Velocity distribution in a creeping flow around a sphere

Input(s)

Pi\boldsymbol{P}_{\boldsymbol{i}}: Input Pressure (psi)

Po\boldsymbol{P}_{\boldsymbol{o}}: Output Pressure (psi)

L: Length (ft)

μa\boldsymbol{\mu}_{\boldsymbol{a}}: Viscosity of A (cP)

μb\boldsymbol{\mu}_{\boldsymbol{b}}: Viscosity of B (cP)

b: Radius (ft)(\mathrm{ft})

x\mathrm{x}: Distance from center (ft)(\mathrm{ft})

Output(s)

v: Velocity (ft/s)(\mathrm{ft} / \mathrm{s})

Formula(s)

v=((PiPo)(b2)2μaL)(2μaμa+mub+(μaμb)x(μa+μb)b(xb)2)v=\left(\frac{\left(P_{i}-P_{o}\right) *\left(b^{2}\right)}{2 * \mu_{a} * L}\right) *\left(\frac{2 * \mu_{a}}{\mu_{a}+m u_{b}}+\frac{\left(\mu_{a}-\mu_{b}\right) * x}{\left(\mu_{a}+\mu_{b}\right) * b}-\left(\frac{x}{b}\right)^{2}\right)

Reference(s)

Bird, R.B., Stewart, W.E. and Lightfoot, E.N. (2002). Transport Phenomena (Second Ed.). John Wiley & Sons, Page: 59.


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