Question

You are working at a catheter company and you are designing a new catheter to measure blood flow in a vessel that is 3mm diameter. The diameter of your catheter can be ignored in your calculations. The catheter measures both an end pressure at the tip and a lateral pressure on the side of the catheter. The company asks you to show (mathematically) how the volumetric flow rate of the blood can be calculated (assuming inviscid flow), and asks you to demonstrate the calculation based on the following measurements they’ve collected: Ptip = 83.0769 mmHg and Pside = 83 mmHg. [10pts]

Answer 1

a)Calculate the area of cross section of artery;

A= π/ 4× d​​​​​​2

= 22/7 ÷4 × (3×10-3) 2

= 7.07 ×10​​​​​​-5

Here, d is the diameter of the pipe.

Substitute 3 mm for d

Calculate the volumetric flow rate of the blood in the artery in terms of:

The formula for the volumetric flow is follows;

q= A×v

Here, q is the flow rate, A is the area of the artery and v is the average velocity

Substitute, for A is 7.07× 10-5 and v = 0.28m/s average velocity

Therefore, the volumetric flow rate of the blood in the artery is = 7.07×10-5 × 0.28m/s

= 1.97× 10-5 L/s