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 = 1.4 mn = 0.014

Water flows uniformly 1.4 m deep in a rectangular unfinished concrete channel 6 m wide (Manning n = 0.014). The bed slope is S = 0.004. Use Manning’s equation in SI units to find the mean velocity V.

b = 6 my = 1.4 mn = 0.014S = 0.004
V = m/s
2.Easy
b = 4 my = 1.5 mn = 0.014

Water flows uniformly 1.5 m deep in a rectangular unfinished concrete channel 4 m wide (Manning n = 0.014). The bed slope is S = 0.0008. Use Manning’s equation in SI units to find the mean velocity V.

b = 4 my = 1.5 mn = 0.014S = 0.0008
V = m/s
3.Medium
b = 5 my = 0.5 mn = 0.025, S = 0.004

A rectangular gravel channel is 5 m wide. Water flows uniformly 0.5 m deep. Manning n = 0.025 and the bed slope is S = 0.004. Find the flow rate Q in m³/s.

b = 5 my = 0.5 mn = 0.025S = 0.004
Q = m³/s
4.Medium
b = 4 my = 2.3 m3 : 1n = 0.022, S = 0.005

A trapezoidal clean earth channel has a bottom width of 4 m and side slopes of 3:1 (horizontal:vertical). Water flows uniformly 2.3 m deep. Manning n = 0.022 and the bed slope is S = 0.005. Find the flow rate Q in m³/s.

b = 4 my = 2.3 mz = 3n = 0.022S = 0.005
Q = m³/s
5.Hard
D = 450 mmn = 0.013, V = 0.75 m/s

A concrete sewer with an inside diameter of 450 mm (Manning n = 0.013) must reach a self-cleansing velocity of 0.75 m/s when flowing just full. Find the minimum slope S (in m/m).

D = 450 mmn = 0.013V = 0.75 m/s
S = m/m
6.Hard
b = 2 my = 1.6 m1 : 1n = 0.012, Q = 9.9 m³/s

A trapezoidal finished concrete channel with a bottom width of 2 m and side slopes of 1:1 (horizontal:vertical) must carry 9.9 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 = 9.9 m³/sb = 2 my = 1.6 mz = 1n = 0.012
S = m/m

Answer key

  1. 1. V = 4.38 m/s
  2. 2. V = 1.823 m/s
  3. 3. Q = 3.528 m³/s
  4. 4. Q = 98.51 m³/s
  5. 5. S = 0.00175 m/m
  6. 6. S = 0.0005024 m/m

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