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 = 3 my = 1.4 mn = 0.025

Water flows uniformly 1.4 m deep in a rectangular gravel channel 3 m wide (Manning n = 0.025). The bed slope is S = 0.0015. Use Manning’s equation in SI units to find the mean velocity V.

b = 3 my = 1.4 mn = 0.025S = 0.0015
V = m/s
2.Easy
b = 5 my = 1.3 mn = 0.022

Water flows uniformly 1.3 m deep in a rectangular clean earth channel 5 m wide (Manning n = 0.022). The bed slope is S = 0.002. Use Manning’s equation in SI units to find the mean velocity V.

b = 5 my = 1.3 mn = 0.022S = 0.002
V = m/s
3.Medium
b = 1 my = 1.5 m3 : 1n = 0.014, S = 0.0005

A trapezoidal unfinished concrete channel has a bottom width of 1 m and side slopes of 3:1 (horizontal:vertical). Water flows uniformly 1.5 m deep. Manning n = 0.014 and the bed slope is S = 0.0005. Find the flow rate Q in m³/s.

b = 1 my = 1.5 mz = 3n = 0.014S = 0.0005
Q = m³/s
4.Medium
b = 3.5 my = 2.1 mn = 0.015, S = 0.0008

A rectangular brickwork channel is 3.5 m wide. Water flows uniformly 2.1 m deep. Manning n = 0.015 and the bed slope is S = 0.0008. Find the flow rate Q in m³/s.

b = 3.5 my = 2.1 mn = 0.015S = 0.0008
Q = m³/s
5.Hard
D = 200 mmn = 0.013, V = 0.75 m/s

A concrete sewer with an inside diameter of 200 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 = 200 mmn = 0.013V = 0.75 m/s
S = m/m
6.Hard
b = 1 my = 1.7 m2 : 1n = 0.025, Q = 17 m³/s

A trapezoidal gravel channel with a bottom width of 1 m and side slopes of 2:1 (horizontal:vertical) must carry 17 m³/s in uniform flow at a depth of 1.7 m. Manning n = 0.025. Find the required bed slope S (in m/m).

Q = 17 m³/sb = 1 my = 1.7 mz = 2n = 0.025
S = m/m

Answer key

  1. 1. V = 1.249 m/s
  2. 2. V = 1.832 m/s
  3. 3. Q = 11.23 m³/s
  4. 4. Q = 13.44 m³/s
  5. 5. S = 0.005161 m/m
  6. 6. S = 0.00389 m/m

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