Mass rate of flow through annulus

Input(s)

po: Pressure at initial point (Pa)(\mathrm{Pa})

pL\mathrm{pL}: Pressure at point L(Pa)\mathrm{L}(\mathrm{Pa})

R\mathrm{R}: Radius (m)(\mathrm{m})

ρ\rho: Density (kg/m3)\left(\mathrm{kg} / \mathrm{m}^{3}\right)

mu\mathrm{mu}: Viscosity (kg/(ms))(\mathrm{kg} /(\mathrm{ms}))

L: Length (m)(\mathrm{m})

K\mathrm{K}: Boltzmann Constant (m2 kg s2 K1)\left(\mathrm{m}^{2} \mathrm{~kg} \mathrm{~s}^{-2} \mathrm{~K}^{-1}\right)

Output(s)

Ψ\Psi: Mass Rate of Flow (kg/s)(\mathrm{kg} / \mathrm{s})

Formula(s)

Ψ=π(popL)R4ρ8μL((1K4)(1K2)2ln(1K))\Psi=\frac{\pi *(p o-p L) * R^{4} * \rho}{8 * \mu * L} *\left(\left(1-K^{4}\right)-\frac{\left(1-K^{2}\right)^{2}}{\ln \left(\frac{1}{K}\right)}\right)

Reference(s)

Transport Phenomena, Second Edition, Bird, Chapter 2.


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