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 = 1.3 mn = 0.014

Water flows uniformly 1.3 m deep in a rectangular unfinished concrete channel 5.5 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 = 5.5 my = 1.3 mn = 0.014S = 0.0008
V = m/s
2.Easy
b = 5.5 my = 1.2 mn = 0.012

Water flows uniformly 1.2 m deep in a rectangular finished concrete channel 5.5 m wide (Manning n = 0.012). The bed slope is S = 0.0008. Use Manning’s equation in SI units to find the mean velocity V.

b = 5.5 my = 1.2 mn = 0.012S = 0.0008
V = m/s
3.Medium
D = 900 mmn = 0.013, S = 0.004

A concrete storm sewer with an inside diameter of 900 mm flows half full. Manning n = 0.013 and the slope is S = 0.004. Find the flow rate Q in m³/s.

D = 900 mmn = 0.013S = 0.004
Q = m³/s
4.Medium
b = 4 my = 1.8 mn = 0.014, S = 0.0015

A rectangular unfinished concrete channel is 4 m wide. Water flows uniformly 1.8 m deep. Manning n = 0.014 and the bed slope is S = 0.0015. Find the flow rate Q in m³/s.

b = 4 my = 1.8 mn = 0.014S = 0.0015
Q = m³/s
5.Hard
b = 4.5 my = 1 m1 : 1n = 0.014, Q = 7.3 m³/s

A trapezoidal unfinished concrete channel with a bottom width of 4.5 m and side slopes of 1:1 (horizontal:vertical) must carry 7.3 m³/s in uniform flow at a depth of 1 m. Manning n = 0.014. Find the required bed slope S (in m/m).

Q = 7.3 m³/sb = 4.5 my = 1 mz = 1n = 0.014
S = m/m
6.Hard
b = 1.5 my = 2.3 m3 : 1n = 0.014, Q = 44 m³/s

A trapezoidal unfinished concrete channel with a bottom width of 1.5 m and side slopes of 3:1 (horizontal:vertical) must carry 44 m³/s in uniform flow at a depth of 2.3 m. Manning n = 0.014. Find the required bed slope S (in m/m).

Q = 44 m³/sb = 1.5 my = 2.3 mz = 3n = 0.014
S = m/m

Answer key

  1. 1. V = 1.859 m/s
  2. 2. V = 2.091 m/s
  3. 3. Q = 0.5725 m³/s
  4. 4. Q = 19.21 m³/s
  5. 5. S = 0.0005063 m/m
  6. 6. S = 0.0007937 m/m

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