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Maximum Horizontal Particle Excursion at Node Formula

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Maximum Horizontal Particle Excursion refers to the maximum distance that a particle can travel horizontally from its initial position under the influence of a wave or current. Check FAQs

X = (H w \cdot \frac{T n}{2} \cdot π) \cdot \sqrt{\frac{[g]}{D}}

X - Maximum Horizontal Particle Excursion?H_w - Standing Wave Height of Ocean?T_n - Natural Free Oscillating Period of a Basin?D - Water Depth?[g] - Gravitational acceleration on Earth?π - Archimedes' constant?

Maximum Horizontal Particle Excursion at Node Example

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Here is how the Maximum Horizontal Particle Excursion at Node equation looks like with Values.

Here is how the Maximum Horizontal Particle Excursion at Node equation looks like with Units.

Here is how the Maximum Horizontal Particle Excursion at Node equation looks like.

7.8881 = (1.01 \cdot \frac{5.5}{2} \cdot 3.1416) \cdot \sqrt{\frac{9.8066}{12}}

7.8881m = (1.01m \cdot \frac{5.5s}{2} \cdot 3.1416) \cdot \sqrt{\frac{9.8066m/s²}{12m}}

7.8881 = (1.01 \cdot \frac{5.5}{2} \cdot 3.1416) \cdot \sqrt{\frac{9.8066}{12}}

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Maximum Horizontal Particle Excursion at Node Solution

Follow our step by step solution on how to calculate Maximum Horizontal Particle Excursion at Node?

FIRST Step Consider the formula

X = (H w \cdot \frac{T n}{2} \cdot π) \cdot \sqrt{\frac{[g]}{D}}

Next Step Substitute values of Variables

∴

X = (1.01m \cdot \frac{5.5s}{2} \cdot π) \cdot \sqrt{\frac{[g]}{12m}}

Next Step Substitute values of Constants

∴

X = (1.01m \cdot \frac{5.5s}{2} \cdot 3.1416) \cdot \sqrt{\frac{9.8066m/s²}{12m}}

Next Step Prepare to Evaluate

∴

X = (1.01 \cdot \frac{5.5}{2} \cdot 3.1416) \cdot \sqrt{\frac{9.8066}{12}}

Next Step Evaluate

∴

X = 7.88812265680199m

LAST Step Rounding Answer

∴

X = 7.8881m

Maximum Horizontal Particle Excursion at Node Formula Elements

Variables

Constants

Functions

Maximum Horizontal Particle Excursion

Maximum Horizontal Particle Excursion refers to the maximum distance that a particle can travel horizontally from its initial position under the influence of a wave or current.

Symbol: X

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Maximum Horizontal Particle Excursion

Standing Wave Height of Ocean

Standing Wave Height of Ocean results when two equal waves are going in opposite direction.

Symbol: H_w

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Standing Wave Height of Ocean

Natural Free Oscillating Period of a Basin

Natural Free Oscillating Period of a Basin referred to as the natural period or resonant period, is the time it takes for a wave to travel from one end of the basin to the other and back again.

Symbol: T_n

Measurement: TimeUnit: s

Note: Value can be positive or negative.

Formulas to find Natural Free Oscillating Period of a Basin

Water Depth

Water Depth is the vertical distance from the surface of a water body (such as an ocean, sea, or lake) to the bottom.

Symbol: D

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Water Depth

Gravitational acceleration on Earth

Gravitational acceleration on Earth means that the velocity of an object in free fall will increase by 9.8 m/s2 every second.

Symbol: [g]

Value: 9.80665 m/s²

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

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)

Other formulas in Harbor Oscillations category

Go Maximum Oscillation Period corresponding to Fundamental Mode

T 1 = 2 \cdot \frac{L ba}{\sqrt{[g] \cdot D}}

Go Basin Length along axis given Maximum Oscillation Period corresponding to Fundamental Mode

L ba = T 1 \cdot \frac{\sqrt{[g] \cdot D}}{2}

Go Water Depth given Maximum Oscillation Period corresponding to Fundamental Mode

d = \frac{{(2 \cdot \frac{L ba}{T n})}^{2}}{[g]}

Go Period for Fundamental Mode

T n = \frac{4 \cdot L ba}{\sqrt{[g] \cdot d}}

How to Evaluate Maximum Horizontal Particle Excursion at Node?

Maximum Horizontal Particle Excursion at Node evaluator uses Maximum Horizontal Particle Excursion = (Standing Wave Height of Ocean*Natural Free Oscillating Period of a Basin/2*pi)*sqrt([g]/Water Depth) to evaluate the Maximum Horizontal Particle Excursion, The Maximum Horizontal Particle Excursion at Node formula is defined as the integral dependent on wave characteristics. For shallow water waves, water parcels make elliptical motions, horizontal excursion is independent of depth, while vertical excursion decays linearly with depth and collapses to purely horizontal motion near bottom. Maximum Horizontal Particle Excursion is denoted by X symbol.

How to evaluate Maximum Horizontal Particle Excursion at Node using this online evaluator? To use this online evaluator for Maximum Horizontal Particle Excursion at Node, enter Standing Wave Height of Ocean (H_w), Natural Free Oscillating Period of a Basin (T_n) & Water Depth (D) and hit the calculate button.

FAQs on Maximum Horizontal Particle Excursion at Node

What is the formula to find Maximum Horizontal Particle Excursion at Node?

The formula of Maximum Horizontal Particle Excursion at Node is expressed as Maximum Horizontal Particle Excursion = (Standing Wave Height of Ocean*Natural Free Oscillating Period of a Basin/2*pi)*sqrt([g]/Water Depth). Here is an example- 7.888123 = (1.01*5.5/2*pi)*sqrt([g]/12).

How to calculate Maximum Horizontal Particle Excursion at Node?

With Standing Wave Height of Ocean (H_w), Natural Free Oscillating Period of a Basin (T_n) & Water Depth (D) we can find Maximum Horizontal Particle Excursion at Node using the formula - Maximum Horizontal Particle Excursion = (Standing Wave Height of Ocean*Natural Free Oscillating Period of a Basin/2*pi)*sqrt([g]/Water Depth). This formula also uses Gravitational acceleration on Earth, Archimedes' constant and Square Root (sqrt) function(s).

Can the Maximum Horizontal Particle Excursion at Node be negative?

Yes, the Maximum Horizontal Particle Excursion at Node, measured in Length can be negative.

Which unit is used to measure Maximum Horizontal Particle Excursion at Node?

Maximum Horizontal Particle Excursion at Node is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Maximum Horizontal Particle Excursion at Node can be measured.

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Maximum Horizontal Particle Excursion at Node Formula

Maximum Horizontal Particle Excursion at Node Example

Maximum Horizontal Particle Excursion at Node Solution

Maximum Horizontal Particle Excursion at Node Formula Elements

Other formulas in Harbor Oscillations category

How to Evaluate Maximum Horizontal Particle Excursion at Node?

FAQs on Maximum Horizontal Particle Excursion at Node

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