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Straight Labyrinth Seal Flow Equation and Calculator

Fluids Flow Design and Engineering

Straight Labyrinth Seal using Martin’s Equation and Calculator

Martin's equation is used for compressible flow with straight-through seals

Figure 1 Straight Labyrinth Seal

Preview Straight Labyrinth using Martin’s Equation Calculator

Martin’s equation for mass flow for straight labyrinth seals

Eq. 1

${\displaystyle m=A\cdot <!--\; \cdot \; -->p_{to}\sqrt{\frac{1-<!--\; -\; -->(p_n/p_{t0}{)}^2}{R\cdot <!--\; \cdot \; -->T_{t0}\cdot <!--\; \cdot \; -->[n-<!--\; -\; -->ln(p_n/p_{t0})]}}}$

where

m = mass flow rate (kg/s)
A = annular clearance area of the seal (m²)
p_t0 = upstream total pressure (Pa)
p_n = downstream static pressure (Pa)
R = characteristic gas constant (J / kg-K)
T_t0 = upstream total temperature (K)
n = number of labyrinth fins (-)

The mass flow function, Q, provides a convenient means for comparing the relative performance of different seals. This is defined by

Eq. 2

${\displaystyle Q=\frac{m\sqrt{T_{t0}}}{A\cdot <!--\; \cdot \; -->p_{t0}}}$

Substitution for the mass flow function Eq. 2 in Eq. 1 gives

Eq. 3

${\displaystyle Q=\sqrt{\frac{1-<!--\; -\; -->(p_n/p_{t0}{)}^2}{R[n-<!--\; -\; -->ln(p_n/p_{t0})]}}}$

The flow characteristics for a straight labyrinth for compressible flow, using Eq 3 is illustrated in Figure 1.

Figure 1 Labyrinth mass flow function modeled using Eq 3 (R = 287 J/Kg-K)

Mechanical Design Engineering Handbook
Peter R. N. Childs
2014

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