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 mn = 0.022

Water flows uniformly 2 m deep in a rectangular clean earth channel 5 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 = 5 my = 2 mn = 0.022S = 0.004
V = m/s
2.Easy
b = 2.5 my = 1.6 mn = 0.014

Water flows uniformly 1.6 m deep in a rectangular unfinished concrete channel 2.5 m wide (Manning n = 0.014). The bed slope is S = 0.0005. Use Manning’s equation in SI units to find the mean velocity V.

b = 2.5 my = 1.6 mn = 0.014S = 0.0005
V = m/s
3.Medium
b = 2.5 my = 0.6 m1.5 : 1n = 0.022, S = 0.0005

A trapezoidal clean earth channel has a bottom width of 2.5 m and side slopes of 1.5:1 (horizontal:vertical). Water flows uniformly 0.6 m deep. Manning n = 0.022 and the bed slope is S = 0.0005. Find the flow rate Q in m³/s.

b = 2.5 my = 0.6 mz = 1.5n = 0.022S = 0.0005
Q = m³/s
4.Medium
b = 1 my = 2.1 m1.5 : 1n = 0.014, S = 0.004

A trapezoidal unfinished concrete channel has a bottom width of 1 m and side slopes of 1.5:1 (horizontal:vertical). Water flows uniformly 2.1 m deep. Manning n = 0.014 and the bed slope is S = 0.004. Find the flow rate Q in m³/s.

b = 1 my = 2.1 mz = 1.5n = 0.014S = 0.004
Q = m³/s
5.Hard
b = 4.5 my = 1.5 mn = 0.03, Q = 9.4 m³/s

A rectangular grass-lined earth channel 4.5 m wide must carry 9.4 m³/s in uniform flow at a depth of 1.5 m. Manning n = 0.03. Find the required bed slope S (in m/m).

Q = 9.4 m³/sb = 4.5 my = 1.5 mn = 0.03
S = m/m
6.Hard
D = 200 mmn = 0.013, V = 0.6 m/s

A concrete sewer with an inside diameter of 200 mm (Manning n = 0.013) must reach a self-cleansing velocity of 0.6 m/s when flowing just full. Find the minimum slope S (in m/m).

D = 200 mmn = 0.013V = 0.6 m/s
S = m/m

Answer key

  1. 1. V = 3.084 m/s
  2. 2. V = 1.261 m/s
  3. 3. Q = 1.195 m³/s
  4. 4. Q = 39.81 m³/s
  5. 5. S = 0.002009 m/m
  6. 6. S = 0.003303 m/m

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