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 = 2.4 mn = 0.022

Water flows uniformly 2.4 m deep in a rectangular clean earth channel 4 m wide (Manning n = 0.022). The bed slope is S = 0.004. Use Manning’s equation in SI units to find the mean velocity V.

b = 4 my = 2.4 mn = 0.022S = 0.004
V = m/s
2.Easy
b = 3 my = 1.7 mn = 0.022

Water flows uniformly 1.7 m deep in a rectangular clean earth channel 3 m wide (Manning n = 0.022). The bed slope is S = 0.005. Use Manning’s equation in SI units to find the mean velocity V.

b = 3 my = 1.7 mn = 0.022S = 0.005
V = m/s
3.Medium
b = 3.5 my = 2.2 m3 : 1n = 0.025, S = 0.0005

A trapezoidal gravel channel has a bottom width of 3.5 m and side slopes of 3:1 (horizontal:vertical). Water flows uniformly 2.2 m deep. Manning n = 0.025 and the bed slope is S = 0.0005. Find the flow rate Q in m³/s.

b = 3.5 my = 2.2 mz = 3n = 0.025S = 0.0005
Q = m³/s
4.Medium
b = 1.5 my = 0.7 m3 : 1n = 0.03, S = 0.003

A trapezoidal grass-lined earth channel has a bottom width of 1.5 m and side slopes of 3:1 (horizontal:vertical). Water flows uniformly 0.7 m deep. Manning n = 0.03 and the bed slope is S = 0.003. Find the flow rate Q in m³/s.

b = 1.5 my = 0.7 mz = 3n = 0.03S = 0.003
Q = m³/s
5.Hard
b = 1 my = 1.5 m1 : 1n = 0.014, Q = 6.1 m³/s

A trapezoidal unfinished concrete channel with a bottom width of 1 m and side slopes of 1:1 (horizontal:vertical) must carry 6.1 m³/s in uniform flow at a depth of 1.5 m. Manning n = 0.014. Find the required bed slope S (in m/m).

Q = 6.1 m³/sb = 1 my = 1.5 mz = 1n = 0.014
S = m/m
6.Hard
b = 2 my = 1 mn = 0.014, Q = 2 m³/s

A rectangular unfinished concrete channel 2 m wide must carry 2 m³/s in uniform flow at a depth of 1 m. Manning n = 0.014. Find the required bed slope S (in m/m).

Q = 2 m³/sb = 2 my = 1 mn = 0.014
S = m/m

Answer key

  1. 1. V = 3.046 m/s
  2. 2. V = 2.763 m/s
  3. 3. Q = 23.38 m³/s
  4. 4. Q = 2.601 m³/s
  5. 5. S = 0.0008107 m/m
  6. 6. S = 0.0004939 m/m

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