Flow of power law fluid through a narrow slit

Input(s)

W: Width (cm)(\mathrm{cm})

B: Breadth (cm)(\mathrm{cm})

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

ρ\rho: Density of Fluid (g/cc)(\mathrm{g} / \mathrm{cc})

PO\boldsymbol{P}_{\boldsymbol{O}}: Input Pressure (Pa)(\mathrm{Pa})

PL\boldsymbol{P}_{\boldsymbol{L}}: Output Pressure (Pa)(\mathrm{Pa})

m\mathrm{m}: Power Law Constant (dimensionless)

n: Power Law Constant 2 (dimensionless)

Output(s)

w: Mass Rate of Flow (g/s)(\mathrm{g} / \mathrm{s})

Formula(s)

w=(2 W( B2)ρ(1n)+2)(((POPL) B m L)1n)\mathrm{w}=\left(\frac{2 * \mathrm{~W} *\left(\mathrm{~B}^{2}\right) * \rho}{\left(\frac{1}{\mathrm{n}}\right)+2}\right) *\left(\left(\frac{\left(\mathrm{P}_{\mathrm{O}}-\mathrm{P}_{\mathrm{L}}\right) * \mathrm{~B}}{\mathrm{~m} * \mathrm{~L}}\right)^{\frac{1}{\mathrm{n}}}\right)

Reference(s)

Bird, R.B., Stewart, W.E. and Lightfoot, E.N. (2002). Transport Phenomena (Second Ed.). John Wiley & Sons, Chapter: 8, Page: 243 .


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