Answer to Question #6702 in Mechanics | Relativity for yah

Question

the pressure inside a 1.0cm radius vessel carrying blood with a speed of 0.50m/s is 5200 Newton/ square meter, while the pressure outside is 3200 Newton/ square meter. to what radius must the vessel be reduced so that the outside pressure is greater than that inside, thus making the vessel close at the constriction?

Answer 1

Let's find the area of the vessel:

S = 4πr² = 4π1² = 4π.

We denote the inside pressure force by Fi and outside pressure force by Fo. When the radius is r=1 the values of these forces are:

Fi = S*5200 = 4π5200 = 20800π,
Fo = S*3200 = 4π3200 = 12800π.

We see that Fi > Fo.

We know that inside pressure force is constant under the volume changes. Let's denote the new radius of the vessel by R.

Fi = Fo
20800π = 3200*4πR² ==> R = sqrt(20800/4/3200) = sqrt(1.625) = 1.2747

So, the vessel must expand a bit, then the outside pressure will grow up.