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 = 2.1 mn = 0.025

Water flows uniformly 2.1 m deep in a rectangular gravel channel 6 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 = 6 my = 2.1 mn = 0.025S = 0.002
V = m/s
2.Easy
b = 3.5 my = 2 mn = 0.025

Water flows uniformly 2 m deep in a rectangular gravel channel 3.5 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 = 3.5 my = 2 mn = 0.025S = 0.0015
V = m/s
3.Medium
b = 2.5 my = 1.4 mn = 0.022, S = 0.0008

A rectangular clean earth channel is 2.5 m wide. Water flows uniformly 1.4 m deep. Manning n = 0.022 and the bed slope is S = 0.0008. Find the flow rate Q in m³/s.

b = 2.5 my = 1.4 mn = 0.022S = 0.0008
Q = m³/s
4.Medium
b = 2.5 my = 1 mn = 0.025, S = 0.005

A rectangular gravel channel is 2.5 m wide. Water flows uniformly 1 m deep. Manning n = 0.025 and the bed slope is S = 0.005. Find the flow rate Q in m³/s.

b = 2.5 my = 1 mn = 0.025S = 0.005
Q = m³/s
5.Hard
b = 4.5 my = 2.2 m2 : 1n = 0.015, Q = 45 m³/s

A trapezoidal brickwork channel with a bottom width of 4.5 m and side slopes of 2:1 (horizontal:vertical) must carry 45 m³/s in uniform flow at a depth of 2.2 m. Manning n = 0.015. Find the required bed slope S (in m/m).

Q = 45 m³/sb = 4.5 my = 2.2 mz = 2n = 0.015
S = m/m
6.Hard
b = 2 my = 1.3 m1 : 1n = 0.022, Q = 7.2 m³/s

A trapezoidal clean earth channel with a bottom width of 2 m and side slopes of 1:1 (horizontal:vertical) must carry 7.2 m³/s in uniform flow at a depth of 1.3 m. Manning n = 0.022. Find the required bed slope S (in m/m).

Q = 7.2 m³/sb = 2 my = 1.3 mz = 1n = 0.022
S = m/m

Answer key

  1. 1. V = 2.059 m/s
  2. 2. V = 1.48 m/s
  3. 3. Q = 3.412 m³/s
  4. 4. Q = 4.779 m³/s
  5. 5. S = 0.0007845 m/m
  6. 6. S = 0.001981 m/m

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