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 = 5.5 my = 2.2 mn = 0.03

Water flows uniformly 2.2 m deep in a rectangular grass-lined earth channel 5.5 m wide (Manning n = 0.03). The bed slope is S = 0.001. Use Manning’s equation in SI units to find the mean velocity V.

b = 5.5 my = 2.2 mn = 0.03S = 0.001
V = m/s
2.Easy
b = 1.5 my = 1.6 mn = 0.014

Water flows uniformly 1.6 m deep in a rectangular unfinished concrete channel 1.5 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 = 1.5 my = 1.6 mn = 0.014S = 0.0008
V = m/s
3.Medium
b = 1.5 my = 0.7 m2 : 1n = 0.025, S = 0.001

A trapezoidal gravel channel has a bottom width of 1.5 m and side slopes of 2:1 (horizontal:vertical). Water flows uniformly 0.7 m deep. Manning n = 0.025 and the bed slope is S = 0.001. Find the flow rate Q in m³/s.

b = 1.5 my = 0.7 mz = 2n = 0.025S = 0.001
Q = m³/s
4.Medium
b = 3 my = 0.9 m1 : 1n = 0.014, S = 0.004

A trapezoidal unfinished concrete channel has a bottom width of 3 m and side slopes of 1:1 (horizontal:vertical). Water flows uniformly 0.9 m deep. Manning n = 0.014 and the bed slope is S = 0.004. Find the flow rate Q in m³/s.

b = 3 my = 0.9 mz = 1n = 0.014S = 0.004
Q = m³/s
5.Hard
D = 200 mmn = 0.013, V = 1 m/s

A concrete sewer with an inside diameter of 200 mm (Manning n = 0.013) must reach a self-cleansing velocity of 1 m/s when flowing just full. Find the minimum slope S (in m/m).

D = 200 mmn = 0.013V = 1 m/s
S = m/m
6.Hard
b = 1.5 my = 2.2 m1 : 1n = 0.022, Q = 11 m³/s

A trapezoidal clean earth channel with a bottom width of 1.5 m and side slopes of 1:1 (horizontal:vertical) must carry 11 m³/s in uniform flow at a depth of 2.2 m. Manning n = 0.022. Find the required bed slope S (in m/m).

Q = 11 m³/sb = 1.5 my = 2.2 mz = 1n = 0.022
S = m/m

Answer key

  1. 1. V = 1.205 m/s
  2. 2. V = 1.291 m/s
  3. 3. Q = 1.482 m³/s
  4. 4. Q = 11.69 m³/s
  5. 5. S = 0.009175 m/m
  6. 6. S = 0.0008239 m/m

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