Set down for Regular Waves Solution

STEP 0: Pre-Calculation Summary
Formula Used
Mean Water Surface Elevation = (-1/8)*((Wave Height^2*(2*pi/Wavelength))/(sinh(4*pi*Water Depth/Wavelength)))
η' = (-1/8)*((H^2*(2*pi/λ))/(sinh(4*pi*d/λ)))
This formula uses 1 Constants, 1 Functions, 4 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Functions Used
sinh - The hyperbolic sine function, also known as the sinh function, is a mathematical function that is defined as the hyperbolic analogue of the sine function., sinh(Number)
Variables Used
Mean Water Surface Elevation - (Measured in Meter) - Mean Water Surface Elevation about still-water level.
Wave Height - (Measured in Meter) - Wave Height of a surface wave is the difference between the elevations of a crest and a neighboring trough.
Wavelength - (Measured in Meter) - Wavelength can be defined as the distance between two successive crests or troughs of a wave.
Water Depth - (Measured in Meter) - Water Depth of the considered catchment. Water depth means the depth as measured from the water level to the bottom of the considered water body.
STEP 1: Convert Input(s) to Base Unit
Wave Height: 3 Meter --> 3 Meter No Conversion Required
Wavelength: 26.8 Meter --> 26.8 Meter No Conversion Required
Water Depth: 1.05 Meter --> 1.05 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
η' = (-1/8)*((H^2*(2*pi/λ))/(sinh(4*pi*d/λ))) --> (-1/8)*((3^2*(2*pi/26.8))/(sinh(4*pi*1.05/26.8)))
Evaluating ... ...
η' = -0.51466840656291
STEP 3: Convert Result to Output's Unit
-0.51466840656291 Meter --> No Conversion Required
FINAL ANSWER
-0.51466840656291 -0.514668 Meter <-- Mean Water Surface Elevation
(Calculation completed in 00.004 seconds)

Credits

Created by Mithila Muthamma PA
Coorg Institute of Technology (CIT), Coorg
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20 Wave Setup Calculators

Wave Height given Mean Water Surface Elevation set down for Regular Waves
Go Wave Height = -sqrt(Mean Water Surface Elevation*8*sinh(4*pi*Water Depth/Wavelength)/(2*pi/Wavelength))
Set down for Regular Waves
Go Mean Water Surface Elevation = (-1/8)*((Wave Height^2*(2*pi/Wavelength))/(sinh(4*pi*Water Depth/Wavelength)))
Breaker Depth Index given Set-down at Breaker Point at Still-Water Shore Line
Go Breaker Depth Index = sqrt(8/3*((Water Depth at Breaking/(Setup at the Still-Water Shore Line-Set Down at the Breaker Point))-1))
Shoreward Displacement of Shoreline
Go Shoreward Displacement of the Shoreline = Setup at the Still-Water Shore Line/(tan(Beach Slope)-Cross-Shore Balance Momentum)
Wave Height given Cross Shore Component
Go Wave Height = sqrt(Cross-Shore Component/(3/16)*Water Density*[g]*Water Depth)
Setup at Mean Shoreline
Go Setup at the Mean Shoreline = Setup at the Still-Water Shore Line+(Cross-Shore Balance Momentum*Shoreward Displacement of the Shoreline)
Setup at Still-Water Shore Line
Go Setup at the Still-Water Shore Line = Set Down at the Breaker Point+(1/(1+(8/(3*Breaker Depth Index^2))))*Water Depth at Breaking
Water Depth at Breaking given Setdown at Breaker Point at Still-Water Shore Line
Go Water Depth at Breaking = (Setup at the Still-Water Shore Line-Set Down at the Breaker Point)/(1/1+(8/3*Breaker Depth Index^2))
Setdown at Breaker Point at Still-Water Shore Line
Go Set Down at the Breaker Point = Setup at the Still-Water Shore Line-(1/1+(8/3*Breaker Depth Index^2))*Water Depth at Breaking
Water Depth given Cross Shore Component
Go Water Depth = Cross-Shore Component/((3/16)*Water Density*[g]*Wave Height^2)
Deepwater Wave Height given Nonbreaking Upper Limit of Runup on Uniform Slope
Go Deepwater Wave Height = Wave Runup/((2*pi)^0.5*(pi/2*Beach Slope)^(1/4))
Cross-shore Component of Cross-shore directed Radiation Stress
Go Cross-Shore Component = (3/16)*Water Density*[g]*Water Depth*Wave Height^2
Nonbreaking Upper Limit of Runup on Uniform Slope
Go Wave Runup = Deepwater Wave Height*(2*pi)^0.5*(pi/2*Beach Slope)^(1/4)
Beach Slope given Nonbreaking Upper Limit of Runup
Go Beach Slope = pi/2*(Wave Runup/Deepwater Wave Height*(2*pi)^0.5)^4
Surf Similarity Parameter given Wave Runup above Mean Water Level
Go Deepwater Surf Similarity Parameter = Wave Runup/Deepwater Wave Height
Deepwater Wave Height given Wave Runup above Mean Water Level
Go Deepwater Wave Height = Wave Runup/Deepwater Surf Similarity Parameter
Wave Runup above Mean Water Level
Go Wave Runup = Deepwater Wave Height*Deepwater Surf Similarity Parameter
Mean Water Surface Elevation given Total Water Depth
Go Mean Water Surface Elevation = Water Depth-Still-Water Depth
Still Water Depth given Total Water Depth
Go Still-Water Depth = Water Depth-Mean Water Surface Elevation
Total Water Depth
Go Water Depth = Still-Water Depth+Mean Water Surface Elevation

Set down for Regular Waves Formula

Mean Water Surface Elevation = (-1/8)*((Wave Height^2*(2*pi/Wavelength))/(sinh(4*pi*Water Depth/Wavelength)))
η' = (-1/8)*((H^2*(2*pi/λ))/(sinh(4*pi*d/λ)))

What causes Regular Waves?

Waves are most commonly caused by wind. Wind-driven waves, or surface waves, are created by the friction between wind and surface water. As wind blows across the surface of the ocean or a lake, the continual disturbance creates a wave crest. The gravitational pull of the sun and moon on the earth also causes waves

How to Calculate Set down for Regular Waves?

Set down for Regular Waves calculator uses Mean Water Surface Elevation = (-1/8)*((Wave Height^2*(2*pi/Wavelength))/(sinh(4*pi*Water Depth/Wavelength))) to calculate the Mean Water Surface Elevation, The Set down for Regular Waves is defined as the set down in mean water level for a regular wave (wave component) has a single frequency (wavelength) and amplitude (height). Mean Water Surface Elevation is denoted by η' symbol.

How to calculate Set down for Regular Waves using this online calculator? To use this online calculator for Set down for Regular Waves, enter Wave Height (H), Wavelength (λ) & Water Depth (d) and hit the calculate button. Here is how the Set down for Regular Waves calculation can be explained with given input values -> -0.542405 = (-1/8)*((3^2*(2*pi/26.8))/(sinh(4*pi*1.05/26.8))).

FAQ

What is Set down for Regular Waves?
The Set down for Regular Waves is defined as the set down in mean water level for a regular wave (wave component) has a single frequency (wavelength) and amplitude (height) and is represented as η' = (-1/8)*((H^2*(2*pi/λ))/(sinh(4*pi*d/λ))) or Mean Water Surface Elevation = (-1/8)*((Wave Height^2*(2*pi/Wavelength))/(sinh(4*pi*Water Depth/Wavelength))). Wave Height of a surface wave is the difference between the elevations of a crest and a neighboring trough, Wavelength can be defined as the distance between two successive crests or troughs of a wave & Water Depth of the considered catchment. Water depth means the depth as measured from the water level to the bottom of the considered water body.
How to calculate Set down for Regular Waves?
The Set down for Regular Waves is defined as the set down in mean water level for a regular wave (wave component) has a single frequency (wavelength) and amplitude (height) is calculated using Mean Water Surface Elevation = (-1/8)*((Wave Height^2*(2*pi/Wavelength))/(sinh(4*pi*Water Depth/Wavelength))). To calculate Set down for Regular Waves, you need Wave Height (H), Wavelength (λ) & Water Depth (d). With our tool, you need to enter the respective value for Wave Height, Wavelength & Water Depth and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
How many ways are there to calculate Mean Water Surface Elevation?
In this formula, Mean Water Surface Elevation uses Wave Height, Wavelength & Water Depth. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • Mean Water Surface Elevation = Water Depth-Still-Water Depth
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