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 = 1.3 mn = 0.012

Water flows uniformly 1.3 m deep in a rectangular finished concrete channel 6 m wide (Manning n = 0.012). The bed slope is S = 0.001. Use Manning’s equation in SI units to find the mean velocity V.

b = 6 my = 1.3 mn = 0.012S = 0.001
V = m/s
2.Easy
b = 5 my = 1.3 mn = 0.03

Water flows uniformly 1.3 m deep in a rectangular grass-lined earth channel 5 m wide (Manning n = 0.03). The bed drops 3 m per kilometre. Use Manning’s equation in SI units to find the mean velocity V.

b = 5 my = 1.3 mn = 0.03drop = 3 m/km
V = m/s
3.Medium
b = 1.5 my = 1 m1.5 : 1n = 0.025, S = 0.0008

A trapezoidal gravel channel has a bottom width of 1.5 m and side slopes of 1.5:1 (horizontal:vertical). Water flows uniformly 1 m deep. Manning n = 0.025 and the bed slope is S = 0.0008. Find the flow rate Q in m³/s.

b = 1.5 my = 1 mz = 1.5n = 0.025S = 0.0008
Q = m³/s
4.Medium
b = 2 my = 0.7 m1 : 1n = 0.014, S = 0.0015

A trapezoidal unfinished concrete channel has a bottom width of 2 m and side slopes of 1:1 (horizontal:vertical). Water flows uniformly 0.7 m deep. Manning n = 0.014 and the bed slope is S = 0.0015. Find the flow rate Q in m³/s.

b = 2 my = 0.7 mz = 1n = 0.014S = 0.0015
Q = m³/s
5.Hard
D = 600 mmn = 0.013, V = 0.75 m/s

A concrete sewer with an inside diameter of 600 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 = 600 mmn = 0.013V = 0.75 m/s
S = m/m
6.Hard
b = 4 my = 0.5 mn = 0.03, Q = 1.1 m³/s

A rectangular grass-lined earth channel 4 m wide must carry 1.1 m³/s in uniform flow at a depth of 0.5 m. Manning n = 0.03. Find the required bed slope S (in m/m).

Q = 1.1 m³/sb = 4 my = 0.5 mn = 0.03
S = m/m

Answer key

  1. 1. V = 2.469 m/s
  2. 2. V = 1.645 m/s
  3. 3. Q = 2.381 m³/s
  4. 4. Q = 3.183 m³/s
  5. 5. S = 0.001193 m/m
  6. 6. S = 0.0009238 m/m

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