Answer:
a) the tubular resistance of the blood vessel is 6.88 Gpa.s/m³.
b) the flow rate is 5.8 ml/min
Explanation:
Given the data in the question;
Length of blood vessel L = 1 m
radius r = 1 mm = 0.001 m
blood viscosity μ = 2.7 × 10⁻³ pa.s = 2.7 × 10⁻³ × 10⁻⁹ Gpa.s = 2.7 × 10⁻¹² Gpa.s
Now, we know that Resistance = 8μL / πr⁴
so we substitute
Resistance = [8 × (2.7 × 10⁻¹²) × 1] / [π(0.001)⁴]
Resistance = [2.16 × 10⁻¹¹] / [3.14159 × 10⁻¹²]
Resistance = 6.8755 ≈ 6.88 Gpa.s/m³
Therefore, the tubular resistance of the blood vessel is 6.88 Gpa.s/m³.
b)
blood pressure at the inlet of the vessel = 43 mm Hg
blood pressure at the outlet of the vessel = 38 mm Hg
flow rate = ?
we know that;
flow rate Q = ΔP / R
where ΔP is change in pressure and R is resistance.
ΔP = Inlet pressure - Outlet pressure = 43 - 38 = 5 mm Hg = 665 pa
R = 6.8755 Gpa.s/m³ = { 6.8755 × 10⁹ / 60 × 10⁶ } = 114.5916 pa.min.ml⁻¹
so we substitute
Q = 665 pa / 114.5916 pa.m.ml⁻¹
Q = 5.8 ml/min
Therefore, the flow rate is 5.8 ml/min
