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 = 5 my = 1.8 mn = 0.025

Water flows uniformly 1.8 m deep in a rectangular gravel channel 5 m wide (Manning n = 0.025). The bed slope is S = 0.001. Use Manning’s equation in SI units to find the mean velocity V.

b = 5 my = 1.8 mn = 0.025S = 0.001
V = m/s
2.Easy
b = 5 my = 1.5 mn = 0.012

Water flows uniformly 1.5 m deep in a rectangular finished concrete channel 5 m wide (Manning n = 0.012). The bed drops 0.8 m per kilometre. Use Manning’s equation in SI units to find the mean velocity V.

b = 5 my = 1.5 mn = 0.012drop = 0.8 m/km
V = m/s
3.Medium
b = 1.5 my = 1.8 m1.5 : 1n = 0.03, S = 0.001

A trapezoidal grass-lined earth channel has a bottom width of 1.5 m and side slopes of 1.5:1 (horizontal:vertical). Water flows uniformly 1.8 m deep. Manning n = 0.03 and the bed slope is S = 0.001. Find the flow rate Q in m³/s.

b = 1.5 my = 1.8 mz = 1.5n = 0.03S = 0.001
Q = m³/s
4.Medium
b = 3 my = 1.4 m1 : 1n = 0.022, S = 0.0015

A trapezoidal clean earth channel has a bottom width of 3 m and side slopes of 1:1 (horizontal:vertical). Water flows uniformly 1.4 m deep. Manning n = 0.022 and the bed slope is S = 0.0015. Find the flow rate Q in m³/s.

b = 3 my = 1.4 mz = 1n = 0.022S = 0.0015
Q = m³/s
5.Hard
b = 3 my = 2.3 mn = 0.025, Q = 8.2 m³/s

A rectangular gravel channel 3 m wide must carry 8.2 m³/s in uniform flow at a depth of 2.3 m. Manning n = 0.025. Find the required bed slope S (in m/m).

Q = 8.2 m³/sb = 3 my = 2.3 mn = 0.025
S = m/m
6.Hard
D = 250 mmn = 0.013, V = 0.75 m/s

A concrete sewer with an inside diameter of 250 mm (Manning n = 0.013) must reach a self-cleansing velocity of 0.75 m/s when flowing just full. Find the minimum slope S (in m/m).

D = 250 mmn = 0.013V = 0.75 m/s
S = m/m

Answer key

  1. 1. V = 1.304 m/s
  2. 2. V = 2.258 m/s
  3. 3. Q = 7.68 m³/s
  4. 4. Q = 9.997 m³/s
  5. 5. S = 0.001004 m/m
  6. 6. S = 0.003833 m/m

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