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 = 1 my = 0.9 mn = 0.03

Water flows uniformly 0.9 m deep in a rectangular grass-lined earth channel 1 m wide (Manning n = 0.03). The bed slope is S = 0.002. Use Manning’s equation in SI units to find the mean velocity V.

b = 1 my = 0.9 mn = 0.03S = 0.002
V = m/s
2.Easy
b = 2 my = 2.2 mn = 0.03

Water flows uniformly 2.2 m deep in a rectangular grass-lined earth channel 2 m wide (Manning n = 0.03). The bed slope is S = 0.0005. Use Manning’s equation in SI units to find the mean velocity V.

b = 2 my = 2.2 mn = 0.03S = 0.0005
V = m/s
3.Medium
b = 2.5 my = 1.4 m2 : 1n = 0.022, S = 0.003

A trapezoidal clean earth channel has a bottom width of 2.5 m and side slopes of 2:1 (horizontal:vertical). Water flows uniformly 1.4 m deep. Manning n = 0.022 and the bed slope is S = 0.003. Find the flow rate Q in m³/s.

b = 2.5 my = 1.4 mz = 2n = 0.022S = 0.003
Q = m³/s
4.Medium
b = 2.5 my = 0.9 m3 : 1n = 0.015, S = 0.001

A trapezoidal brickwork channel has a bottom width of 2.5 m and side slopes of 3:1 (horizontal:vertical). Water flows uniformly 0.9 m deep. Manning n = 0.015 and the bed slope is S = 0.001. Find the flow rate Q in m³/s.

b = 2.5 my = 0.9 mz = 3n = 0.015S = 0.001
Q = m³/s
5.Hard
b = 6 my = 2.3 m1.5 : 1n = 0.012, Q = 54 m³/s

A trapezoidal finished concrete channel with a bottom width of 6 m and side slopes of 1.5:1 (horizontal:vertical) must carry 54 m³/s in uniform flow at a depth of 2.3 m. Manning n = 0.012. Find the required bed slope S (in m/m).

Q = 54 m³/sb = 6 my = 2.3 mz = 1.5n = 0.012
S = m/m
6.Hard
b = 2.5 my = 1 mn = 0.025, Q = 1.9 m³/s

A rectangular gravel channel 2.5 m wide must carry 1.9 m³/s in uniform flow at a depth of 1 m. Manning n = 0.025. Find the required bed slope S (in m/m).

Q = 1.9 m³/sb = 2.5 my = 1 mn = 0.025
S = m/m

Answer key

  1. 1. V = 0.6995 m/s
  2. 2. V = 0.5806 m/s
  3. 3. Q = 16.54 m³/s
  4. 4. Q = 6.793 m³/s
  5. 5. S = 0.0005083 m/m
  6. 6. S = 0.0007904 m/m

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