Blood in a carotid artery carrying blood to the head is moving at 0.15 m/s when it reaches a section where plaque has narrowed the artery to 74 % of its diameter. What pressure drop occurs when the blood reaches this narrow section? Ignore the blood viscosity.

Following are the equation of continuation expression:

are the initial area and velocity, respectively, and are the end area and velocity.

Therefore,

Using the Bernoulli equation at the height of constant.  

Let the Human bool is the average density then:  

Learn more about the blood viscosity:

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26.9 Pa

Explanation:

We can answer this question by using the continuity equation, which states that the volume flow rate of a fluid in a pipe must be constant; mathematically:

(1)

where

is the cross-sectional area of the 1st section of the pipe

is the cross-sectional area of the 2nd section of the pipe

is the velocity of the 1st section of the pipe

is the velocity of the 2nd section of the pipe

In this problem we have:

is the velocity of blood in the 1st section

The diameter of the 2nd section is 74% of that of the 1st section, so

The cross-sectional area is proportional to the square of the diameter, so:

And solving eq.(1) for v2, we find the final velocity:

Now we can use Bernoulli's equation to find the pressure drop:

where

is the blood density

are the initial and final pressure

So the pressure drop is:

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