Phase Velocity in Axial Direction Calculator

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✖Helix Pitch, which represents the distance between consecutive turns along the helix.ⓘ Helix Pitch [p]			+10% -10%
✖Relative Permeability is the ratio of effective permeability of a particular fluid at a particular saturation to absolute permeability of that fluid at total saturation.ⓘ Relative Permeability [μ_r]			+10% -10%
✖Permittivity of Dielectric refers to the ability to store electrical energy in an electric field.ⓘ Permittivity of Dielectric [ε]			+10% -10%
✖Diameter of Helix is the distance across the widest part of the helix.ⓘ Diameter of Helix [d]			+10% -10%

✖Phase Velocity in Axial Direction refers to the speed at which the phase of a wave propagates along the axis of a structure or medium.ⓘ Phase Velocity in Axial Direction [v_pe]

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Formula

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Phase Velocity in Axial Direction

Formula

v pe = \frac{p}{\sqrt{μ r \cdot ε \cdot ((p^{2}) + {(π \cdot d)}^{2})}}

Example

0.125039 m/s = \frac{4.5 m}{\sqrt{1.3 H/m \cdot 7.8 F/m \cdot (({4.5 m}^{2}) + {(π \cdot 3.3 m)}^{2})}}

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Phase Velocity in Axial Direction Solution

STEP 0: Pre-Calculation Summary

Formula Used

Phase Velocity in Axial Direction = Helix Pitch/(sqrt(Relative Permeability*Permittivity of Dielectric*((Helix Pitch^2)+(pi*Diameter of Helix)^2)))
v_pe = p/(sqrt(μ_r*ε*((p^2)+(pi*d)^2)))
This formula uses 1 Constants, 1 Functions, 5 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

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., sqrt(Number)

Variables Used

Phase Velocity in Axial Direction - (Measured in Meter per Second) - Phase Velocity in Axial Direction refers to the speed at which the phase of a wave propagates along the axis of a structure or medium.
Helix Pitch - (Measured in Meter) - Helix Pitch, which represents the distance between consecutive turns along the helix.
Relative Permeability - (Measured in Henry per Meter) - Relative Permeability is the ratio of effective permeability of a particular fluid at a particular saturation to absolute permeability of that fluid at total saturation.
Permittivity of Dielectric - (Measured in Farad per Meter) - Permittivity of Dielectric refers to the ability to store electrical energy in an electric field.
Diameter of Helix - (Measured in Meter) - Diameter of Helix is the distance across the widest part of the helix.

STEP 1: Convert Input(s) to Base Unit

Helix Pitch: 4.5 Meter --> 4.5 Meter No Conversion Required
Relative Permeability: 1.3 Henry per Meter --> 1.3 Henry per Meter No Conversion Required
Permittivity of Dielectric: 7.8 Farad per Meter --> 7.8 Farad per Meter No Conversion Required
Diameter of Helix: 3.3 Meter --> 3.3 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

v_pe = p/(sqrt(μ_r*ε*((p^2)+(pi*d)^2))) --> 4.5/(sqrt(1.3*7.8*((4.5^2)+(pi*3.3)^2)))

Evaluating ... ...

v_pe = 0.125039461283172

STEP 3: Convert Result to Output's Unit

0.125039461283172 Meter per Second --> No Conversion Required

FINAL ANSWER

0.125039461283172 ≈ 0.125039 Meter per Second <-- Phase Velocity in Axial Direction

(Calculation completed in 00.004 seconds)

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Created by Zaheer Sheik

Seshadri Rao Gudlavalleru Engineering College (SRGEC), Gudlavalleru

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Phase Velocity in Axial Direction Formula

Phase Velocity in Axial Direction = Helix Pitch/(sqrt(Relative Permeability*Permittivity of Dielectric*((Helix Pitch^2)+(pi*Diameter of Helix)^2)))
v_pe = p/(sqrt(μ_r*ε*((p^2)+(pi*d)^2)))

What is Phase Velocity in Axial Direction?

Phase velocity in the axial direction describes the speed at which the phase of a wave progresses along the length or axis of a medium or structure. It indicates how rapidly the phase of the wave changes as it travels through the medium or along the structure. This concept is essential for understanding wave propagation phenomena in different contexts, such as electromagnetic waves in transmission lines or acoustic waves in air or water. By knowing the phase velocity in the axial direction, we can analyze how waves behave as they propagate through various mediums and structures.

How to Calculate Phase Velocity in Axial Direction?

Phase Velocity in Axial Direction calculator uses Phase Velocity in Axial Direction = Helix Pitch/(sqrt(Relative Permeability*Permittivity of Dielectric*((Helix Pitch^2)+(pi*Diameter of Helix)^2))) to calculate the Phase Velocity in Axial Direction, The Phase Velocity in Axial Direction formula is defined refers to the speed at which the phase of a wave propagates along the axis of a structure or medium. It describes how quickly the phase of the wave changes as it travels along the length of the structure or medium in the axial (longitudinal) direction. Phase Velocity in Axial Direction is denoted by v_pe symbol.

How to calculate Phase Velocity in Axial Direction using this online calculator? To use this online calculator for Phase Velocity in Axial Direction, enter Helix Pitch (p), Relative Permeability (μ_r), Permittivity of Dielectric (ε) & Diameter of Helix (d) and hit the calculate button. Here is how the Phase Velocity in Axial Direction calculation can be explained with given input values -> 0.125039 = 4.5/(sqrt(1.3*7.8*((4.5^2)+(pi*3.3)^2))).

FAQ

What is Phase Velocity in Axial Direction?

The Phase Velocity in Axial Direction formula is defined refers to the speed at which the phase of a wave propagates along the axis of a structure or medium. It describes how quickly the phase of the wave changes as it travels along the length of the structure or medium in the axial (longitudinal) direction and is represented as v_pe = p/(sqrt(μ_r*ε*((p^2)+(pi*d)^2))) or Phase Velocity in Axial Direction = Helix Pitch/(sqrt(Relative Permeability*Permittivity of Dielectric*((Helix Pitch^2)+(pi*Diameter of Helix)^2))). Helix Pitch, which represents the distance between consecutive turns along the helix, Relative Permeability is the ratio of effective permeability of a particular fluid at a particular saturation to absolute permeability of that fluid at total saturation, Permittivity of Dielectric refers to the ability to store electrical energy in an electric field & Diameter of Helix is the distance across the widest part of the helix.

How to calculate Phase Velocity in Axial Direction?

The Phase Velocity in Axial Direction formula is defined refers to the speed at which the phase of a wave propagates along the axis of a structure or medium. It describes how quickly the phase of the wave changes as it travels along the length of the structure or medium in the axial (longitudinal) direction is calculated using Phase Velocity in Axial Direction = Helix Pitch/(sqrt(Relative Permeability*Permittivity of Dielectric*((Helix Pitch^2)+(pi*Diameter of Helix)^2))). To calculate Phase Velocity in Axial Direction, you need Helix Pitch (p), Relative Permeability (μ_r), Permittivity of Dielectric (ε) & Diameter of Helix (d). With our tool, you need to enter the respective value for Helix Pitch, Relative Permeability, Permittivity of Dielectric & Diameter of Helix and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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