==== Calculator of inductance of a straight tubular conductor ====
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| {{/calculator/icon_calc.png?60&nolink}} | //[[user/Stan Zurek]], Calculator of inductance of a straight tubular conductor, Encyclopedia Magnetica//, \\ https://www.e-magnetica.pl/doku.php/calculator/inductance_of_straight_tube, {accessed: @YEAR@-@MONTH@-@DAY@} |
| {{/wiki/logo.png?20&nolink}} //See more: [[/Calculators of inductance]]// ||
Definition of the dimensions of a **straight round tube** or pipe
[[/file/inductance_of_straight_tube_png|{{/inductance_of_straight_tube.png}}]]
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[[/Inductance]] of a straight round tubular conductor (extruded cylindrical tube or pipe) made from non-magnetic material ([[/relative permeability]] μr = 1) can be calculated with the the equation as specified below.
//Note: Several assumptions are made for all these equations: 1) The return path is **not** considered so the total inductance of the complete circuit can be significantly different. 2) The length of the wire is assumed to be significantly longer than its diameter(s) (d,D << l), otherwise the calculation errors might be excessive. 3) The conductor and the surrounding medium are assumed to be non-magnetic (μr = 1). 4) The equations were converted here to be consistent with [[/SI units]].//
^ Inductance of a straight round tubular conductor ^^^
| // Sources: [1] F.W. Grover, Inductance Calculations: Working Formulas and Tables, ISA, New York, 1982, ISBN 0876645570// |||
| **(1)** \\ //[1] Grover, eq. (11), p. 36// | $$ L_{DC} = \frac{μ_0 ⋅ l}{2⋅π}⋅\left( ln \left( \frac{4⋅l}{D} \right) - 1 + ξ_Z \right) $$ | (H) |
| **(2)** \\ //[1] Grover, Chapter 24, p. 261 \\ (AC high-frequency limit) // | $$ L_{AC, HF} = \frac{μ_0 ⋅ l}{2⋅π}⋅\left( ln \left( \frac{4⋅l}{D} \right) - 1 \right) $$ | (H) |
| **(3)** \\ //[1] Grover, Chapter 24, p. 261 \\ (DC limit for solid wire) // | $$ L_{DC, wire} = \frac{μ_0 ⋅ l}{2⋅π}⋅\left( ln \left( \frac{4⋅l}{D} \right) - \frac{3}{4} \right) $$ | (H) |
| where: $μ_0$ - [[/magnetic permeability of vacuum]] (H/m), $l$ - wire length (m), $D$ - outer diameter (m) of the tube, $d$ - inner diameter (m) of the tube, $ξ_Z$ - Grover's zeta function (unitless), which is tabulated in [1] Table 4, and can be approximated with the following polynomial ([[Approximation of Grover zeta|see more]]): |||
| (1.1) \\ Grover's Table 4 with Zurek's approximation by polynomials | $$ ξ_Z = 0.1705⋅z^3 - 0.3979⋅z^2 - 0.0214⋅z + 0.25 $$ | (unitless) |
| (1.2) \\ ratio $z$ of diameters | $$ z = d/D $$ | (unitless) |
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{{tag>Calculators Inductance_of_straight_tube Inductance_of_straight_pipe Inductance_of_straight_cylinder }}