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 = 5 my = 2.1 mn = 0.025

Water flows uniformly 2.1 m deep in a rectangular gravel channel 5 m wide (Manning n = 0.025). The bed slope is S = 0.001. Use Manning’s equation in SI units to find the mean velocity V.

b = 5 my = 2.1 mn = 0.025S = 0.001
V = m/s
2.Easy
b = 5.5 my = 2.5 mn = 0.03

Water flows uniformly 2.5 m deep in a rectangular grass-lined earth channel 5.5 m wide (Manning n = 0.03). The bed drops 3 m per kilometre. Use Manning’s equation in SI units to find the mean velocity V.

b = 5.5 my = 2.5 mn = 0.03drop = 3 m/km
V = m/s
3.Medium
b = 2 my = 2.1 m3 : 1n = 0.025, S = 0.0015

A trapezoidal gravel channel has a bottom width of 2 m and side slopes of 3:1 (horizontal:vertical). Water flows uniformly 2.1 m deep. Manning n = 0.025 and the bed slope is S = 0.0015. Find the flow rate Q in m³/s.

b = 2 my = 2.1 mz = 3n = 0.025S = 0.0015
Q = m³/s
4.Medium
b = 2 my = 0.5 mn = 0.03, S = 0.005

A rectangular grass-lined earth channel is 2 m wide. Water flows uniformly 0.5 m deep. Manning n = 0.03 and the bed slope is S = 0.005. Find the flow rate Q in m³/s.

b = 2 my = 0.5 mn = 0.03S = 0.005
Q = m³/s
5.Hard
b = 5.5 my = 0.7 m3 : 1n = 0.03, Q = 4.5 m³/s

A trapezoidal grass-lined earth channel with a bottom width of 5.5 m and side slopes of 3:1 (horizontal:vertical) must carry 4.5 m³/s in uniform flow at a depth of 0.7 m. Manning n = 0.03. Find the required bed slope S (in m/m).

Q = 4.5 m³/sb = 5.5 my = 0.7 mz = 3n = 0.03
S = m/m
6.Hard
D = 375 mmn = 0.013, V = 1.2 m/s

A concrete sewer with an inside diameter of 375 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 = 375 mmn = 0.013V = 1.2 m/s
S = m/m

Answer key

  1. 1. V = 1.381 m/s
  2. 2. V = 2.185 m/s
  3. 3. Q = 29.48 m³/s
  4. 4. Q = 1.133 m³/s
  5. 5. S = 0.001479 m/m
  6. 6. S = 0.005714 m/m

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