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 = 6 my = 2 mn = 0.022

Water flows uniformly 2 m deep in a rectangular clean earth channel 6 m wide (Manning n = 0.022). The bed drops 1.5 m per kilometre. Use Manning’s equation in SI units to find the mean velocity V.

b = 6 my = 2 mn = 0.022drop = 1.5 m/km
V = m/s
2.Easy
b = 3 my = 1.5 mn = 0.025

Water flows uniformly 1.5 m deep in a rectangular gravel channel 3 m wide (Manning n = 0.025). The bed slope is S = 0.004. Use Manning’s equation in SI units to find the mean velocity V.

b = 3 my = 1.5 mn = 0.025S = 0.004
V = m/s
3.Medium
b = 1 my = 2.1 m2 : 1n = 0.014, S = 0.0015

A trapezoidal unfinished concrete channel has a bottom width of 1 m and side slopes of 2:1 (horizontal:vertical). Water flows uniformly 2.1 m deep. Manning n = 0.014 and the bed slope is S = 0.0015. Find the flow rate Q in m³/s.

b = 1 my = 2.1 mz = 2n = 0.014S = 0.0015
Q = m³/s
4.Medium
b = 6 my = 2.2 m3 : 1n = 0.03, S = 0.003

A trapezoidal grass-lined earth channel has a bottom width of 6 m and side slopes of 3:1 (horizontal:vertical). Water flows uniformly 2.2 m deep. Manning n = 0.03 and the bed slope is S = 0.003. Find the flow rate Q in m³/s.

b = 6 my = 2.2 mz = 3n = 0.03S = 0.003
Q = m³/s
5.Hard
b = 4 my = 1.2 m2 : 1n = 0.025, Q = 15 m³/s

A trapezoidal gravel channel with a bottom width of 4 m and side slopes of 2:1 (horizontal:vertical) must carry 15 m³/s in uniform flow at a depth of 1.2 m. Manning n = 0.025. Find the required bed slope S (in m/m).

Q = 15 m³/sb = 4 my = 1.2 mz = 2n = 0.025
S = m/m
6.Hard
b = 5 my = 0.6 m1 : 1n = 0.022, Q = 4.3 m³/s

A trapezoidal clean earth channel with a bottom width of 5 m and side slopes of 1:1 (horizontal:vertical) must carry 4.3 m³/s in uniform flow at a depth of 0.6 m. Manning n = 0.022. Find the required bed slope S (in m/m).

Q = 4.3 m³/sb = 5 my = 0.6 mz = 1n = 0.022
S = m/m

Answer key

  1. 1. V = 1.988 m/s
  2. 2. V = 2.088 m/s
  3. 3. Q = 31.23 m³/s
  4. 4. Q = 63.09 m³/s
  5. 5. S = 0.003107 m/m
  6. 6. S = 0.001988 m/m

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