Mathematics, 19.09.2019 06:30, ana5246
The velocity v of blood that flows in a blood vessel with radius r and length ℓ at a distance r from the central axis is v(r) = p 4ηℓ (r2 − r2) where p is the pressure difference between the ends of the vessel and η is the viscosity of the blood. find the average velocity vave (with respect to r) over the interval 0 ≤ r ≤ r. (use eta for η. use capital p for pressure.)
Answers: 1
![\displaystyle The \ dataset \ sum = \frac{P}{4 \cdot \eta \cdot l} \cdot\int\limits^R_0 {\displaystyle \left (R^2 - r^2 \right)} \, dr = \mathbf{ \frac{P}{4 \cdot \eta \cdot l} \cdot \left [R^2\cdot r - \frac{r^3}{3} \right]^R_0}](/tpl/images/0242/3477/b6638.png)
![\displaystyle \frac{P}{4 \cdot \eta \cdot l} \cdot \left [R^2\cdot r - \frac{r^3}{3} \right]^R_0= \frac{P}{4 \cdot \eta \cdot l} \cdot\frac{2\cdot R^3}{3} = \mathbf{\frac{P\cdot R^3}{6 \cdot \eta \cdot l}}](/tpl/images/0242/3477/f4b44.png)
, is therefore;
is the radius of the vessel, and that 
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