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 mn = 0.022

Water flows uniformly 1 m deep in a rectangular clean earth channel 2 m wide (Manning n = 0.022). The bed slope is S = 0.005. Use Manning’s equation in SI units to find the mean velocity V.

b = 2 my = 1 mn = 0.022S = 0.005
V = m/s
2.Easy
b = 4.5 my = 1 mn = 0.025

Water flows uniformly 1 m deep in a rectangular gravel channel 4.5 m wide (Manning n = 0.025). The bed slope is S = 0.0005. Use Manning’s equation in SI units to find the mean velocity V.

b = 4.5 my = 1 mn = 0.025S = 0.0005
V = m/s
3.Medium
b = 4 my = 1.7 m1 : 1n = 0.015, S = 0.001

A trapezoidal brickwork channel has a bottom width of 4 m and side slopes of 1:1 (horizontal:vertical). Water flows uniformly 1.7 m deep. Manning n = 0.015 and the bed slope is S = 0.001. Find the flow rate Q in m³/s.

b = 4 my = 1.7 mz = 1n = 0.015S = 0.001
Q = m³/s
4.Medium
b = 2 my = 2.1 mn = 0.03, S = 0.0015

A rectangular grass-lined earth channel is 2 m wide. Water flows uniformly 2.1 m deep. Manning n = 0.03 and the bed slope is S = 0.0015. Find the flow rate Q in m³/s.

b = 2 my = 2.1 mn = 0.03S = 0.0015
Q = m³/s
5.Hard
b = 6 my = 0.8 mn = 0.015, Q = 17 m³/s

A rectangular brickwork channel 6 m wide must carry 17 m³/s in uniform flow at a depth of 0.8 m. Manning n = 0.015. Find the required bed slope S (in m/m).

Q = 17 m³/sb = 6 my = 0.8 mn = 0.015
S = m/m
6.Hard
b = 5 my = 1.6 m1 : 1n = 0.022, Q = 33 m³/s

A trapezoidal clean earth channel with a bottom width of 5 m and side slopes of 1:1 (horizontal:vertical) must carry 33 m³/s in uniform flow at a depth of 1.6 m. Manning n = 0.022. Find the required bed slope S (in m/m).

Q = 33 m³/sb = 5 my = 1.6 mz = 1n = 0.022
S = m/m

Answer key

  1. 1. V = 2.025 m/s
  2. 2. V = 0.7 m/s
  3. 3. Q = 21.77 m³/s
  4. 4. Q = 4.182 m³/s
  5. 5. S = 0.005208 m/m
  6. 6. S = 0.004119 m/m

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