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 = 2.5 my = 1.2 mn = 0.015

Water flows uniformly 1.2 m deep in a rectangular brickwork channel 2.5 m wide (Manning n = 0.015). The bed slope is S = 0.001. Use Manning’s equation in SI units to find the mean velocity V.

b = 2.5 my = 1.2 mn = 0.015S = 0.001
V = m/s
2.Easy
b = 3.5 my = 2.4 mn = 0.03

Water flows uniformly 2.4 m deep in a rectangular grass-lined earth channel 3.5 m wide (Manning n = 0.03). The bed slope is S = 0.005. Use Manning’s equation in SI units to find the mean velocity V.

b = 3.5 my = 2.4 mn = 0.03S = 0.005
V = m/s
3.Medium
b = 2 my = 2.1 mn = 0.03, S = 0.004

A rectangular grass-lined earth channel is 2 m wide. Water flows uniformly 2.1 m deep. Manning n = 0.03 and the bed slope is S = 0.004. Find the flow rate Q in m³/s.

b = 2 my = 2.1 mn = 0.03S = 0.004
Q = m³/s
4.Medium
b = 4.5 my = 1.4 m1.5 : 1n = 0.022, S = 0.004

A trapezoidal clean earth channel has a bottom width of 4.5 m and side slopes of 1.5:1 (horizontal:vertical). Water flows uniformly 1.4 m deep. Manning n = 0.022 and the bed slope is S = 0.004. Find the flow rate Q in m³/s.

b = 4.5 my = 1.4 mz = 1.5n = 0.022S = 0.004
Q = m³/s
5.Hard
b = 5 my = 2.3 mn = 0.03, Q = 14 m³/s

A rectangular grass-lined earth channel 5 m wide must carry 14 m³/s in uniform flow at a depth of 2.3 m. Manning n = 0.03. Find the required bed slope S (in m/m).

Q = 14 m³/sb = 5 my = 2.3 mn = 0.03
S = m/m
6.Hard
b = 1 my = 2.1 m3 : 1n = 0.025, Q = 41 m³/s

A trapezoidal gravel channel with a bottom width of 1 m and side slopes of 3:1 (horizontal:vertical) must carry 41 m³/s in uniform flow at a depth of 2.1 m. Manning n = 0.025. Find the required bed slope S (in m/m).

Q = 41 m³/sb = 1 my = 2.1 mz = 3n = 0.025
S = m/m

Answer key

  1. 1. V = 1.52 m/s
  2. 2. V = 2.376 m/s
  3. 3. Q = 6.83 m³/s
  4. 4. Q = 25.99 m³/s
  5. 5. S = 0.001048 m/m
  6. 6. S = 0.004068 m/m

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