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.

New worksheetPractise online with hints

For teachers: free to print, copy and use in class. Every new worksheet has new values and its own answer key. A link to ExamProblems on your course page is appreciated.

Name: ____________________   Date: ____________

1.Easy
b = 3.5 my = 1.9 mn = 0.022

Water flows uniformly 1.9 m deep in a rectangular clean earth channel 3.5 m wide (Manning n = 0.022). The bed slope is S = 0.0008. Use Manning’s equation in SI units to find the mean velocity V.

b = 3.5 my = 1.9 mn = 0.022S = 0.0008
V = m/s
2.Easy
b = 3 my = 1.7 mn = 0.015

Water flows uniformly 1.7 m deep in a rectangular brickwork channel 3 m wide (Manning n = 0.015). The bed drops 0.8 m per kilometre. Use Manning’s equation in SI units to find the mean velocity V.

b = 3 my = 1.7 mn = 0.015drop = 0.8 m/km
V = m/s
3.Medium
D = 300 mmn = 0.013, S = 0.0008

A concrete storm sewer with an inside diameter of 300 mm flows just full (as an open channel, not under pressure). Manning n = 0.013 and the slope is S = 0.0008. Find the flow rate Q in m³/s.

D = 300 mmn = 0.013S = 0.0008
Q = m³/s
4.Medium
D = 900 mmn = 0.013, S = 0.003

A concrete storm sewer with an inside diameter of 900 mm flows half full. Manning n = 0.013 and the slope is S = 0.003. Find the flow rate Q in m³/s.

D = 900 mmn = 0.013S = 0.003
Q = m³/s
5.Hard
D = 450 mmn = 0.013, V = 0.6 m/s

A concrete sewer with an inside diameter of 450 mm (Manning n = 0.013) must reach a self-cleansing velocity of 0.6 m/s when flowing just full. Find the minimum slope S (in m/m).

D = 450 mmn = 0.013V = 0.6 m/s
S = m/m
6.Hard
b = 4.5 my = 0.7 m2 : 1n = 0.015, Q = 5.8 m³/s

A trapezoidal brickwork channel with a bottom width of 4.5 m and side slopes of 2:1 (horizontal:vertical) must carry 5.8 m³/s in uniform flow at a depth of 0.7 m. Manning n = 0.015. Find the required bed slope S (in m/m).

Q = 5.8 m³/sb = 4.5 my = 0.7 mz = 2n = 0.015
S = m/m

Answer key

  1. 1. V = 1.208 m/s
  2. 2. V = 1.621 m/s
  3. 3. Q = 0.02735 m³/s
  4. 4. Q = 0.4958 m³/s
  5. 5. S = 0.00112 m/m
  6. 6. S = 0.001006 m/m

Full step-by-step solutions: practise this topic on examproblems.com.