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 = 1.9 mn = 0.012

Water flows uniformly 1.9 m deep in a rectangular finished concrete channel 4.5 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 = 4.5 my = 1.9 mn = 0.012S = 0.0015
V = m/s
2.Easy
b = 2.5 my = 0.7 mn = 0.015

Water flows uniformly 0.7 m deep in a rectangular brickwork channel 2.5 m wide (Manning n = 0.015). The bed slope is S = 0.002. Use Manning’s equation in SI units to find the mean velocity V.

b = 2.5 my = 0.7 mn = 0.015S = 0.002
V = m/s
3.Medium
b = 1.5 my = 2.1 mn = 0.015, S = 0.001

A rectangular brickwork channel is 1.5 m wide. Water flows uniformly 2.1 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 = 2.1 mn = 0.015S = 0.001
Q = m³/s
4.Medium
D = 300 mmn = 0.013, S = 0.003

A concrete storm sewer with an inside diameter of 300 mm flows half full. Manning n = 0.013 and the slope is S = 0.003. Find the flow rate Q in m³/s.

D = 300 mmn = 0.013S = 0.003
Q = m³/s
5.Hard
b = 1.5 my = 2.5 m1 : 1n = 0.014, Q = 31 m³/s

A trapezoidal unfinished concrete channel with a bottom width of 1.5 m and side slopes of 1:1 (horizontal:vertical) must carry 31 m³/s in uniform flow at a depth of 2.5 m. Manning n = 0.014. Find the required bed slope S (in m/m).

Q = 31 m³/sb = 1.5 my = 2.5 mz = 1n = 0.014
S = m/m
6.Hard
b = 3.5 my = 1.9 mn = 0.015, Q = 12 m³/s

A rectangular brickwork channel 3.5 m wide must carry 12 m³/s in uniform flow at a depth of 1.9 m. Manning n = 0.015. Find the required bed slope S (in m/m).

Q = 12 m³/sb = 3.5 my = 1.9 mn = 0.015
S = m/m

Answer key

  1. 1. V = 3.292 m/s
  2. 2. V = 1.747 m/s
  3. 3. Q = 4.472 m³/s
  4. 4. Q = 0.02648 m³/s
  5. 5. S = 0.001534 m/m
  6. 6. S = 0.0008297 m/m

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