The blood speed in a normal segment of a horizontal artery is 0.140 m/s. An abnormal segment of the artery is narrowed down by an arteriosclerotic plaque to one-fourth the normal cross-sectional area. What is the difference in blood pressures between the normal and constricted segments of the artery?

Respuesta :

Answer:

[tex]96[/tex]Pa

Explanation:

Let "n" represents the normal flow condition and "a" represents the abnormal flow condition.

As per continuity equation -

[tex]v_{n}*A_{n}= v_{a}*A_{a}[/tex]----------- Eq (1)

Where "v" represents the velocity and "a" represents the area of artery

Given-

[tex]A_a=\frac{A_n}{4}[/tex]

Substituting the above relation in equation (1), we get -

[tex]v_a = \frac{v_n*A_n}{A_a}\\ v_a= 4v_n\\[/tex]

As per Bernoulli's theorem, we know that -

[tex]P_a-P_n= \frac{1}{2}pv_a^2-\frac{1}{2}pv_n^2\\P_a-P_n=\frac{1}{2}p[\frac{v_a*A_a}{A_n} ]^2\\P_a-P_n=\frac{1}{2}pv_n^2[16-1]\\P_a-P_n=\frac{1}{2}*1060*(0.11)^2*15\\P_a-P_n=96[/tex]Pa