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 = 3.5 my = 1.4 mn = 0.014

Water flows uniformly 1.4 m deep in a rectangular unfinished concrete channel 3.5 m wide (Manning n = 0.014). The bed drops 5 m per kilometre. Use Manning’s equation in SI units to find the mean velocity V.

b = 3.5 my = 1.4 mn = 0.014drop = 5 m/km
V = m/s
2.Easy
b = 2.5 my = 1.7 mn = 0.015

Water flows uniformly 1.7 m deep in a rectangular brickwork channel 2.5 m wide (Manning n = 0.015). The bed drops 5 m per kilometre. Use Manning’s equation in SI units to find the mean velocity V.

b = 2.5 my = 1.7 mn = 0.015drop = 5 m/km
V = m/s
3.Medium
D = 900 mmn = 0.013, S = 0.002

A concrete storm sewer with an inside diameter of 900 mm flows half full. Manning n = 0.013 and the slope is S = 0.002. Find the flow rate Q in m³/s.

D = 900 mmn = 0.013S = 0.002
Q = m³/s
4.Medium
b = 3 my = 1 mn = 0.015, S = 0.001

A rectangular brickwork channel is 3 m wide. Water flows uniformly 1 m deep. Manning n = 0.015 and the bed slope is S = 0.001. Find the flow rate Q in m³/s.

b = 3 my = 1 mn = 0.015S = 0.001
Q = m³/s
5.Hard
b = 1.5 my = 1.7 m1 : 1n = 0.022, Q = 5 m³/s

A trapezoidal clean earth channel with a bottom width of 1.5 m and side slopes of 1:1 (horizontal:vertical) must carry 5 m³/s in uniform flow at a depth of 1.7 m. Manning n = 0.022. Find the required bed slope S (in m/m).

Q = 5 m³/sb = 1.5 my = 1.7 mz = 1n = 0.022
S = m/m
6.Hard
b = 1 my = 0.6 mn = 0.025, Q = 0.39 m³/s

A rectangular gravel channel 1 m wide must carry 0.39 m³/s in uniform flow at a depth of 0.6 m. Manning n = 0.025. Find the required bed slope S (in m/m).

Q = 0.39 m³/sb = 1 my = 0.6 mn = 0.025
S = m/m

Answer key

  1. 1. V = 4.272 m/s
  2. 2. V = 3.788 m/s
  3. 3. Q = 0.4048 m³/s
  4. 4. Q = 4.499 m³/s
  5. 5. S = 0.0004981 m/m
  6. 6. S = 0.001493 m/m

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