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 = 1.4 mn = 0.025

Water flows uniformly 1.4 m deep in a rectangular gravel channel 4 m wide (Manning n = 0.025). The bed drops 5 m per kilometre. Use Manning’s equation in SI units to find the mean velocity V.

b = 4 my = 1.4 mn = 0.025drop = 5 m/km
V = m/s
2.Easy
b = 1 my = 2.5 mn = 0.025

Water flows uniformly 2.5 m deep in a rectangular gravel channel 1 m wide (Manning n = 0.025). The bed drops 5 m per kilometre. Use Manning’s equation in SI units to find the mean velocity V.

b = 1 my = 2.5 mn = 0.025drop = 5 m/km
V = m/s
3.Medium
b = 1 my = 2.2 m1.5 : 1n = 0.014, S = 0.0005

A trapezoidal unfinished concrete channel has a bottom width of 1 m and side slopes of 1.5:1 (horizontal:vertical). Water flows uniformly 2.2 m deep. Manning n = 0.014 and the bed slope is S = 0.0005. Find the flow rate Q in m³/s.

b = 1 my = 2.2 mz = 1.5n = 0.014S = 0.0005
Q = m³/s
4.Medium
b = 2 my = 1.4 m1 : 1n = 0.022, S = 0.002

A trapezoidal clean earth channel has a bottom width of 2 m and side slopes of 1:1 (horizontal:vertical). 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 = 2 my = 1.4 mz = 1n = 0.022S = 0.002
Q = m³/s
5.Hard
b = 5.5 my = 0.7 m1.5 : 1n = 0.022, Q = 4.1 m³/s

A trapezoidal clean earth channel with a bottom width of 5.5 m and side slopes of 1.5:1 (horizontal:vertical) must carry 4.1 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 = 4.1 m³/sb = 5.5 my = 0.7 mz = 1.5n = 0.022
S = m/m
6.Hard
b = 4 my = 1.7 m1 : 1n = 0.025, Q = 16 m³/s

A trapezoidal gravel channel with a bottom width of 4 m and side slopes of 1:1 (horizontal:vertical) must carry 16 m³/s in uniform flow at a depth of 1.7 m. Manning n = 0.025. Find the required bed slope S (in m/m).

Q = 16 m³/sb = 4 my = 1.7 mz = 1n = 0.025
S = m/m

Answer key

  1. 1. V = 2.485 m/s
  2. 2. V = 1.578 m/s
  3. 3. Q = 15.7 m³/s
  4. 4. Q = 8.329 m³/s
  5. 5. S = 0.0008162 m/m
  6. 6. S = 0.0015 m/m

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