).

Q = 3.5 m³/sb = 3 my = 1.2 mn = 0.03
S = m/m
6.Hard
b = 1.5 my = 0.7 m3 : 1n = 0.022, Q = 3.5 m³/s

A trapezoidal clean earth channel with a bottom width of 1.5 m and side slopes of 3:1 (horizontal:vertical) must carry 3.5 m³/s in uniform flow at a depth of 0.7 m. Manning n = 0.022. Find the required bed slope S (in m/m).

Q = 3.5 m³/sb = 1.5 my = 0.7 mz = 3n = 0.022
S = m/m

Answer key

  1. 1. V = 1.663 m/s
  2. 2. V = 1.054 m/s
  3. 3. Q = 21.49 m³/s
  4. 4. Q = 5.078 m³/s
  5. 5. S = 0.001461 m/m
  6. 6. S = 0.00292 m/m

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