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.

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1.Easy
b = 5 my = 1.9 mn = 0.015

Water flows uniformly 1.9 m deep in a rectangular brickwork channel 5 m wide (Manning n = 0.015). The bed slope is S = 0.005. Use Manning’s equation in SI units to find the mean velocity V.

b = 5 my = 1.9 mn = 0.015S = 0.005
V = m/s
2.Easy
b = 1 my = 0.9 mn = 0.022

Water flows uniformly 0.9 m deep in a rectangular clean earth channel 1 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 = 1 my = 0.9 mn = 0.022S = 0.001
V = m/s
3.Medium
b = 5.5 my = 0.7 mn = 0.014, S = 0.003

A rectangular unfinished concrete channel is 5.5 m wide. Water flows uniformly 0.7 m deep. Manning n = 0.014 and the bed slope is S = 0.003. Find the flow rate Q in m³/s.

b = 5.5 my = 0.7 mn = 0.014S = 0.003
Q = m³/s
4.Medium
b = 4 my = 2.3 m1 : 1n = 0.012, S = 0.002

A trapezoidal finished concrete channel has a bottom width of 4 m and side slopes of 1:1 (horizontal:vertical). Water flows uniformly 2.3 m deep. Manning n = 0.012 and the bed slope is S = 0.002. Find the flow rate Q in m³/s.

b = 4 my = 2.3 mz = 1n = 0.012S = 0.002
Q = m³/s
5.Hard
b = 2 my = 0.8 mn = 0.015, Q = 3.4 m³/s

A rectangular brickwork channel 2 m wide must carry 3.4 m³/s in uniform flow at a depth of 0.8 m. Manning n = 0.015. Find the required bed slope S (in m/m).

Q = 3.4 m³/sb = 2 my = 0.8 mn = 0.015
S = m/m
6.Hard
b = 3.5 my = 2.1 mn = 0.012, Q = 19 m³/s

A rectangular finished concrete channel 3.5 m wide must carry 19 m³/s in uniform flow at a depth of 2.1 m. Manning n = 0.012. Find the required bed slope S (in m/m).

Q = 19 m³/sb = 3.5 my = 2.1 mn = 0.012
S = m/m

Answer key

  1. 1. V = 4.961 m/s
  2. 2. V = 0.6745 m/s
  3. 3. Q = 10.21 m³/s
  4. 4. Q = 66.91 m³/s
  5. 5. S = 0.002996 m/m
  6. 6. S = 0.001024 m/m

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