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 my = 2 mn = 0.022

Water flows uniformly 2 m deep in a rectangular clean earth channel 1 m wide (Manning n = 0.022). The bed slope is S = 0.004. Use Manning’s equation in SI units to find the mean velocity V.

b = 1 my = 2 mn = 0.022S = 0.004
V = m/s
2.Easy
b = 4 my = 1.5 mn = 0.022

Water flows uniformly 1.5 m deep in a rectangular clean earth channel 4 m wide (Manning n = 0.022). The bed slope is S = 0.001. Use Manning’s equation in SI units to find the mean velocity V.

b = 4 my = 1.5 mn = 0.022S = 0.001
V = m/s
3.Medium
b = 1.5 my = 2.2 m1.5 : 1n = 0.022, S = 0.001

A trapezoidal clean earth channel has a bottom width of 1.5 m and side slopes of 1.5:1 (horizontal:vertical). Water flows uniformly 2.2 m deep. Manning n = 0.022 and the bed slope is S = 0.001. Find the flow rate Q in m³/s.

b = 1.5 my = 2.2 mz = 1.5n = 0.022S = 0.001
Q = m³/s
4.Medium
b = 6 my = 1.6 m1.5 : 1n = 0.025, S = 0.004

A trapezoidal gravel channel has a bottom width of 6 m and side slopes of 1.5:1 (horizontal:vertical). Water flows uniformly 1.6 m deep. Manning n = 0.025 and the bed slope is S = 0.004. Find the flow rate Q in m³/s.

b = 6 my = 1.6 mz = 1.5n = 0.025S = 0.004
Q = m³/s
5.Hard
D = 250 mmn = 0.013, V = 0.75 m/s

A concrete sewer with an inside diameter of 250 mm (Manning n = 0.013) must reach a self-cleansing velocity of 0.75 m/s when flowing just full. Find the minimum slope S (in m/m).

D = 250 mmn = 0.013V = 0.75 m/s
S = m/m
6.Hard
b = 5.5 my = 1.8 m2 : 1n = 0.015, Q = 48 m³/s

A trapezoidal brickwork channel with a bottom width of 5.5 m and side slopes of 2:1 (horizontal:vertical) must carry 48 m³/s in uniform flow at a depth of 1.8 m. Manning n = 0.015. Find the required bed slope S (in m/m).

Q = 48 m³/sb = 5.5 my = 1.8 mz = 2n = 0.015
S = m/m

Answer key

  1. 1. V = 1.561 m/s
  2. 2. V = 1.297 m/s
  3. 3. Q = 16.37 m³/s
  4. 4. Q = 37.15 m³/s
  5. 5. S = 0.003833 m/m
  6. 6. S = 0.0015 m/m

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