Calculus for Cardiologists!

The Law of Laminar Flow states that the velocity of blood, v in a cylindrical blood vessel at a distance, r from its central axis is given by:

$v(r) = \frac{P}{4 \cdot n \cdot l} \cdot (R^{2} - r^{2})$ ,

where R is the radius of the blood vessel and l is the length of the blood vessel. The constant P is the difference in pressure between the ends of the blood vessel, whereas the other constant n is the viscosity of the blood.

Find an expression for the flux (volume of flow per unit time) of the blood through the blood vessel. This expression for the flux is called Poiseuille's Law

If your answer is of the form $\frac {A \cdot (π - B + 1) \cdot (P ^ C) \cdot (R - D + 2) ^ {2 + E}}{(5 + F) \cdot n ^ {G - 6} \cdot H \cdot l}$ , where A, B, C, D, E, F, G and H are non-negative integers ; submit the value $A + B ^ {2} + C ^ {3} + D ^ {4} + E ^ {5} + F ^ {6} + G ^ {7} + H ^ {8}$

Courtesy: Stewart Calculus Early Transcendentals Sixth Edition