Question

If the radius of a blood vessel drops to 84.0% of its original radius because of the buildup of plaque, and the body responds by increasing the pressure difference across the blood vessel by 10.0%, what will have happened to the flow rate? The flow rate will have changed to ...... % of its original value.

Answer 1

To develop this problem it is necessary to apply the equations concerning Bernoulli's law of conservation of flow.

From Bernoulli it is possible to express the change in pressure as

$\Delta P = \frac{1}{2}\rho (v_1^2-v_2^2)+ \rho g (h_1h_2)$

Where,

$v_i =$Velocity

$\rho =$ Density

g = Gravitational acceleration

h = Height

From the given values the change of flow is given as

$R = r^4P$

Therefore between the two states we have to

$\frac{R_2}{R_1} = \frac{r_2^4 P_2}{r_1^4 P_1} *100\%$

$\frac{R_2}{R_1} = \frac{84^4 (110)}{100^4*(100)} *100\%$

$\frac{R_2}{R_1} = 54.77\%$

The flow rate will have changed to 54.77 % of its original value.