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 my = 1.1 mn = 0.03

Water flows uniformly 1.1 m deep in a rectangular grass-lined earth channel 2 m wide (Manning n = 0.03). The bed slope is S = 0.0015. Use Manning’s equation in SI units to find the mean velocity V.

b = 2 my = 1.1 mn = 0.03S = 0.0015
V = m/s
2.Easy
b = 1 my = 1.1 mn = 0.025

Water flows uniformly 1.1 m deep in a rectangular gravel channel 1 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 = 1 my = 1.1 mn = 0.025S = 0.001
V = m/s
3.Medium
b = 5.5 my = 2.4 m1 : 1n = 0.03, S = 0.0008

A trapezoidal grass-lined earth channel has a bottom width of 5.5 m and side slopes of 1:1 (horizontal:vertical). Water flows uniformly 2.4 m deep. Manning n = 0.03 and the bed slope is S = 0.0008. Find the flow rate Q in m³/s.

b = 5.5 my = 2.4 mz = 1n = 0.03S = 0.0008
Q = m³/s
4.Medium
b = 4.5 my = 2.1 m1 : 1n = 0.03, S = 0.005

A trapezoidal grass-lined earth 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 = 0.03 and the bed slope is S = 0.005. Find the flow rate Q in m³/s.

b = 4.5 my = 2.1 mz = 1n = 0.03S = 0.005
Q = m³/s
5.Hard
D = 200 mmn = 0.013, V = 0.6 m/s

A concrete sewer with an inside diameter of 200 mm (Manning n = 0.013) must reach a self-cleansing velocity of 0.6 m/s when flowing just full. Find the minimum slope S (in m/m).

D = 200 mmn = 0.013V = 0.6 m/s
S = m/m
6.Hard
b = 4 my = 1.8 m1.5 : 1n = 0.022, Q = 38 m³/s

A trapezoidal clean earth channel with a bottom width of 4 m and side slopes of 1.5:1 (horizontal:vertical) must carry 38 m³/s in uniform flow at a depth of 1.8 m. Manning n = 0.022. Find the required bed slope S (in m/m).

Q = 38 m³/sb = 4 my = 1.8 mz = 1.5n = 0.022
S = m/m

Answer key

  1. 1. V = 0.8389 m/s
  2. 2. V = 0.6207 m/s
  3. 3. Q = 23.87 m³/s
  4. 4. Q = 39.46 m³/s
  5. 5. S = 0.003303 m/m
  6. 6. S = 0.00399 m/m

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