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 = 2 my = 1.9 mn = 0.022

Water flows uniformly 1.9 m deep in a rectangular clean earth channel 2 m wide (Manning n = 0.022). The bed slope is S = 0.0005. Use Manning’s equation in SI units to find the mean velocity V.

b = 2 my = 1.9 mn = 0.022S = 0.0005
V = m/s
2.Easy
b = 3.5 my = 2.4 mn = 0.015

Water flows uniformly 2.4 m deep in a rectangular brickwork channel 3.5 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 = 3.5 my = 2.4 mn = 0.015drop = 5 m/km
V = m/s
3.Medium
D = 600 mmn = 0.013, S = 0.0005

A concrete storm sewer with an inside diameter of 600 mm flows just full (as an open channel, not under pressure). Manning n = 0.013 and the slope is S = 0.0005. Find the flow rate Q in m³/s.

D = 600 mmn = 0.013S = 0.0005
Q = m³/s
4.Medium
b = 2.5 my = 0.9 m3 : 1n = 0.022, S = 0.0005

A trapezoidal clean earth channel has a bottom width of 2.5 m and side slopes of 3:1 (horizontal:vertical). Water flows uniformly 0.9 m deep. Manning n = 0.022 and the bed slope is S = 0.0005. Find the flow rate Q in m³/s.

b = 2.5 my = 0.9 mz = 3n = 0.022S = 0.0005
Q = m³/s
5.Hard
D = 450 mmn = 0.013, V = 1.2 m/s

A concrete sewer with an inside diameter of 450 mm (Manning n = 0.013) must reach a self-cleansing velocity of 1.2 m/s when flowing just full. Find the minimum slope S (in m/m).

D = 450 mmn = 0.013V = 1.2 m/s
S = m/m
6.Hard
b = 4.5 my = 1.7 m2 : 1n = 0.03, Q = 21 m³/s

A trapezoidal grass-lined earth channel with a bottom width of 4.5 m and side slopes of 2:1 (horizontal:vertical) must carry 21 m³/s in uniform flow at a depth of 1.7 m. Manning n = 0.03. Find the required bed slope S (in m/m).

Q = 21 m³/sb = 4.5 my = 1.7 mz = 2n = 0.03
S = m/m

Answer key

  1. 1. V = 0.7667 m/s
  2. 2. V = 4.752 m/s
  3. 3. Q = 0.1373 m³/s
  4. 4. Q = 3.275 m³/s
  5. 5. S = 0.004481 m/m
  6. 6. S = 0.001915 m/m

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