Final answer:
The flow rate through the artery is approximately 2.61 x 10^{-14} {m}^3/s.
Step-by-step explanation:
The flow rate (Q) through a cylindrical tube (like an artery) can be calculated using Poiseuille's Law, which is given by the formula:
Q = {π . r^4 , ΔP} / {8 . η .L}
where:
- Q is the flow rate,
- π is the mathematical constant pi (approximately 3.14159),
- r is the radius of the tube,
- ΔP is the pressure drop across the tube,
- η is the viscosity of the fluid,
- L is the length of the tube.
Given values:
- r = 2.5 x 10^{-6} m (radius),
- Δ P = 1.55 x 10^3 Pa (pressure drop),
- η = 2.084 η 10^{-3} Pa·s (viscosity),
- L = 1.1 x 10^{-3} m (length).
Now, substitute these values into the formula:
Q = {3.14159 x (2.5 x 10^{-6})^4 x (1.55 x 10^3)} / {8 x 2.084 x 10^{-3} x 1.1 x 10^{-3}}
Let's calculate the flow rate (Q) using the provided values:
Q = {3.14159 x (2.5 x 10^{-6})^4 x (1.55 x 10^3)} / {8 x 2.084 x 10^{-3} x 1.1 x 10^{-3}}
Q ≈ {3.14159 x (2.5 x 10^{-6})^4 x (1.55 x 10^3)} / {8 x 2.084 x 10^{-3} x 1.1 x 10^{-3}}
Q ≈ {3.14159 x 9.765625 x 10^{-26} x 1.55 x 10^3} / {1.81648 x 10^{-8}}
Q ≈ {3.065041012 x 10^{-25} x 1.55 x 10^3} / {1.81648 x 10^{-8}} \]
Q ≈ {4.74658652 x 10^{-22}} / {1.81648 x 10^{-8}}
Q ≈ 2.61384 x 10^{-14} m^3/s
So, the flow rate through the artery is approximately \(2.61384 \times 10^{-14} \, \text{m}^3/\text{s}\).