Question

A small artery has a length of 1.1 mm and a radius of 25 μm. If the pressure drop across the artery is 1.3 kPa, calculate the flow rate. The viscosity of the blood is 3 Pa.s.

• A. \(16 \times 10^{-16} \, \text{m}^3/\text{sec}\)
• B. \(25 \times 10^{-17} \, \text{m}^3/\text{sec}\)
• C. \(6 \times 10^{-14} \, \text{m}^3/\text{sec}\)
• D. \(32 \times 10^{-15} \, \text{m}^3/\text{sec}\)

Hint:

To calculate flow rate in fluid dynamics, use Poiseuille's law, which considers the radius, pressure drop, viscosity, and length of the tube.

Answer 1

The Correct Option is A

Using Poiseuille's law, the flow rate \(Q\) is given by: \[ Q = \frac{\pi r^4 \Delta P}{8 \eta L} \] Where: - \(r = 25 \, \mu m = 25 \times 10^{-6} \, \text{m}\) (radius) - \(\Delta P = 1.3 \, \text{kPa} = 1.3 \times 10^3 \, \text{Pa}\) (pressure drop) - \(\eta = 3 \, \text{Pa.s}\) (viscosity) - \(L = 1.1 \, \text{mm} = 1.1 \times 10^{-3} \, \text{m}\) (length)
Substituting the values: \[ Q = \frac{\pi (25 \times 10^{-6})^4 (1.3 \times 10^3)}{8 \times 3 \times 1.1 \times 10^{-3}} = 16 \times 10^{-16} \, \text{m}^3/\text{sec} \]
Conclusion: The flow rate is \(16 \times 10^{-16} \, \text{m}^3/\text{sec}\), so option (a) is correct.