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 = 2 my = 1.6 mn = 0.022

Water flows uniformly 1.6 m deep in a rectangular clean earth channel 2 m wide (Manning n = 0.022). The bed slope is S = 0.0008. Use Manning’s equation in SI units to find the mean velocity V.

b = 2 my = 1.6 mn = 0.022S = 0.0008
V = m/s
2.Easy
b = 2.5 my = 2.4 mn = 0.014

Water flows uniformly 2.4 m deep in a rectangular unfinished concrete channel 2.5 m wide (Manning n = 0.014). The bed slope is S = 0.0015. Use Manning’s equation in SI units to find the mean velocity V.

b = 2.5 my = 2.4 mn = 0.014S = 0.0015
V = m/s
3.Medium
b = 2.5 my = 1.8 m1.5 : 1n = 0.03, S = 0.002

A trapezoidal grass-lined earth channel has a bottom width of 2.5 m and side slopes of 1.5:1 (horizontal:vertical). Water flows uniformly 1.8 m deep. Manning n = 0.03 and the bed slope is S = 0.002. Find the flow rate Q in m³/s.

b = 2.5 my = 1.8 mz = 1.5n = 0.03S = 0.002
Q = m³/s
4.Medium
b = 5.5 my = 0.5 mn = 0.025, S = 0.0008

A rectangular gravel channel is 5.5 m wide. Water flows uniformly 0.5 m deep. Manning n = 0.025 and the bed slope is S = 0.0008. Find the flow rate Q in m³/s.

b = 5.5 my = 0.5 mn = 0.025S = 0.0008
Q = m³/s
5.Hard
b = 3.5 my = 1.6 m2 : 1n = 0.012, Q = 20 m³/s

A trapezoidal finished concrete channel with a bottom width of 3.5 m and side slopes of 2:1 (horizontal:vertical) must carry 20 m³/s in uniform flow at a depth of 1.6 m. Manning n = 0.012. Find the required bed slope S (in m/m).

Q = 20 m³/sb = 3.5 my = 1.6 mz = 2n = 0.012
S = m/m
6.Hard
b = 1 my = 2.3 mn = 0.012, Q = 3 m³/s

A rectangular finished concrete channel 1 m wide must carry 3 m³/s in uniform flow at a depth of 2.3 m. Manning n = 0.012. Find the required bed slope S (in m/m).

Q = 3 m³/sb = 1 my = 2.3 mn = 0.012
S = m/m

Answer key

  1. 1. V = 0.9302 m/s
  2. 2. V = 2.427 m/s
  3. 3. Q = 14.33 m³/s
  4. 4. Q = 1.753 m³/s
  5. 5. S = 0.0004972 m/m
  6. 6. S = 0.0008025 m/m

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