Open-Channel Continuity

Q = A V = V b y (rectangle)

Steady continuity: discharge Q is the product of mean velocity and the flow area. For a rectangle A = b y. Combined with Manning it sizes channels. At a junction ΣQ_in = ΣQ_out if storage is neglected.

$Q$ (m³/s): Discharge
$A$ (m²): Area
$V$ (m/s): Mean velocity
$b$ (m): Width
$y$ (m): Depth

Step-by-step solved example

Rectangle b = 3.0 m, y = 1.2 m, V = 0.80 m/s. Q?

Q = AV with A = by for a rectangle.

1. Area
A = 3.0×1.2 = 3.60 m².
2. Q
Q = AV = 3.60×0.80 = 2.88 m³/s.
$Q = 2.88 m^{3} / s$

Answer: 2.88 m³/s

10 practice questions

0/10 correct

1.For a rectangle A =

2.Trapezoid A =

3.If Q is fixed and A halves, V

4.At a branch with no storage, ΣQ_in

5.Units: V in m/s, A in m² → Q in

6.A circle flowing full: A =

7.Wide rectangle with y << b: A ≈

8.Unsteady continuity on a reach includes

9.b = 2 m, y = 0.5 m, Q = 1.0 m³/s. V =

10.Manning plus continuity gives Q =