Question

1. the formula for blood flow rate is given by $f=\frac{p_{1}-p_{2}}{r}$, where $f$ is the flow rate, $p_{1}$ the initial pressure, $p_{2}$ the final pressure, and $r$ the resistance created by blood vessel size. which formula can not be derived from the given formula? 1) $p_{1}=fr + p_{2}$ 2) $p_{2}=p_{1}-fr$ 3) $r = f(p_{2}-p_{1})$ 4) $r=\frac{p_{1}-p_{2}}{f}$

Explanation:

Step1: Start with given formula

$F=\frac{p_1 - p_2}{r}$

Step2: Cross - multiply to solve for $p_1$

$Fr=p_1 - p_2$, then $p_1=Fr + p_2$ (matches 1)

Step3: Rearrange to solve for $p_2$

$Fr=p_1 - p_2$ can be rewritten as $p_2=p_1 - Fr$ (matches 2)

Step4: Cross - multiply to solve for $r$

$Fr=p_1 - p_2$, then $r=\frac{p_1 - p_2}{F}$ (matches 4)

Step5: Analyze option 3

Starting from $F=\frac{p_1 - p_2}{r}$, we cannot get $r = F(p_2 - p_1)$

Answer:

1. $r = F(p_2 - p_1)$