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 = 0.4 mn = 0.014

Water flows uniformly 0.4 m deep in a rectangular unfinished concrete channel 1 m wide (Manning n = 0.014). The bed slope is S = 0.0008. Use Manning’s equation in SI units to find the mean velocity V.

b = 1 my = 0.4 mn = 0.014S = 0.0008
V = m/s
2.Easy
b = 3.5 my = 0.6 mn = 0.012

Water flows uniformly 0.6 m deep in a rectangular finished concrete channel 3.5 m wide (Manning n = 0.012). The bed slope is S = 0.003. Use Manning’s equation in SI units to find the mean velocity V.

b = 3.5 my = 0.6 mn = 0.012S = 0.003
V = m/s
3.Medium
b = 2 my = 2.3 mn = 0.014, S = 0.0015

A rectangular unfinished concrete channel is 2 m wide. Water flows uniformly 2.3 m deep. Manning n = 0.014 and the bed slope is S = 0.0015. Find the flow rate Q in m³/s.

b = 2 my = 2.3 mn = 0.014S = 0.0015
Q = m³/s
4.Medium
b = 3 my = 0.8 m1 : 1n = 0.014, S = 0.0015

A trapezoidal unfinished concrete channel has a bottom width of 3 m and side slopes of 1:1 (horizontal:vertical). Water flows uniformly 0.8 m deep. Manning n = 0.014 and the bed slope is S = 0.0015. Find the flow rate Q in m³/s.

b = 3 my = 0.8 mz = 1n = 0.014S = 0.0015
Q = m³/s
5.Hard
b = 2.5 my = 2.3 m1 : 1n = 0.012, Q = 24 m³/s

A trapezoidal finished concrete channel with a bottom width of 2.5 m and side slopes of 1:1 (horizontal:vertical) must carry 24 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 = 24 m³/sb = 2.5 my = 2.3 mz = 1n = 0.012
S = m/m
6.Hard
b = 6 my = 1.2 mn = 0.025, Q = 7.4 m³/s

A rectangular gravel channel 6 m wide must carry 7.4 m³/s in uniform flow at a depth of 1.2 m. Manning n = 0.025. Find the required bed slope S (in m/m).

Q = 7.4 m³/sb = 6 my = 1.2 mn = 0.025
S = m/m

Answer key

  1. 1. V = 0.7412 m/s
  2. 2. V = 2.668 m/s
  3. 3. Q = 10 m³/s
  4. 4. Q = 5.833 m³/s
  5. 5. S = 0.0005187 m/m
  6. 6. S = 0.0008109 m/m

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