Culvert formula (Water Overlay): Difference between revisions

Revision as of 09:55, 6 October 2020

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

The actual 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})

The radius of the culvert:

r={\frac {D}{2}}

The height of the water column at either end of the culvert, relative to the culvert, is calculated:

w_{l}=\max(0,w_{l}-B_{c})

w_{r}=\max(0,w_{r}-B_{c})

Flow depth d is:

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

The loss coefficient for the culvert is calculated:

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

The hydraulic radius R_h is calculated using the formula's in the image on the right.

The potential flow through the culvert is then calculated:

C=U\cdot K\cdot {\sqrt {2g\cdot abs(w_{l}-w_{r})}}

Finally the actual amount of water flow is calculated:

\Delta f={\frac {\Delta t\cdot C}{\Delta x}}

Where:

$D$ = The CULVERT_DIAMETER attribute of the culvert.
$T_{c}$ = The CULVERT_THRESHOLD attribute of the culvert.
$B_{c}$ = The surface height of the base of the culvert.
$w_{l}eft$ = The water level on the left side of the culvert, relative to datum.
$w_{r}ight$ = The water level on the right side of the culvert, relative to datum.
$R_{h}$ = The hydraulic radius in the culvert^[1].
$K$ = Flow area, based on the height of the water in the (circular) culvert.
$g$ = Acceleration factor of GRAVITY, defined for the Water Overlay.
$L$ = 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.
$C$ = The potential rate of water flow through the culvert.
$\Delta f$ = The water flow which takes place.
$\Delta t$ = Computational timestep.
$\Delta x$ = Cell size.

References

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

Models

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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 • Results • Simulation data

[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 26: / Line 26: @@
 Where:
-* D = The [[Culvert diameter (Water Overlay)|CULVERT_DIAMETER]] attribute of the culvert.
+* <math>D</math> = The [[Culvert diameter (Water Overlay)|CULVERT_DIAMETER]] attribute of the culvert.
-* T<sub>c</sub> = The [[Culvert threshold (Water Overlay)|CULVERT_THRESHOLD]] attribute of the culvert.
+* <math>T_c</math> = The [[Culvert threshold (Water Overlay)|CULVERT_THRESHOLD]] attribute of the culvert.
-* B<sub>c</sub> = The [[Terrain height (Water Overlay)|surface height]] of the base of the culvert.
+* <math>B_c</math> = The [[Terrain height (Water Overlay)|surface height]] of the base of the culvert.
-* w<sub>left</sub> = The [[Surface water level formula (Water Overlay)|water level]] on the left side of the culvert, relative to {{datum}}.
+* <math>w_left</math> = The [[Surface water level formula (Water Overlay)|water level]] on the left side of the culvert, relative to {{datum}}.
-* w<sub>right</sub> = The [[Surface water level formula (Water Overlay)|water level]] on the right side of the culvert, relative to {{datum}}.
+* <math>w_right</math> = The [[Surface water level formula (Water Overlay)|water level]] on the right side of the culvert, relative to {{datum}}.
-* R<sub>h</sub> = The hydraulic radius in the culvert<ref name="hydradius"/>.
+* <math>R_h</math> = The hydraulic radius in the culvert<ref name="hydradius"/>.
-* K = Flow area, based on the height of the water in the (circular) culvert.
+* <math>K</math> = Flow area, based on the height of the water in the (circular) culvert.
-* g = Acceleration factor of [[Gravity (Water Overlay)|GRAVITY]], defined for the Water Overlay.
+* <math>g</math> = Acceleration factor of [[Gravity (Water Overlay)|GRAVITY]], defined for the Water Overlay.
-* L = The length of the culvert, calculated as the distance between the culvert's endpoints.
+* <math>L</math> = The length of the culvert, calculated as the distance between the culvert's endpoints.
-* U = Loss coefficient for  culverts.
+* <math>U</math> = Loss coefficient for  culverts.
-* n = The [[Culvert n (Water Overlay)|CULVERT_N]] attribute of the culvert.
+* <math>n</math> = The [[Culvert n (Water Overlay)|CULVERT_N]] attribute of the culvert.
-* C = The potential rate of water flow through the culvert.
+* <math>C</math> = The potential rate of water flow through the culvert.
-* Δf = The water flow which takes place.
+* <math>\Delta f</math> = The water flow which takes place.
-* Δt = Computational timestep.
+* <math>\Delta t</math> = Computational timestep.
-* Δx = Cell size.
+* <math>\Delta x</math> = Cell size.
 ==Related==

Culvert formula (Water Overlay): Difference between revisions

Revision as of 09:55, 6 October 2020

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References

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