How to do this physics problem?
The buildup of plaque on the walls of an artery may decrease its diameter from 1.1 cm to 0.85 cm. The speed of blood flow was 13 cm/s before reaching the region of plaque buildup.
(a) Find the speed of blood flow within the plaque region. ? cm/s
(b) Find the pressure drop within the plaque region. ? Pa
PS. Sorry I am not providing any context, cos I seriously am clueless what to do. I'd appreciate any help. Thanks in advance.
Comments
a.) area x velocity = area x velocity
1.1(13) = 0.85v
v = 16.8 cm/sec
b.) P1 + 1/2dv1*2 = P2 + 1/2dv2*2
P1 - P2 = 1/2d(v2*2 - v1*2)
change in pressure = 1/2(16.8*2 - 13*2) = 56.6 x density Pa
Hope that helps...
The design of this problem is bad, there are a number of problems:
1. Arteries are not rigid pipes, they flex with pressure - this is why you have a detectable pulse.
2. The heart is not a static system, there are feedback mechanisms to maintain constant flow no matter what the pressure drop.
3. Blood is a non-newtonian fluid, it's viscosity is not constant.
4. Because of the pulse, you need to use a form of Bernoulli's principle that has not been generally solved
But if you were pumping a newtonian fluid through a rigid pipe, then the area times the velocity would be a constant, so
1.1^2*13=.85^2*V will give you the velocity.
If we further, falsely, assume that the simple linear form of Bernoulli's principle applies, then 1/2*rho*13^2 + p(1) = 1/2*r*V^2 + p(2) or
p(1)-p(2) = 1/2*rho*13^2-V^2) where rho is the density of blood. I guess with all the other assumptions we're making, we can go ahead and assume that rho ~ 1.025
I can tell you a) is 13*(1.1/.85)^2 cm/s because it has to speed up by that factor since the cross sectional area goes down by that factor. But I don't know how much the Bernoulli effect makes the pressure go down in an incompressible fluid. I assume not very much, but I don't know.
a) The flow rate stays constant.
Q=VA
V1*A1=V2*A2
For a circular cross section, area is a function of d^2.
V1*d1^2=V2*d2^2
V2=V1*(d1/d2)^2=13(1.1/0.85)^2=21.8 cm/s
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b) Use Bernoulli's equation with no change in elevation z,
p1+(1/2)rv1^2=p2+(1/2)rv2^2
p2-p1=(1/2)r(v1^2-v2^2)
p2-p1=(1/2)rv1^2*(1-(d1/d2)^2)
Where p is pressure and r is the density of blood.
r=1060 kg/m^3
v1=13 cm/s=0.13 m/s
p2-p1=(1/2)(1060)(0.13)^2(1-(1.1/0.85)^2)=-6.04 Pa
physics problem
the galaxies rotate at speeds inconsistent with their apparent mass is because we do see all of it. I am referring to it as being the theoretical Dark Matter. There are very strong proofs that indicates that dark matter exist. One the is the inconsistent speed of and apparent mass. dark matter makes up about 75% to 80% of the matter in the Universe...
let me take a crack at it