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Water Surface above Bottom Formula

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Water Surface Ordinate is defined as the vertical distance between two points on the water plane. Check FAQs

y s' = D w + H w \cdot {(sech (\sqrt{(\frac{3}{4}) \cdot (\frac{H w}{{D w}^{3}})} \cdot (x - (C \cdot t))))}^{2}

y_s' - Water Surface Ordinate?D_w - Water Depth from Bed?H_w - Height of the Wave?x - Spatial (Progressive Wave)?C - Celerity of the Wave?t - Temporal (Progressive Wave)?

Water Surface above Bottom Example

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Here is how the Water Surface above Bottom equation looks like with Values.

Here is how the Water Surface above Bottom equation looks like with Units.

Here is how the Water Surface above Bottom equation looks like.

45.0004 = 45 + 14 \cdot {(sech (\sqrt{(\frac{3}{4}) \cdot (\frac{14}{45^{3}})} \cdot (50 - (24.05 \cdot 25))))}^{2}

45.0004 = 45m + 14m \cdot {(sech (\sqrt{(\frac{3}{4}) \cdot (\frac{14m}{{45m}^{3}})} \cdot (50 - (24.05m/s \cdot 25))))}^{2}

45.0004 = 45 + 14 \cdot {(sech (\sqrt{(\frac{3}{4}) \cdot (\frac{14}{45^{3}})} \cdot (50 - (24.05 \cdot 25))))}^{2}

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Water Surface above Bottom Solution

Follow our step by step solution on how to calculate Water Surface above Bottom?

FIRST Step Consider the formula

y s' = D w + H w \cdot {(sech (\sqrt{(\frac{3}{4}) \cdot (\frac{H w}{{D w}^{3}})} \cdot (x - (C \cdot t))))}^{2}

Next Step Substitute values of Variables

∴

y s' = 45m + 14m \cdot {(sech (\sqrt{(\frac{3}{4}) \cdot (\frac{14m}{{45m}^{3}})} \cdot (50 - (24.05m/s \cdot 25))))}^{2}

Next Step Prepare to Evaluate

∴

y s' = 45 + 14 \cdot {(sech (\sqrt{(\frac{3}{4}) \cdot (\frac{14}{45^{3}})} \cdot (50 - (24.05 \cdot 25))))}^{2}

Next Step Evaluate

∴

y s' = 45.0004059473241

LAST Step Rounding Answer

∴

y s' = 45.0004

Water Surface above Bottom Formula Elements

Variables

Functions

Water Surface Ordinate

Water Surface Ordinate is defined as the vertical distance between two points on the water plane.

Symbol: y_s'

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Water Surface Ordinate

Water Depth from Bed

Water Depth from Bed means the depth as measured from the water level to the bottom of the considered water body.

Symbol: D_w

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Water Depth from Bed

Height of the Wave

Height of the Wave is the difference between the elevations of a crest and a neighboring trough.

Symbol: H_w

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Height of the Wave

Spatial (Progressive Wave)

Spatial (Progressive Wave) is a wave that continuously travels in a medium in the same direction minus the changes.

Symbol: x

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Spatial (Progressive Wave)

Celerity of the Wave

Celerity of the Wave refers to the speed at which a wave propagates through a medium.

Symbol: C

Measurement: SpeedUnit: m/s

Note: Value should be greater than 0.

Formulas to find Celerity of the Wave

Temporal (Progressive Wave)

Temporal (Progressive Wave) is a wave which generally travels continuously in a medium of the same direction without the change in its amplitude.

Symbol: t

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Temporal (Progressive Wave)

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

sech

The hyperbolic secant function is a hyperbolic function that is the reciprocal of the hyperbolic cosine function.

Syntax: sech(Number)

Other formulas in Solitary Wave category

Go Volume of Water above Still Water Level per Unit Crest Width

V = {((\frac{16}{3}) \cdot {D w}^{3} \cdot H w)}^{0.5}

Go Water Depth given Volume of Water within Wave above Still Water Level

D w = {(\frac{{(V)}^{2}}{(\frac{16}{3}) \cdot H w})}^{\frac{1}{3}}

Go Wave Height given Celerity of Solitary Wave

H w = (\frac{C^{2}}{[g]}) - D w

Go Water Depth given Celerity of Solitary Wave

D w = (\frac{C^{2}}{[g]}) - H w

How to Evaluate Water Surface above Bottom?

Water Surface above Bottom evaluator uses Water Surface Ordinate = Water Depth from Bed+Height of the Wave*(sech(sqrt((3/4)*(Height of the Wave/Water Depth from Bed^3))*(Spatial (Progressive Wave)-(Celerity of the Wave*Temporal (Progressive Wave)))))^2 to evaluate the Water Surface Ordinate, The Water Surface above Bottom means is defined as the height above bottom, in relation to mean sea level, of floods of various magnitudes and frequencies in floodplains of coastal or riverine areas. Water Surface Ordinate is denoted by y_s' symbol.

How to evaluate Water Surface above Bottom using this online evaluator? To use this online evaluator for Water Surface above Bottom, enter Water Depth from Bed (D_w), Height of the Wave (H_w), Spatial (Progressive Wave) (x), Celerity of the Wave (C) & Temporal (Progressive Wave) (t) and hit the calculate button.

FAQs on Water Surface above Bottom

What is the formula to find Water Surface above Bottom?

The formula of Water Surface above Bottom is expressed as Water Surface Ordinate = Water Depth from Bed+Height of the Wave*(sech(sqrt((3/4)*(Height of the Wave/Water Depth from Bed^3))*(Spatial (Progressive Wave)-(Celerity of the Wave*Temporal (Progressive Wave)))))^2. Here is an example- 45.00041 = 45+14*(sech(sqrt((3/4)*(14/45^3))*(50-(24.05*25))))^2.

How to calculate Water Surface above Bottom?

With Water Depth from Bed (D_w), Height of the Wave (H_w), Spatial (Progressive Wave) (x), Celerity of the Wave (C) & Temporal (Progressive Wave) (t) we can find Water Surface above Bottom using the formula - Water Surface Ordinate = Water Depth from Bed+Height of the Wave*(sech(sqrt((3/4)*(Height of the Wave/Water Depth from Bed^3))*(Spatial (Progressive Wave)-(Celerity of the Wave*Temporal (Progressive Wave)))))^2. This formula also uses Square Root (sqrt), Hyperbolic Secant (sech) function(s).

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Water Surface above Bottom Formula

Water Surface above Bottom Example

Water Surface above Bottom Solution

Water Surface above Bottom Formula Elements

Other formulas in Solitary Wave category

How to Evaluate Water Surface above Bottom?

FAQs on Water Surface above Bottom

Variable Name