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 = 2.5 my = 2.3 mn = 0.012

Water flows uniformly 2.3 m deep in a rectangular finished concrete channel 2.5 m wide (Manning n = 0.012). The bed slope is S = 0.002. Use Manning’s equation in SI units to find the mean velocity V.

b = 2.5 my = 2.3 mn = 0.012S = 0.002
V = m/s
2.Easy
b = 2 my = 0.8 mn = 0.012

Water flows uniformly 0.8 m deep in a rectangular finished concrete channel 2 m wide (Manning n = 0.012). The bed slope is S = 0.0015. Use Manning’s equation in SI units to find the mean velocity V.

b = 2 my = 0.8 mn = 0.012S = 0.0015
V = m/s
3.Medium
b = 1.5 my = 2.4 mn = 0.015, S = 0.001

A rectangular brickwork channel is 1.5 m wide. Water flows uniformly 2.4 m deep. Manning n = 0.015 and the bed slope is S = 0.001. Find the flow rate Q in m³/s.

b = 1.5 my = 2.4 mn = 0.015S = 0.001
Q = m³/s
4.Medium
b = 3.5 my = 0.7 m1 : 1n = 0.022, S = 0.0005

A trapezoidal clean earth channel has a bottom width of 3.5 m and side slopes of 1:1 (horizontal:vertical). Water flows uniformly 0.7 m deep. Manning n = 0.022 and the bed slope is S = 0.0005. Find the flow rate Q in m³/s.

b = 3.5 my = 0.7 mz = 1n = 0.022S = 0.0005
Q = m³/s
5.Hard
b = 2.5 my = 1 mn = 0.012, Q = 3.1 m³/s

A rectangular finished concrete channel 2.5 m wide must carry 3.1 m³/s in uniform flow at a depth of 1 m. Manning n = 0.012. Find the required bed slope S (in m/m).

Q = 3.1 m³/sb = 2.5 my = 1 mn = 0.012
S = m/m
6.Hard
D = 375 mmn = 0.013, V = 0.9 m/s

A concrete sewer with an inside diameter of 375 mm (Manning n = 0.013) must reach a self-cleansing velocity of 0.9 m/s when flowing just full. Find the minimum slope S (in m/m).

D = 375 mmn = 0.013V = 0.9 m/s
S = m/m

Answer key

  1. 1. V = 3.238 m/s
  2. 2. V = 1.88 m/s
  3. 3. Q = 5.226 m³/s
  4. 4. Q = 1.973 m³/s
  5. 5. S = 0.0004848 m/m
  6. 6. S = 0.003214 m/m

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