Calculating h for Blood Transfusion Needle

In summary, calculating the value of h for a blood transfusion needle is important for determining the appropriate size of the needle needed for a specific patient and type of blood transfusion. The ideal h value is typically between 0.5 and 1.5, and it is calculated by dividing the viscosity of blood by the flow rate of blood. There are several factors that can affect the value of h, including blood viscosity, flow rate, needle length and diameter, and patient factors. Accurate calculation of h is crucial for preventing complications and ensuring the safety and comfort of the patient during the transfusion.
  • #1
Dr.Wasim
12
0

Homework Statement



A patient is to be given a blood transfusion. If the inside diameter of the 4.0 cm long
needle is 0.40 mm, the blood pressure in the arm is 2400 Pa, and the required flow is 4.0
cm³/min, how high h should the bottle be placed? (ρ = 1050 kg/m³, η =0.0040 Pa·s)



Homework Equations



I don't know how to do this question

please help me through " Poisieulles' equation " only

Best Wishes for you
 
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  • #2
Hi Dr.Wasim! :wink:

Poiseuille's equation is change in pressure = 8ηLQ/πr4
see http://en.wikipedia.org/wiki/Poiseuille%27s_law" for details.

Show us what you get. :smile:
 
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  • #3


Hello,

Thank you for reaching out for help with this question. I would be happy to assist you in solving this problem using Poiseuille's equation.

Poiseuille's equation is used to calculate the flow rate of a fluid through a cylindrical tube, such as a needle. The equation is as follows:

Q = (πΔPd^4)/(8ηL)

Where Q is the flow rate, ΔP is the pressure difference, d is the diameter of the tube, η is the viscosity of the fluid, and L is the length of the tube.

To solve for h, we need to rearrange this equation to isolate for L, the length of the tube. The rearranged equation would be:

L = (πΔPd^4)/(8ηQ)

Now, let's plug in the given values into this equation:

L = (π(2400 Pa)(0.40 mm)^4)/(8(0.0040 Pa·s)(4.0 cm^3/min))

Note that we need to convert the units to be consistent. We can convert 0.40 mm to meters by dividing by 1000, and 4.0 cm^3/min to m^3/s by dividing by 60000.

L = (π(2400 Pa)(0.00000016 m)^4)/(8(0.0040 Pa·s)(0.000000067 m^3/s))

Simplifying this, we get:

L = 0.0000019 m

Now, we can use this value of L to calculate the height h of the bottle using the following equation:

h = L - (d/2)

Where d is the diameter of the needle. Plugging in the values, we get:

h = (0.0000019 m) - (0.00040 m/2)

h = 0.0000015 m

Therefore, the bottle should be placed at a height of 0.0000015 meters, or 1.5 millimeters, above the patient's arm to achieve a flow rate of 4.0 cm^3/min.

I hope this explanation helps you understand how to solve this problem using Poiseuille's equation. If you have any further questions, please do not hesitate to reach out.

Best wishes to you as well!
 

1. What is the purpose of calculating h for blood transfusion needle?

The calculation of h for blood transfusion needle is important because it helps determine the appropriate size of the needle needed for a specific patient and type of blood transfusion. This ensures that the needle is not too large or too small, which can lead to complications such as blood flow obstruction or excessive bleeding.

2. How is h calculated for blood transfusion needle?

The value of h for a blood transfusion needle is calculated by dividing the viscosity of the blood by the flow rate of the blood. The viscosity of blood can vary depending on factors such as temperature and hematocrit levels, so it is important to use the most accurate value for the calculation.

3. What is the ideal value of h for a blood transfusion needle?

The ideal value of h for a blood transfusion needle is typically between 0.5 and 1.5. This range ensures that the needle is large enough to allow for an adequate flow of blood, but not so large that it can cause damage to the blood vessels or increase the risk of air embolism.

4. What factors can affect the value of h for a blood transfusion needle?

There are several factors that can affect the value of h for a blood transfusion needle, including the viscosity of the blood, the flow rate of the blood, the length and diameter of the needle, and the angle of insertion. Other factors such as patient age, weight, and underlying medical conditions may also play a role in determining the appropriate h value.

5. Why is it important to accurately calculate h for a blood transfusion needle?

Accurately calculating the value of h for a blood transfusion needle is crucial because it can help prevent complications during the transfusion process. Using a needle with the wrong h value can result in various issues such as blood clots, bruising, or inadequate blood flow. It is also essential for ensuring the safety and comfort of the patient during the transfusion.

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