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 = 1.5 my = 0.7 mn = 0.012

Water flows uniformly 0.7 m deep in a rectangular finished concrete channel 1.5 m wide (Manning n = 0.012). The bed slope is S = 0.004. Use Manning’s equation in SI units to find the mean velocity V.

b = 1.5 my = 0.7 mn = 0.012S = 0.004
V = m/s
2.Easy
b = 5 my = 2.3 mn = 0.022

Water flows uniformly 2.3 m deep in a rectangular clean earth channel 5 m wide (Manning n = 0.022). The bed slope is S = 0.0008. Use Manning’s equation in SI units to find the mean velocity V.

b = 5 my = 2.3 mn = 0.022S = 0.0008
V = m/s
3.Medium
b = 4 my = 1.3 mn = 0.015, S = 0.003

A rectangular brickwork channel is 4 m wide. Water flows uniformly 1.3 m deep. Manning n = 0.015 and the bed slope is S = 0.003. Find the flow rate Q in m³/s.

b = 4 my = 1.3 mn = 0.015S = 0.003
Q = m³/s
4.Medium
b = 2.5 my = 2.2 mn = 0.012, S = 0.001

A rectangular finished concrete channel is 2.5 m wide. Water flows uniformly 2.2 m deep. Manning n = 0.012 and the bed slope is S = 0.001. Find the flow rate Q in m³/s.

b = 2.5 my = 2.2 mn = 0.012S = 0.001
Q = m³/s
5.Hard
b = 2.5 my = 1.3 mn = 0.03, Q = 1.8 m³/s

A rectangular grass-lined earth channel 2.5 m wide must carry 1.8 m³/s in uniform flow at a depth of 1.3 m. Manning n = 0.03. Find the required bed slope S (in m/m).

Q = 1.8 m³/sb = 2.5 my = 1.3 mn = 0.03
S = m/m
6.Hard
b = 6 my = 0.9 m1.5 : 1n = 0.022, Q = 11 m³/s

A trapezoidal clean earth channel with a bottom width of 6 m and side slopes of 1.5:1 (horizontal:vertical) must carry 11 m³/s in uniform flow at a depth of 0.9 m. Manning n = 0.022. Find the required bed slope S (in m/m).

Q = 11 m³/sb = 6 my = 0.9 mz = 1.5n = 0.022
S = m/m

Answer key

  1. 1. V = 2.677 m/s
  2. 2. V = 1.45 m/s
  3. 3. Q = 16.2 m³/s
  4. 4. Q = 12.46 m³/s
  5. 5. S = 0.0005034 m/m
  6. 6. S = 0.002091 m/m

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