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 = 2.4 mn = 0.012

Water flows uniformly 2.4 m deep in a rectangular finished concrete channel 5 m wide (Manning n = 0.012). The bed drops 1 m per kilometre. Use Manning’s equation in SI units to find the mean velocity V.

b = 5 my = 2.4 mn = 0.012drop = 1 m/km
V = m/s
2.Easy
b = 2 my = 0.6 mn = 0.015

Water flows uniformly 0.6 m deep in a rectangular brickwork channel 2 m wide (Manning n = 0.015). The bed drops 3 m per kilometre. Use Manning’s equation in SI units to find the mean velocity V.

b = 2 my = 0.6 mn = 0.015drop = 3 m/km
V = m/s
3.Medium
b = 1 my = 2 m1.5 : 1n = 0.025, S = 0.0015

A trapezoidal gravel channel has a bottom width of 1 m and side slopes of 1.5:1 (horizontal:vertical). Water flows uniformly 2 m deep. Manning n = 0.025 and the bed slope is S = 0.0015. Find the flow rate Q in m³/s.

b = 1 my = 2 mz = 1.5n = 0.025S = 0.0015
Q = m³/s
4.Medium
b = 3.5 my = 1.8 mn = 0.012, S = 0.0008

A rectangular finished concrete channel is 3.5 m wide. Water flows uniformly 1.8 m deep. Manning n = 0.012 and the bed slope is S = 0.0008. Find the flow rate Q in m³/s.

b = 3.5 my = 1.8 mn = 0.012S = 0.0008
Q = m³/s
5.Hard
b = 3 my = 2.2 m1 : 1n = 0.015, Q = 39 m³/s

A trapezoidal brickwork channel with a bottom width of 3 m and side slopes of 1:1 (horizontal:vertical) must carry 39 m³/s in uniform flow at a depth of 2.2 m. Manning n = 0.015. Find the required bed slope S (in m/m).

Q = 39 m³/sb = 3 my = 2.2 mz = 1n = 0.015
S = m/m
6.Hard
b = 5 my = 1 mn = 0.015, Q = 15 m³/s

A rectangular brickwork channel 5 m wide must carry 15 m³/s in uniform flow at a depth of 1 m. Manning n = 0.015. Find the required bed slope S (in m/m).

Q = 15 m³/sb = 5 my = 1 mn = 0.015
S = m/m

Answer key

  1. 1. V = 3.016 m/s
  2. 2. V = 1.899 m/s
  3. 3. Q = 12.18 m³/s
  4. 4. Q = 13.71 m³/s
  5. 5. S = 0.001962 m/m
  6. 6. S = 0.003171 m/m

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