Mass flow rate in a rotating cone pump

Input(s)

$\boldsymbol{P}_{\boldsymbol{o}}$: Input Pressure (psi)

$\boldsymbol{P}_{L}$: Output Pressure $(\mathrm{psi})$

L: Length (ft)

B: Distance from Centre (ft)

$\rho$: Density $(\mathrm{ppg})$

$\mathrm{z}$: Distance from Input Side $(\mathrm{ft})$

$\beta$: Inclination (rad)

$\mu$: Viscosity $(\mathrm{cP})$

Output(s)

w: Mass Flow rate $(\mathrm{lb} / \mathrm{s})$

Formula(s)

$$ \mathrm{w}=\frac{-2 *\left(\mathrm{P}_{\mathrm{o}}-\mathrm{P}_{\mathrm{L}}\right) *\left(\mathrm{~B}^{3}\right) * \rho * 2 * \pi * \mathrm{z} * \sin (\beta)}{3} * \mathrm{~L} * \mu $$

Reference(s)

Bird, R.B., Stewart, W.E. and Lightfoot, E.N. (2002). Transport Phenomena (Second Ed.). John Wiley \& Sons, Chapter: 2, Page: 72.