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Depth of Centroid given Center of Pressure Formula

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The Depth of Centroid is the vertical distance from a reference point to the centroid of a fluid's surface, influencing pressure distribution in fluid mechanics. Check FAQs

D = \frac{h ✶ \cdot S W + \sqrt{{(h ✶ \cdot S W)}^{2} + 4 \cdot S W \cdot I}}{2 \cdot S W}

D - Depth of Centroid?h^✶ - Center of Pressure?S_W - Surface Area?I - Moment of Inertia?

Depth of Centroid given Center of Pressure Example

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Here is how the Depth of Centroid given Center of Pressure equation looks like with Values.

Here is how the Depth of Centroid given Center of Pressure equation looks like with Units.

Here is how the Depth of Centroid given Center of Pressure equation looks like.

100.1185 = \frac{100 \cdot 3000 + \sqrt{{(100 \cdot 3000)}^{2} + 4 \cdot 3000 \cdot 3.56}}{2 \cdot 3000}

100.1185cm = \frac{100cm \cdot 3000m² + \sqrt{{(100cm \cdot 3000m²)}^{2} + 4 \cdot 3000m² \cdot 3.56kg·m²}}{2 \cdot 3000m²}

100.1185 = \frac{100 \cdot 3000 + \sqrt{{(100 \cdot 3000)}^{2} + 4 \cdot 3000 \cdot 3.56}}{2 \cdot 3000}

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Depth of Centroid given Center of Pressure Solution

Follow our step by step solution on how to calculate Depth of Centroid given Center of Pressure?

FIRST Step Consider the formula

D = \frac{h ✶ \cdot S W + \sqrt{{(h ✶ \cdot S W)}^{2} + 4 \cdot S W \cdot I}}{2 \cdot S W}

Next Step Substitute values of Variables

∴

D = \frac{100cm \cdot 3000m² + \sqrt{{(100cm \cdot 3000m²)}^{2} + 4 \cdot 3000m² \cdot 3.56kg·m²}}{2 \cdot 3000m²}

Next Step Convert Units

∴

D = \frac{1m \cdot 3000m² + \sqrt{{(1m \cdot 3000m²)}^{2} + 4 \cdot 3000m² \cdot 3.56kg·m²}}{2 \cdot 3000m²}

Next Step Prepare to Evaluate

∴

D = \frac{1 \cdot 3000 + \sqrt{{(1 \cdot 3000)}^{2} + 4 \cdot 3000 \cdot 3.56}}{2 \cdot 3000}

Next Step Evaluate

∴

D = 1.00118526182108m

Next Step Convert to Output's Unit

∴

D = 100.118526182108cm

LAST Step Rounding Answer

∴

D = 100.1185cm

Depth of Centroid given Center of Pressure Formula Elements

Variables

Functions

Depth of Centroid

The Depth of Centroid is the vertical distance from a reference point to the centroid of a fluid's surface, influencing pressure distribution in fluid mechanics.

Symbol: D

Measurement: LengthUnit: cm

Note: Value can be positive or negative.

Formulas to find Depth of Centroid

Center of Pressure

The Center of Pressure is the point on a submerged surface where the total pressure force acts, influencing the stability and behavior of submerged objects in fluid mechanics.

Symbol: h^✶

Measurement: LengthUnit: cm

Note: Value can be positive or negative.

Formulas to find Center of Pressure

Surface Area

The Surface Area is the total area that the surface of an object occupies, influencing fluid interactions and pressure distribution in mechanical systems.

Symbol: S_W

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Surface Area

Moment of Inertia

Moment of Inertia of the section about an axis parallel to the free surface passing through the centroid of the area.

Symbol: I

Measurement: Moment of InertiaUnit: kg·m²

Note: Value can be positive or negative.

Formulas to find Moment of Inertia

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 Pressure Relations category

Go Absolute Pressure at Height h

P abs = P atm + y l \cdot h a

Go Center of Pressure on Inclined Plane

h ✶ = D + \frac{I \cdot \sin (Θ) \cdot \sin (Θ)}{A wet \cdot D}

Go Differential Pressure between Two Points

Δp = γ 1 \cdot h 1 - γ 2 \cdot h 2

Go Center of Pressure

h ✶ = D + \frac{I}{A wet \cdot D}

How to Evaluate Depth of Centroid given Center of Pressure?

Depth of Centroid given Center of Pressure evaluator uses Depth of Centroid = (Center of Pressure*Surface Area+sqrt((Center of Pressure*Surface Area)^2+4*Surface Area*Moment of Inertia))/(2*Surface Area) to evaluate the Depth of Centroid, Depth of Centroid given Center of Pressure formula is defined as a method to determine the vertical position of the centroid of a submerged surface, taking into account the effects of fluid pressure and the surface area in contact with the fluid. Depth of Centroid is denoted by D symbol.

How to evaluate Depth of Centroid given Center of Pressure using this online evaluator? To use this online evaluator for Depth of Centroid given Center of Pressure, enter Center of Pressure (h^✶), Surface Area (S_W) & Moment of Inertia (I) and hit the calculate button.

FAQs on Depth of Centroid given Center of Pressure

What is the formula to find Depth of Centroid given Center of Pressure?

The formula of Depth of Centroid given Center of Pressure is expressed as Depth of Centroid = (Center of Pressure*Surface Area+sqrt((Center of Pressure*Surface Area)^2+4*Surface Area*Moment of Inertia))/(2*Surface Area). Here is an example- 10117.29 = (1*3000+sqrt((1*3000)^2+4*3000*3.56))/(2*3000).

How to calculate Depth of Centroid given Center of Pressure?

With Center of Pressure (h^✶), Surface Area (S_W) & Moment of Inertia (I) we can find Depth of Centroid given Center of Pressure using the formula - Depth of Centroid = (Center of Pressure*Surface Area+sqrt((Center of Pressure*Surface Area)^2+4*Surface Area*Moment of Inertia))/(2*Surface Area). This formula also uses Square Root (sqrt) function(s).

Can the Depth of Centroid given Center of Pressure be negative?

Yes, the Depth of Centroid given Center of Pressure, measured in Length can be negative.

Which unit is used to measure Depth of Centroid given Center of Pressure?

Depth of Centroid given Center of Pressure is usually measured using the Centimeter[cm] for Length. Meter[cm], Millimeter[cm], Kilometer[cm] are the few other units in which Depth of Centroid given Center of Pressure can be measured.

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Depth of Centroid given Center of Pressure Formula

Depth of Centroid given Center of Pressure Example

Depth of Centroid given Center of Pressure Solution

Depth of Centroid given Center of Pressure Formula Elements

Other formulas in Pressure Relations category

How to Evaluate Depth of Centroid given Center of Pressure?

FAQs on Depth of Centroid given Center of Pressure

Variable Name