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 = 3 my = 2.5 mn = 0.014

Water flows uniformly 2.5 m deep in a rectangular unfinished concrete channel 3 m wide (Manning n = 0.014). The bed slope is S = 0.0015. Use Manning’s equation in SI units to find the mean velocity V.

b = 3 my = 2.5 mn = 0.014S = 0.0015
V = m/s
2.Easy
b = 4.5 my = 0.8 mn = 0.014

Water flows uniformly 0.8 m deep in a rectangular unfinished concrete channel 4.5 m wide (Manning n = 0.014). The bed drops 0.5 m per kilometre. Use Manning’s equation in SI units to find the mean velocity V.

b = 4.5 my = 0.8 mn = 0.014drop = 0.5 m/km
V = m/s
3.Medium
b = 5 my = 2.4 mn = 0.015, S = 0.0015

A rectangular brickwork channel is 5 m wide. Water flows uniformly 2.4 m deep. Manning n = 0.015 and the bed slope is S = 0.0015. Find the flow rate Q in m³/s.

b = 5 my = 2.4 mn = 0.015S = 0.0015
Q = m³/s
4.Medium
b = 1.5 my = 1.5 mn = 0.014, S = 0.0015

A rectangular unfinished concrete channel is 1.5 m wide. Water flows uniformly 1.5 m deep. Manning n = 0.014 and the bed slope is S = 0.0015. Find the flow rate Q in m³/s.

b = 1.5 my = 1.5 mn = 0.014S = 0.0015
Q = m³/s
5.Hard
b = 4.5 my = 2.2 mn = 0.012, Q = 20 m³/s

A rectangular finished concrete channel 4.5 m wide must carry 20 m³/s in uniform flow at a depth of 2.2 m. Manning n = 0.012. Find the required bed slope S (in m/m).

Q = 20 m³/sb = 4.5 my = 2.2 mn = 0.012
S = m/m
6.Hard
b = 2.5 my = 0.6 mn = 0.025, Q = 0.93 m³/s

A rectangular gravel channel 2.5 m wide must carry 0.93 m³/s in uniform flow at a depth of 0.6 m. Manning n = 0.025. Find the required bed slope S (in m/m).

Q = 0.93 m³/sb = 2.5 my = 0.6 mn = 0.025
S = m/m

Answer key

  1. 1. V = 2.65 m/s
  2. 2. V = 1.124 m/s
  3. 3. Q = 35.46 m³/s
  4. 4. Q = 3.921 m³/s
  5. 5. S = 0.0005099 m/m
  6. 6. S = 0.0008007 m/m

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