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 my = 1.3 mn = 0.022

Water flows uniformly 1.3 m deep in a rectangular clean earth channel 4 m wide (Manning n = 0.022). The bed drops 2 m per kilometre. Use Manning’s equation in SI units to find the mean velocity V.

b = 4 my = 1.3 mn = 0.022drop = 2 m/km
V = m/s
2.Easy
b = 3 my = 1.6 mn = 0.03

Water flows uniformly 1.6 m deep in a rectangular grass-lined earth channel 3 m wide (Manning n = 0.03). The bed drops 1.5 m per kilometre. Use Manning’s equation in SI units to find the mean velocity V.

b = 3 my = 1.6 mn = 0.03drop = 1.5 m/km
V = m/s
3.Medium
b = 2.5 my = 1 mn = 0.012, S = 0.003

A rectangular finished concrete channel is 2.5 m wide. Water flows uniformly 1 m deep. Manning n = 0.012 and the bed slope is S = 0.003. Find the flow rate Q in m³/s.

b = 2.5 my = 1 mn = 0.012S = 0.003
Q = m³/s
4.Medium
D = 750 mmn = 0.013, S = 0.0008

A concrete storm sewer with an inside diameter of 750 mm flows half full. Manning n = 0.013 and the slope is S = 0.0008. Find the flow rate Q in m³/s.

D = 750 mmn = 0.013S = 0.0008
Q = m³/s
5.Hard
b = 5 my = 2.2 m1 : 1n = 0.014, Q = 40 m³/s

A trapezoidal unfinished concrete channel with a bottom width of 5 m and side slopes of 1:1 (horizontal:vertical) must carry 40 m³/s in uniform flow at a depth of 2.2 m. Manning n = 0.014. Find the required bed slope S (in m/m).

Q = 40 m³/sb = 5 my = 2.2 mz = 1n = 0.014
S = m/m
6.Hard
b = 2 my = 2.5 m2 : 1n = 0.022, Q = 43 m³/s

A trapezoidal clean earth channel with a bottom width of 2 m and side slopes of 2:1 (horizontal:vertical) must carry 43 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 = 43 m³/sb = 2 my = 2.5 mz = 2n = 0.022
S = m/m

Answer key

  1. 1. V = 1.734 m/s
  2. 2. V = 1.088 m/s
  3. 3. Q = 7.711 m³/s
  4. 4. Q = 0.1574 m³/s
  5. 5. S = 0.0007894 m/m
  6. 6. S = 0.002002 m/m

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