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 = 2.5 my = 0.4 mn = 0.012

Water flows uniformly 0.4 m deep in a rectangular finished concrete channel 2.5 m wide (Manning n = 0.012). The bed slope is S = 0.0015. Use Manning’s equation in SI units to find the mean velocity V.

b = 2.5 my = 0.4 mn = 0.012S = 0.0015
V = m/s
2.Easy
b = 2 my = 1.7 mn = 0.022

Water flows uniformly 1.7 m deep in a rectangular clean earth channel 2 m wide (Manning n = 0.022). The bed slope is S = 0.004. Use Manning’s equation in SI units to find the mean velocity V.

b = 2 my = 1.7 mn = 0.022S = 0.004
V = m/s
3.Medium
b = 3 my = 0.9 mn = 0.012, S = 0.0015

A rectangular finished concrete channel is 3 m wide. Water flows uniformly 0.9 m deep. Manning n = 0.012 and the bed slope is S = 0.0015. Find the flow rate Q in m³/s.

b = 3 my = 0.9 mn = 0.012S = 0.0015
Q = m³/s
4.Medium
b = 6 my = 1 m1.5 : 1n = 0.025, S = 0.0008

A trapezoidal gravel channel has a bottom width of 6 m and side slopes of 1.5:1 (horizontal:vertical). Water flows uniformly 1 m deep. Manning n = 0.025 and the bed slope is S = 0.0008. Find the flow rate Q in m³/s.

b = 6 my = 1 mz = 1.5n = 0.025S = 0.0008
Q = m³/s
5.Hard
b = 3 my = 2.4 m3 : 1n = 0.012, Q = 96 m³/s

A trapezoidal finished concrete channel with a bottom width of 3 m and side slopes of 3:1 (horizontal:vertical) must carry 96 m³/s in uniform flow at a depth of 2.4 m. Manning n = 0.012. Find the required bed slope S (in m/m).

Q = 96 m³/sb = 3 my = 2.4 mz = 3n = 0.012
S = m/m
6.Hard
b = 4 my = 0.5 mn = 0.022, Q = 1.4 m³/s

A rectangular clean earth channel 4 m wide must carry 1.4 m³/s in uniform flow at a depth of 0.5 m. Manning n = 0.022. Find the required bed slope S (in m/m).

Q = 1.4 m³/sb = 4 my = 0.5 mn = 0.022
S = m/m

Answer key

  1. 1. V = 1.456 m/s
  2. 2. V = 2.112 m/s
  3. 3. Q = 5.938 m³/s
  4. 4. Q = 7.195 m³/s
  5. 5. S = 0.001489 m/m
  6. 6. S = 0.0008047 m/m

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