Culvert formula (Water Overlay): Difference between revisions

Latest revision as of 12:39, 12 November 2026

Flow through culverts is based on an open channel flow calculation.

The actual datum height of the culvert is at least the height of the terrain on either end of the culvert and the provided threshold height:

B_{c} = \max (T_{c}, B_{l}, B_{r})

For circular culverts, the flow height $h_{f}$ is:

h_{f} = \max (0, \min (D, \max (w_{l}, w_{r}) - B_{c}))

For rectangular culverts, the flow height $h_{f}$ is:

h_{f} = \max (0, \min (H, \max (w_{l}, w_{r}) - B_{c}))

The loss coefficient for the culvert is calculated:

U = \sqrt{\frac{1}{1 + \frac{2 g \cdot n^{2} \cdot l e n g t h}{R_{h}^{\frac{4}{3}}}}}

The hydraulic radius $R_{h}$ is calculated as:

R_{h} = \frac{A}{P_{w}}

For circular culverts, the flow area $A$ and the wetted perimeter $P_{w}$ are calculated using the formulas in the image below.

Where the radius of the culvert:

r = \frac{D}{2}

For rectangular culverts, the flow area and wetted perimeter are calculated as follows:

A = h_{f} \cdot D

$P_{w} = {\begin{matrix} D + 2 h_{f}, & if h_{f} < H \\ 2 D + 2 H, & if h_{f} \geq H \end{matrix}$

The potential flow through the culvert is then calculated:

Q = U \cdot K \cdot \sqrt{2 g \cdot ‖ w_{l} - w_{r} ‖}

Finally the actual amount of water flow is calculated:

Δ f = \frac{Δ t \cdot Q}{Δ x}

Where:

$D$ = The CULVERT_DIAMETER attribute of the culvert, representing either the inside diameter of a circular culvert or the inside width of a rectangular culvert.
$H$ = The CULVERT_RECTANGULAR_HEIGHT attribute of the culvert, representing the inside height of a rectangular culvert.
$h_{f}$ = The (flow) height of the water inside the culvert.
$T_{c}$ = The CULVERT_THRESHOLD attribute of the culvert.
$B_{c}$ = The datum height of the base of the culvert.
$w_{l}$ = The water level on the left end of the culvert, relative to datum.
$w_{r}$ = The water level on the right end of the culvert, relative to datum.
$R_{h}$ = The hydraulic radius in the culvert^[1].
$P_{w}$ = The wetted perimeter.
$A$ = The flow area.
$K$ = Circular flow area, based on the height of the water in the (circular) culvert.
$g$ = the acceleration due to gravity, set to 9.80665.
$L$ = The length of the culvert, calculated as the distance between the culvert's endpoints.
$U$ = Loss coefficient for culverts.
$n$ = The CULVERT_N attribute of the culvert.
$Q$ = The potential rate of water flow through the culvert in $m^{3} s^{- 1}$ .
$Δ f$ = The water flow which takes place.
$Δ t$ = Computational timestep in seconds.
$Δ x$ = Cell size in meters.

The following topics are related to this formula.

Structures: Culvert
Models: Surface model

References

↑ Hydraulic Radius Equations Formulas Calculator ∙ Found at: https://www.ajdesigner.com/phphydraulicradius/hydraulic_radius_equation_pipe.php ∙ (last visited: 2019-02-11)

Models

Surface • Ground • Rain • Evapotranspiration • Infiltration • Elevation • Breach • Sewer • Storage • Tracer flow • Border • Order
Model formulas

Timestep • Season • Surface water level • Groundwater level
Flow formulas

Surface flow • Surface infiltration • Ground flow • Ground infiltration • Surface evaporation • Ground evaporation • Ground bottom flow
Hydraulic structure formulas

Culvert • Weir • Breach growth • Breach flow • Pump • Sewer Overflow • Inlet • Drainage
Related

Building attributes • Hydrological features • Hydraulic structures • Terrain attributes • Model attributes • Prequels • Results • Simulation data

[ref-hydradius-1] Hydraulic Radius Equations Formulas Calculator ∙ Found at: https://www.ajdesigner.com/phphydraulicradius/hydraulic_radius_equation_pipe.php ∙ (last visited: 2019-02-11)

[1]

@@ Line 5: / Line 5: @@
 For circular culverts, the flow height <math>h_f</math> is:
-: <math>h_f = \max(0,\min(D,\max (w_{l}, w_{r})-B_c)))</math>
+: <math>h_f = \max(0,\min(D,\max (w_{l}, w_{r})-B_c))</math>
-For rectangular culverts, the flow depth h is:
+For rectangular culverts, the flow height <math>h_f</math> is:
-: <math>h_f = \max(0,\min(H,\max (w_{l}, w_{r})-B_c)))</math>
+: <math>h_f = \max(0,\min(H,\max (w_{l}, w_{r})-B_c))</math>
 The loss coefficient for the culvert is calculated:
@@ Line 15: / Line 15: @@
 : <math>R_h = \frac{A}{P_w}</math>
-For circular culverts, the flow area <math>A</math> and the wetted perimeter <math>P_w</math> is calculated using the formula's in the image below.
+For circular culverts, the flow area <math>A</math> and the wetted perimeter <math>P_w</math> are calculated using the formulas in the image below.
 [[File:Hydraulic_radius.png|left]]{{clear}}
 Where the radius of the culvert:
 : <math>r = \frac{D}{2}</math>
-For rectangular culverts, the flow area and wetted perimeter is calculated as followed:
+For rectangular culverts, the flow area and wetted perimeter are calculated as follows:
 : <math>A = h_f \cdot D</math>
 <math>
@@ Line 45: / Line 45: @@
 * <math>w_{r}</math> = The [[Surface water level formula (Water Overlay)|water level]] on the right end of the culvert, relative to {{datum}}.
 * <math>R_h</math> = The hydraulic radius in the culvert{{ref|hydradius}}.
-* <math>R_w</math> = The wetted perimeter.
+* <math>P_w</math> = The wetted perimeter.
 * <math>A</math> = The flow area.
 * <math>K</math> = Circular flow area, based on the height of the water in the (circular) culvert.

Culvert formula (Water Overlay): Difference between revisions

Latest revision as of 12:39, 12 November 2026

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