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 = 4.5 my = 1.7 mn = 0.015

Water flows uniformly 1.7 m deep in a rectangular brickwork channel 4.5 m wide (Manning n = 0.015). The bed slope is S = 0.001. Use Manning’s equation in SI units to find the mean velocity V.

b = 4.5 my = 1.7 mn = 0.015S = 0.001
V = m/s
2.Easy
b = 5.5 my = 1.8 mn = 0.012

Water flows uniformly 1.8 m deep in a rectangular finished concrete channel 5.5 m wide (Manning n = 0.012). The bed drops 0.8 m per kilometre. Use Manning’s equation in SI units to find the mean velocity V.

b = 5.5 my = 1.8 mn = 0.012drop = 0.8 m/km
V = m/s
3.Medium
D = 1200 mmn = 0.013, S = 0.001

A concrete storm sewer with an inside diameter of 1200 mm flows just full (as an open channel, not under pressure). Manning n = 0.013 and the slope is S = 0.001. Find the flow rate Q in m³/s.

D = 1200 mmn = 0.013S = 0.001
Q = m³/s
4.Medium
b = 4.5 my = 1.1 mn = 0.015, S = 0.005

A rectangular brickwork channel is 4.5 m wide. Water flows uniformly 1.1 m deep. Manning n = 0.015 and the bed slope is S = 0.005. Find the flow rate Q in m³/s.

b = 4.5 my = 1.1 mn = 0.015S = 0.005
Q = m³/s
5.Hard
b = 1 my = 1.1 m1.5 : 1n = 0.022, Q = 4.2 m³/s

A trapezoidal clean earth channel with a bottom width of 1 m and side slopes of 1.5:1 (horizontal:vertical) must carry 4.2 m³/s in uniform flow at a depth of 1.1 m. Manning n = 0.022. Find the required bed slope S (in m/m).

Q = 4.2 m³/sb = 1 my = 1.1 mz = 1.5n = 0.022
S = m/m
6.Hard
b = 6 my = 1.1 m2 : 1n = 0.012, Q = 26 m³/s

A trapezoidal finished concrete channel with a bottom width of 6 m and side slopes of 2:1 (horizontal:vertical) must carry 26 m³/s in uniform flow at a depth of 1.1 m. Manning n = 0.012. Find the required bed slope S (in m/m).

Q = 26 m³/sb = 6 my = 1.1 mz = 2n = 0.012
S = m/m

Answer key

  1. 1. V = 2.063 m/s
  2. 2. V = 2.493 m/s
  3. 3. Q = 1.233 m³/s
  4. 4. Q = 19.07 m³/s
  5. 5. S = 0.002044 m/m
  6. 6. S = 0.001544 m/m

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