[difficult] bernoulli's equation

[Bob Loblaw]

Homework Statement

In an aortic aneurysm, a bulge forms where the walls of the aorta are weakened. If blood flowing through the aorta (radius 1.1 cm) enters an aneurysm with a radius of 3.1 cm, how much on average is the blood pressure higher inside the aneurysm than the pressure in the unenlarged part of the aorta? The average flow rate through the aorta is 110 cm3/s. Assume the blood is non-viscous and the patient is lying down so there is no change in height.

? Pa

Homework Equations

P = 1/2 (d (V1^2 - V2^2))
where
d = density
V1 = initial velocity
V2 = final velocity

The Attempt at a Solution

to get V1 you have to use Flow rate / pi r^2. When I try to finish the equation, I notice that I need the density of blood but none is given in the text nor in the homework. Is there a way to solve this without knowing blood density? Or do I have to find a value online?

Could anybody help?

 

[anathema]

Thank you for your question. The equation you are using to solve for the pressure difference is correct, but you are missing a key variable - the change in height. Since the patient is lying down, there is no change in height and therefore the pressure difference due to gravity can be ignored.

To solve for the density of blood, we can use the average density of human blood, which is approximately 1060 kg/m^3. This value may vary slightly depending on factors such as age and health, but it should give you a good estimate for your calculations.

I hope this helps. Let me know if you have any further questions.



Scientist

 

[ogb p]

I understand your frustration with the lack of information provided in this problem. However, it is important to note that the density of blood can vary depending on factors such as age, gender, and health conditions. In this case, it would be best to assume a standard value for blood density, such as 1.06 g/cm3, which is commonly used in similar problems. This value can be found in many reliable sources, such as medical textbooks or online databases. Alternatively, you can also use the given information and equations to solve for the pressure difference using a variable for density, and then use that value to solve for the actual pressure difference using a more accurate density value if it is provided later in the problem. I hope this helps.