# Question about Poisseuille's law and blood flow

• don_anon25
In summary, the conversation discusses the equation for rate of flow and the known values for pressure drop and radius in a coronary artery. The question of blood viscosity arises and the source provided states it is approximately three times that of water. The dynamic viscosity of water at 20°C is given as 20.92 Lb_f sec/ft^2, so the dynamic viscosity of blood is estimated to be 62.76 Lb_f sec/ft^2 or 3.0 x 10^6 cP. The conversation concludes with suggestions for dealing with the unknown value for L in the equation.
don_anon25
I know that rate of flow is equal to pi*(P1-P2)*R^4/8nL. For blood in the coronary artery, I know the pressure drop, and the radius of the artery. What is the viscosity of blood? I can't find this value anywhere! And what value should I enter for L (distance L along a tube)? Is there an actual value somewhere for the length of the coronary artery in mm?

According to this source http://www.usc.edu/dept/biomed/bme403/Section_3/viscosity_of_blood.html
The value is approximately three times that of water. So if I use the dynamic viscosity of water at 20°C as
$$\mu_{water} = 20.92 \frac{Lb_f sec}{ft^2}$$, that would mean that $$\mu_{blood} = 3.0 \mu_{water}$$ so...

$$\mu_{blood}= 62.76 \frac{Lb_f sec}{ft^2}$$

$$\mu_{blood}= 3.0 x 10^6 cP$$

I can't really help you in terms of L in your equation. A couple of options would be to a)Leave L blank and express your answers in flow per unit length (which sounds kind of funny but is technically correct). or b)Make an estimation.

Last edited by a moderator:

Thank you for your question. The viscosity of blood can vary depending on factors such as temperature, hematocrit (percentage of red blood cells in blood), and shear rate. According to a study published in the Journal of Clinical Investigation, the viscosity of human blood ranges from 3.5 to 4.5 cP (centipoise) at a shear rate of 100 s-1. However, this value may vary in different individuals and under different conditions.

As for the distance L along a tube, this refers to the length of the artery through which the blood is flowing. The length of the coronary artery can vary from person to person, but on average, it is around 20-30 mm. However, it is important to note that the length of the artery may change depending on factors such as age, disease, and vessel dilation.

In summary, the viscosity of blood and the length of the coronary artery may vary, but you can use the average values mentioned above in your calculations for Poisseuille's law. Additionally, it is always best to consult multiple sources and consider the specific conditions of your experiment when determining these values. I hope this helps.

## 1. What is Poisseuille's law and how does it relate to blood flow?

Poisseauille's law is a physical law that describes the relationship between the pressure, flow rate, and resistance of a fluid flowing through a tube or vessel. In terms of blood flow, it explains how changes in the diameter of a blood vessel can affect the flow of blood through it.

## 2. How is Poisseuille's law used to understand blood flow in the human body?

In the human body, Poisseuille's law is used to understand the factors that can affect blood flow, such as the diameter of blood vessels, the viscosity of blood, and the pressure difference between two points in the circulatory system. It helps us understand how changes in these factors can impact blood flow and potentially lead to health issues.

## 3. Can Poisseuille's law be applied to all blood vessels in the body?

While Poisseuille's law is a helpful tool for understanding blood flow, it is not a perfect model for all blood vessels in the body. Some vessels, such as capillaries, have more complex structures and cannot be accurately described using this law. However, it is still a useful concept for understanding blood flow in larger vessels.

## 4. How does blood viscosity affect blood flow according to Poisseuille's law?

According to Poisseuille's law, blood viscosity plays a significant role in blood flow. Viscosity is a measure of a fluid's resistance to flow, and the thicker the blood, the higher the resistance and the slower the flow. This is why conditions that increase blood viscosity, such as high cholesterol or dehydration, can lead to problems with blood flow.

## 5. What are some practical applications of Poisseuille's law in the medical field?

Poisseauille's law has several practical applications in the medical field. It is used to understand and diagnose conditions that affect blood flow, such as atherosclerosis or anemia. It is also used in the design of medical devices, such as catheters and stents, to ensure proper blood flow through them. Additionally, it is used in the calculation of blood flow rates during medical procedures, such as dialysis or cardiac output measurements.

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