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 = 4.5 my = 1.4 mn = 0.014

Water flows uniformly 1.4 m deep in a rectangular unfinished concrete channel 4.5 m wide (Manning n = 0.014). The bed slope is S = 0.001. Use Manning’s equation in SI units to find the mean velocity V.

b = 4.5 my = 1.4 mn = 0.014S = 0.001
V = m/s
2.Easy
b = 4.5 my = 0.6 mn = 0.03

Water flows uniformly 0.6 m deep in a rectangular grass-lined earth channel 4.5 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 = 4.5 my = 0.6 mn = 0.03S = 0.001
V = m/s
3.Medium
b = 5.5 my = 1.9 m2 : 1n = 0.015, S = 0.003

A trapezoidal brickwork channel has a bottom width of 5.5 m and side slopes of 2:1 (horizontal:vertical). Water flows uniformly 1.9 m deep. Manning n = 0.015 and the bed slope is S = 0.003. Find the flow rate Q in m³/s.

b = 5.5 my = 1.9 mz = 2n = 0.015S = 0.003
Q = m³/s
4.Medium
D = 600 mmn = 0.013, S = 0.003

A concrete storm sewer with an inside diameter of 600 mm flows half full. Manning n = 0.013 and the slope is S = 0.003. Find the flow rate Q in m³/s.

D = 600 mmn = 0.013S = 0.003
Q = m³/s
5.Hard
b = 1.5 my = 2.5 m2 : 1n = 0.022, Q = 55 m³/s

A trapezoidal clean earth channel with a bottom width of 1.5 m and side slopes of 2:1 (horizontal:vertical) must carry 55 m³/s in uniform flow at a depth of 2.5 m. Manning n = 0.022. Find the required bed slope S (in m/m).

Q = 55 m³/sb = 1.5 my = 2.5 mz = 2n = 0.022
S = m/m
6.Hard
b = 4 my = 0.8 m1.5 : 1n = 0.012, Q = 5.5 m³/s

A trapezoidal finished concrete channel with a bottom width of 4 m and side slopes of 1.5:1 (horizontal:vertical) must carry 5.5 m³/s in uniform flow at a depth of 0.8 m. Manning n = 0.012. Find the required bed slope S (in m/m).

Q = 5.5 m³/sb = 4 my = 0.8 mz = 1.5n = 0.012
S = m/m

Answer key

  1. 1. V = 2.047 m/s
  2. 2. V = 0.6405 m/s
  3. 3. Q = 75.37 m³/s
  4. 4. Q = 0.1682 m³/s
  5. 5. S = 0.003983 m/m
  6. 6. S = 0.0004927 m/m

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