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 = 0.6 mn = 0.025

Water flows uniformly 0.6 m deep in a rectangular gravel channel 2.5 m wide (Manning n = 0.025). The bed slope is S = 0.002. Use Manning’s equation in SI units to find the mean velocity V.

b = 2.5 my = 0.6 mn = 0.025S = 0.002
V = m/s
2.Easy
b = 5.5 my = 1.8 mn = 0.015

Water flows uniformly 1.8 m deep in a rectangular brickwork channel 5.5 m wide (Manning n = 0.015). The bed slope is S = 0.001. Use Manning’s equation in SI units to find the mean velocity V.

b = 5.5 my = 1.8 mn = 0.015S = 0.001
V = m/s
3.Medium
b = 4.5 my = 2.1 m1 : 1n = 0.015, S = 0.001

A trapezoidal brickwork channel has a bottom width of 4.5 m and side slopes of 1:1 (horizontal:vertical). Water flows uniformly 2.1 m deep. Manning n = 0.015 and the bed slope is S = 0.001. Find the flow rate Q in m³/s.

b = 4.5 my = 2.1 mz = 1n = 0.015S = 0.001
Q = m³/s
4.Medium
b = 2.5 my = 2.3 mn = 0.012, S = 0.002

A rectangular finished concrete channel is 2.5 m wide. Water flows uniformly 2.3 m deep. Manning n = 0.012 and the bed slope is S = 0.002. Find the flow rate Q in m³/s.

b = 2.5 my = 2.3 mn = 0.012S = 0.002
Q = m³/s
5.Hard
b = 4.5 my = 1.8 m2 : 1n = 0.015, Q = 24 m³/s

A trapezoidal brickwork channel with a bottom width of 4.5 m and side slopes of 2:1 (horizontal:vertical) must carry 24 m³/s in uniform flow at a depth of 1.8 m. Manning n = 0.015. Find the required bed slope S (in m/m).

Q = 24 m³/sb = 4.5 my = 1.8 mz = 2n = 0.015
S = m/m
6.Hard
b = 3 my = 0.8 m1.5 : 1n = 0.022, Q = 3 m³/s

A trapezoidal clean earth channel with a bottom width of 3 m and side slopes of 1.5:1 (horizontal:vertical) must carry 3 m³/s in uniform flow at a depth of 0.8 m. Manning n = 0.022. Find the required bed slope S (in m/m).

Q = 3 m³/sb = 3 my = 0.8 mz = 1.5n = 0.022
S = m/m

Answer key

  1. 1. V = 0.9799 m/s
  2. 2. V = 2.23 m/s
  3. 3. Q = 35.3 m³/s
  4. 4. Q = 18.62 m³/s
  5. 5. S = 0.0004992 m/m
  6. 6. S = 0.0008145 m/m

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