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 = 2.1 mn = 0.014

Water flows uniformly 2.1 m deep in a rectangular unfinished concrete channel 5 m wide (Manning n = 0.014). The bed slope is S = 0.005. Use Manning’s equation in SI units to find the mean velocity V.

b = 5 my = 2.1 mn = 0.014S = 0.005
V = m/s
2.Easy
b = 3.5 my = 2.5 mn = 0.022

Water flows uniformly 2.5 m deep in a rectangular clean earth channel 3.5 m wide (Manning n = 0.022). The bed drops 5 m per kilometre. Use Manning’s equation in SI units to find the mean velocity V.

b = 3.5 my = 2.5 mn = 0.022drop = 5 m/km
V = m/s
3.Medium
b = 5.5 my = 2.5 m3 : 1n = 0.025, S = 0.001

A trapezoidal gravel channel has a bottom width of 5.5 m and side slopes of 3:1 (horizontal:vertical). Water flows uniformly 2.5 m deep. Manning n = 0.025 and the bed slope is S = 0.001. Find the flow rate Q in m³/s.

b = 5.5 my = 2.5 mz = 3n = 0.025S = 0.001
Q = m³/s
4.Medium
b = 2 my = 1.7 m3 : 1n = 0.025, S = 0.005

A trapezoidal gravel channel has a bottom width of 2 m and side slopes of 3:1 (horizontal:vertical). Water flows uniformly 1.7 m deep. Manning n = 0.025 and the bed slope is S = 0.005. Find the flow rate Q in m³/s.

b = 2 my = 1.7 mz = 3n = 0.025S = 0.005
Q = m³/s
5.Hard
b = 6 my = 2.4 mn = 0.022, Q = 50 m³/s

A rectangular clean earth channel 6 m wide must carry 50 m³/s in uniform flow at a depth of 2.4 m. Manning n = 0.022. Find the required bed slope S (in m/m).

Q = 50 m³/sb = 6 my = 2.4 mn = 0.022
S = m/m
6.Hard
b = 5 my = 2.2 m1.5 : 1n = 0.012, Q = 61 m³/s

A trapezoidal finished concrete channel with a bottom width of 5 m and side slopes of 1.5:1 (horizontal:vertical) must carry 61 m³/s in uniform flow at a depth of 2.2 m. Manning n = 0.012. Find the required bed slope S (in m/m).

Q = 61 m³/sb = 5 my = 2.2 mz = 1.5n = 0.012
S = m/m

Answer key

  1. 1. V = 5.516 m/s
  2. 2. V = 3.277 m/s
  3. 3. Q = 54.47 m³/s
  4. 4. Q = 32.91 m³/s
  5. 5. S = 0.003976 m/m
  6. 6. S = 0.001014 m/m

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