Bernoulli's Equation and blood

[texasgrl05]

not sure where to begin...

The blood speed in a normal segment of a horizontal artery is 0.13 m/s. An abnormal segment of the artery is narrowed down by an arteriosclerotic plaque to one-fifth the normal cross-sectional area. What is the difference in blood pressures between the normal and constricted segments of the artery? (See Table 11.1 for appropriate constants.)

 

[dextercioby]

Are you sure you don't need the Poiseuille-Hagen (1839) equation...?

Blood is viscous and it can be modeled by a Newtonian viscous fluid.

Daniel.

 

[texasgrl05]

I have no idea what that is. It just says Bournelli's equation

 

[dextercioby]

Ok.I'm sure it's Daniel Bernoulli.

Use the continuity equation to find the velocity in the other portion of the artery and then Bernoulli's law to find the pressure difference.

Daniel.

 

[abercrombiems02]

Bernoullis eqn says that for incompressible flow we have

P1 + Q1 = P2 + Q2

P corresponds to the static pressure
Q is the dynamic pressure

Q = 1/2pv^2

From the continuity equation we have

mdot1 = mdot2

mdot = density*area*velocity

Assuming INCOMPRESSIBLE
density1 = density2 thus

A1*v1 = A2*v2

A2 = A1/5 Thus v2 = 5*v1

Q1 = 1/2*density of blood*v1^2
Q2 = 1/2*density of blood*(5*v1)^2

P1 + Q1 = P2 + Q2

The change in pressure is P2 - P1

P2 - P1 = 1/2*density of blood*(v1^2 - 25v1^2)

delta P = -12*density of blood*v1^2

notice this value is negative thus the static pressure decreases

The pressure drop is simply 12*density of blood*v1^2