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 = 6 my = 0.7 mn = 0.03

Water flows uniformly 0.7 m deep in a rectangular grass-lined earth channel 6 m wide (Manning n = 0.03). The bed drops 5 m per kilometre. Use Manning’s equation in SI units to find the mean velocity V.

b = 6 my = 0.7 mn = 0.03drop = 5 m/km
V = m/s
2.Easy
b = 4 my = 0.9 mn = 0.022

Water flows uniformly 0.9 m deep in a rectangular clean earth channel 4 m wide (Manning n = 0.022). The bed drops 3 m per kilometre. Use Manning’s equation in SI units to find the mean velocity V.

b = 4 my = 0.9 mn = 0.022drop = 3 m/km
V = m/s
3.Medium
b = 4 my = 0.9 mn = 0.025, S = 0.0005

A rectangular gravel channel is 4 m wide. Water flows uniformly 0.9 m deep. Manning n = 0.025 and the bed slope is S = 0.0005. Find the flow rate Q in m³/s.

b = 4 my = 0.9 mn = 0.025S = 0.0005
Q = m³/s
4.Medium
b = 4 my = 2.3 mn = 0.03, S = 0.004

A rectangular grass-lined earth channel is 4 m wide. Water flows uniformly 2.3 m deep. Manning n = 0.03 and the bed slope is S = 0.004. Find the flow rate Q in m³/s.

b = 4 my = 2.3 mn = 0.03S = 0.004
Q = m³/s
5.Hard
D = 375 mmn = 0.013, V = 0.75 m/s

A concrete sewer with an inside diameter of 375 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 = 375 mmn = 0.013V = 0.75 m/s
S = m/m
6.Hard
b = 5.5 my = 2.4 m2 : 1n = 0.022, Q = 67 m³/s

A trapezoidal clean earth channel with a bottom width of 5.5 m and side slopes of 2:1 (horizontal:vertical) must carry 67 m³/s in uniform flow at a depth of 2.4 m. Manning n = 0.022. Find the required bed slope S (in m/m).

Q = 67 m³/sb = 5.5 my = 2.4 mz = 2n = 0.022
S = m/m

Answer key

  1. 1. V = 1.616 m/s
  2. 2. V = 1.812 m/s
  3. 3. Q = 2.343 m³/s
  4. 4. Q = 20.29 m³/s
  5. 5. S = 0.002232 m/m
  6. 6. S = 0.002029 m/m

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