A small artery has a length of 1.10 × 10 − 3 m and a radius of 2.50 × 10 − 5 m. If the pressure drop across the artery is 1.45 kPa,what is the flow rate through the artery? Assume that the temperature is 37 °C and the viscosity of whole blood is 2.084 × 10 − 3 Pa·s.

Respuesta :

Answer:

The flow rate is [tex]9.7\times 10^{- 11}\ m^{3}/s[/tex]

Solution:

As per the question:

Pressure drop,  = 1.45 kPa = 1450 Pa

Radius of the artery, R = [tex]2.50\times 10^{- 5}\ m[/tex]

length of the artery, L = [tex]1.10\times 10^{- 3}\ m[/tex]

Temperature, T = [tex]37^{\circ}C[/tex]

Viscosity, [tex]\eta = 2.084\times 10^{- 3}\ Pa.s[/tex]

Now,

The flow rate is given by:

[tex]Q = \frac{\pi R^{4}P}{8\eta L}[/tex]

[tex]Q = \frac{\pi (2.50\times 10^{- 5})^{4}\times 1450}{8\times 2.084\times 10^{- 3}\times 1.10\times 10^{- 3}} = 9.7\times 10^{- 11}\ m^{3}/s[/tex]