# When blood flows along a blood vessel, the flux f (the volume of blood per unit time that flows past

###### Question:

that is, f = kr4 where k is some constant. this is known as poiseuille's law. show that the relative change in f (that is, df / f) is about four time the relative change in r.

how will a 5% increase or decrease in the radius of the artery affect the flow of blood?

## Answers

just use this websites https://www.symbolab.com/

Step-by-step explanation:

[tex]\frac{dF}{F}=4\frac{dR}{R}[/tex]

So a 5% relative increase in R would mean a 20% relative increase in F

Step-by-step explanation:

First we need to remind the definition of relative increase of a variable.

For a variable A its relative increase is given by [tex]\frac{dA}{A}[/tex].

Using this, the relative increase in F is [tex]\frac{dF}{F}[/tex] and similarly the relative increase in R is given by [tex]\frac{dR}{R}[/tex].

Let's then start by deriving F with respect to R:

[tex]\frac{dF}{dR}=4kR^3[/tex]

thus

[tex]dF=4kR^3dR[/tex]

[tex]\implies \frac{dF}{F}=\frac{4kR^3dR}{F}[/tex]

[tex]\implies \frac{dF}{F}=\frac{4kR^3dR}{kR^4}[/tex]

[tex]\implies \frac{dF}{F}=4\frac{dR}{R}[/tex].

If we plug the value 5% [tex]\left( \frac{5}{100}\right)[/tex] in [tex]\frac{dR}{R}[/tex] we get

[tex]\frac{dF}{F}=4\times5\%=20\%[/tex]