Solving Blood Pressure Difference with Constricted Artery

[LostInScience]

Homework Statement

Normal blood speed is 0.13 meters/second. If an artery has a narrowing down to one-seventh of the normal cross-sectional area, what is the difference in blood pressures between the normal and constricted segments? Answer is Pascals. Blood density is 1060 kg/meters^3.

I tried this problem using a number of different equations and am just stumped. My answers range from -429.9 to 422.7!

I have tried Pressure 2 - Pressure 1=1/2(Density)(Velocity^2 segment 1 -Velocity^2 segment 2)

I also tried Pressure 2 - Pressure 1 =
1/2(Density)(Velocity^2 segment 1 [(Area 1/Area 2)(Velocity 1)]^2

Am I totally wrong with all of my equations?

Any help would be greatly appreciated!

 

[Nate810]

Homework Equations Pressure 2 - Pressure 1=1/2(Density)(Velocity^2 segment 1 -Velocity^2 segment 2)Pressure 2 - Pressure 1 = 1/2(Density)(Velocity^2 segment 1 [(Area 1/Area 2)(Velocity 1)]^2The Attempt at a Solution I tried this problem using a number of different equations and am just stumped. My answers range from -429.9 to 422.7!

 

[ogb p]

I would approach this problem by first understanding the underlying principles of fluid dynamics. Blood pressure is determined by the force exerted by the blood on the walls of the artery, which is influenced by the velocity and cross-sectional area of the blood flow.

In this case, the narrowing of the artery results in a decrease in cross-sectional area, which leads to an increase in blood velocity. This increase in velocity will result in a decrease in blood pressure according to the Bernoulli's equation (P1 + 1/2ρv1^2 = P2 + 1/2ρv2^2).

To solve for the difference in blood pressure, we can rearrange the equation to P2 - P1 = 1/2ρ(v2^2 - v1^2). Plugging in the given values, we get P2 - P1 = 1/2(1060 kg/m^3)((0.13 m/s)^2 - (0.13 m/s)^2/7^2) = -429.9 Pa.

It is important to note that the answer is negative, indicating a decrease in pressure due to the narrowing of the artery. This is a common result in cases of constricted arteries, where the blood has to flow through a smaller space and therefore experiences a decrease in pressure.

It is also important to consider the assumptions and limitations of the calculations, such as assuming a constant blood velocity and neglecting factors such as viscosity and turbulence. Further research and experiments may be needed to accurately model and predict the effects of constricted arteries on blood pressure.