Information about the Vertical Velocity Profile: Difference between revisions
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==Information about the Vertical Velocity Profile== | ==Information about the Vertical Velocity Profile== | ||
This applet displays a vertical and logarithmical profile of current velocity in an infinitely wide channel. | This applet displays a vertical and logarithmical profile of current velocity in an infinitely wide [[channel]]. | ||
A watercolumn is divided into several horizontal layers. The applet calculates for each layer a horizontal velocity v which is a function of z, the height of each layer relative to the bottom. | A watercolumn is divided into several horizontal layers. The applet calculates for each layer a horizontal velocity v which is a function of z, the height of each layer relative to the bottom. | ||
==Input measures== | ==Input measures== | ||
Bottom Gradient and Water Depth do not need any explanation. | Bottom [[Gradient]] and [[Water depth|Water Depth]] do not need any explanation. | ||
* The Strickler Value defines the bottom shear stress. A higher value stands for a lower stress. | * The Strickler Value defines the bottom [[shear stress]]. A higher value stands for a lower stress. | ||
:Examples: | :Examples: | ||
:sand (Elbe and Weser Estuary): approx. 48 m**(1/3) s**(-1/2) | :sand (Elbe and Weser [[Estuary]]): approx. 48 m**(1/3) s**(-1/2) | ||
:wild creek with rubble: approx. 20 m**(1/3) s**(-1/2) | :wild creek with rubble: approx. 20 m**(1/3) s**(-1/2) | ||
* deltaZ: The watercolumn is divided into several horizontal layers. The user specifies the vertical distance between neighboured layers via the input field deltaZ. For a correct graphical display deltaZ should be smaller than the Log Law's Z0 value. | * deltaZ: The watercolumn is divided into several horizontal layers. The user specifies the vertical distance between neighboured layers via the input field deltaZ. For a correct graphical display deltaZ should be smaller than the Log Law's Z0 value. | ||
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==Output measures== | ==Output measures== | ||
* In this model there is a layer directly above the bottom where the velocity is zero. Log Law's Z0 is the height of this layer. Log Law's Z0 depends on Water Depth and Strickler Value. | * In this [[model]] there is a layer directly above the bottom where the velocity is zero. Log Law's Z0 is the height of this layer. Log Law's Z0 depends on [[Water depth|Water Depth]] and Strickler Value. | ||
* V(H) shows the velocity at the water surface. | * V(H) shows the velocity at the [[water surface]]. | ||
* V DepthAveraged stands for the depth-averaged velocity. The calculation of the average includes the layers with v=0 m/s as well as the layers with v>0 m/s. The calculation is more accurate by using smaller values of deltaZ. | * V DepthAveraged stands for the depth-averaged velocity. The calculation of the average includes the layers with v=0 m/s as well as the layers with v>0 m/s. The calculation is more accurate by using smaller values of deltaZ. | ||
* The result field at the lower right corner of the applet displays a line with pairs (velocity v and height relative to the bottom z) | * The result field at the lower right corner of the applet displays a line with pairs (velocity v and height relative to the bottom z) | ||
Latest revision as of 09:30, 21 October 2022
Author: P. Schade
Information about the Vertical Velocity Profile
This applet displays a vertical and logarithmical profile of current velocity in an infinitely wide channel. A watercolumn is divided into several horizontal layers. The applet calculates for each layer a horizontal velocity v which is a function of z, the height of each layer relative to the bottom.
Input measures
Bottom Gradient and Water Depth do not need any explanation.
- The Strickler Value defines the bottom shear stress. A higher value stands for a lower stress.
- Examples:
- sand (Elbe and Weser Estuary): approx. 48 m**(1/3) s**(-1/2)
- wild creek with rubble: approx. 20 m**(1/3) s**(-1/2)
- deltaZ: The watercolumn is divided into several horizontal layers. The user specifies the vertical distance between neighboured layers via the input field deltaZ. For a correct graphical display deltaZ should be smaller than the Log Law's Z0 value.
Output measures
- In this model there is a layer directly above the bottom where the velocity is zero. Log Law's Z0 is the height of this layer. Log Law's Z0 depends on Water Depth and Strickler Value.
- V(H) shows the velocity at the water surface.
- V DepthAveraged stands for the depth-averaged velocity. The calculation of the average includes the layers with v=0 m/s as well as the layers with v>0 m/s. The calculation is more accurate by using smaller values of deltaZ.
- The result field at the lower right corner of the applet displays a line with pairs (velocity v and height relative to the bottom z)
Physics
Calculation of the horizontal velocity v
- v = sqrt(g * WaterDepth * BottomGradient) / Kappa * ln(z/z0)
- g = 9.81 m/s: gravity
- Kappa = 0.41: Karman constant
- z0 : zero Level of the logarithmic law with
- z0 = (12./30.*WaterDepth) / 10**(StricklerValue * WaterDepth**(1/6) / 18))
The user should consider that this profile is only an approximation. Especially near the bottom the formula simplifies a little bit.
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