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 = 1.5 my = 0.5 mn = 0.03

Water flows uniformly 0.5 m deep in a rectangular grass-lined earth channel 1.5 m wide (Manning n = 0.03). The bed slope is S = 0.0008. Use Manning’s equation in SI units to find the mean velocity V.

b = 1.5 my = 0.5 mn = 0.03S = 0.0008
V = m/s
2.Easy
b = 5 my = 0.8 mn = 0.022

Water flows uniformly 0.8 m deep in a rectangular clean earth channel 5 m wide (Manning n = 0.022). The bed slope is S = 0.002. Use Manning’s equation in SI units to find the mean velocity V.

b = 5 my = 0.8 mn = 0.022S = 0.002
V = m/s
3.Medium
b = 3 my = 1.2 m2 : 1n = 0.014, S = 0.0015

A trapezoidal unfinished concrete channel has a bottom width of 3 m and side slopes of 2:1 (horizontal:vertical). Water flows uniformly 1.2 m deep. Manning n = 0.014 and the bed slope is S = 0.0015. Find the flow rate Q in m³/s.

b = 3 my = 1.2 mz = 2n = 0.014S = 0.0015
Q = m³/s
4.Medium
D = 1200 mmn = 0.013, S = 0.004

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 = 0.004. Find the flow rate Q in m³/s.

D = 1200 mmn = 0.013S = 0.004
Q = m³/s
5.Hard
b = 4.5 my = 1.8 mn = 0.025, Q = 13 m³/s

A rectangular gravel channel 4.5 m wide must carry 13 m³/s in uniform flow at a depth of 1.8 m. Manning n = 0.025. Find the required bed slope S (in m/m).

Q = 13 m³/sb = 4.5 my = 1.8 mn = 0.025
S = m/m
6.Hard
b = 5.5 my = 0.6 m2 : 1n = 0.025, Q = 6.3 m³/s

A trapezoidal gravel channel with a bottom width of 5.5 m and side slopes of 2:1 (horizontal:vertical) must carry 6.3 m³/s in uniform flow at a depth of 0.6 m. Manning n = 0.025. Find the required bed slope S (in m/m).

Q = 6.3 m³/sb = 5.5 my = 0.6 mz = 2n = 0.025
S = m/m

Answer key

  1. 1. V = 0.4225 m/s
  2. 2. V = 1.456 m/s
  3. 3. Q = 15.12 m³/s
  4. 4. Q = 2.466 m³/s
  5. 5. S = 0.00161 m/m
  6. 6. S = 0.00396 m/m

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