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 = 2.3 mn = 0.015

Water flows uniformly 2.3 m deep in a rectangular brickwork channel 1 m wide (Manning n = 0.015). The bed drops 4 m per kilometre. Use Manning’s equation in SI units to find the mean velocity V.

b = 1 my = 2.3 mn = 0.015drop = 4 m/km
V = m/s
2.Easy
b = 4 my = 1.1 mn = 0.025

Water flows uniformly 1.1 m deep in a rectangular gravel channel 4 m wide (Manning n = 0.025). The bed slope is S = 0.0015. Use Manning’s equation in SI units to find the mean velocity V.

b = 4 my = 1.1 mn = 0.025S = 0.0015
V = m/s
3.Medium
b = 3.5 my = 1.4 m1 : 1n = 0.014, S = 0.0015

A trapezoidal unfinished concrete channel has a bottom width of 3.5 m and side slopes of 1:1 (horizontal:vertical). Water flows uniformly 1.4 m deep. Manning n = 0.014 and the bed slope is S = 0.0015. Find the flow rate Q in m³/s.

b = 3.5 my = 1.4 mz = 1n = 0.014S = 0.0015
Q = m³/s
4.Medium
b = 6 my = 1.2 m1 : 1n = 0.025, S = 0.001

A trapezoidal gravel channel has a bottom width of 6 m and side slopes of 1:1 (horizontal:vertical). Water flows uniformly 1.2 m deep. Manning n = 0.025 and the bed slope is S = 0.001. Find the flow rate Q in m³/s.

b = 6 my = 1.2 mz = 1n = 0.025S = 0.001
Q = m³/s
5.Hard
b = 2 my = 1.8 m1.5 : 1n = 0.015, Q = 25 m³/s

A trapezoidal brickwork channel with a bottom width of 2 m and side slopes of 1.5:1 (horizontal:vertical) must carry 25 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 = 25 m³/sb = 2 my = 1.8 mz = 1.5n = 0.015
S = m/m
6.Hard
b = 4.5 my = 1.1 mn = 0.014, Q = 6.5 m³/s

A rectangular unfinished concrete channel 4.5 m wide must carry 6.5 m³/s in uniform flow at a depth of 1.1 m. Manning n = 0.014. Find the required bed slope S (in m/m).

Q = 6.5 m³/sb = 4.5 my = 1.1 mn = 0.014
S = m/m

Answer key

  1. 1. V = 2.33 m/s
  2. 2. V = 1.233 m/s
  3. 3. Q = 17.95 m³/s
  4. 4. Q = 10.34 m³/s
  5. 5. S = 0.001974 m/m
  6. 6. S = 0.000506 m/m

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