This question is incomplete, the complete question is;
- Calculate the difference in blood pressure between the feet and top of the head of a person who is 1.80m Tall
- Consider a cylindrical segment of a blood vessel 2.70 cm long and 3.10 mm in diameter. What additional outward force would such a vessel need to withstand in the person's feet compared to a similar vessel in her head
Answer:
- the difference in blood pressure is 18698.4 Pa
- the additional outward force F is 4.86 N
Explanation:
Given the data in the question;
we know that the expression for difference in blood pressure is;
ΔP = pgh
where p is density = 1060 kg/m³
g is acceleration due to gravity = 9.8 m/s²
and h is height = 1.80 m
now we substitute
ΔP = 1060 × 9.8 × 1.80
ΔP = 18698.4 Pa
therefore the difference in blood pressure is 18698.4 Pa
Also given that;
diameter of blood vessel d = 3.10 mm
radius r = 3.10 mm / 2 = 1.55 mm = 0.00155 m
length l = 2.70 cm = 0.027 m
Surface area of the cylindrical segment of a blood vessel is
A = 2πrl
we substitute
A = 2 × π × 0.00155 × 0.027
A = 2.6 × 10⁻⁴ m²
so
the required for will be;
F = PA
we substitute
F = 18698.4 Pa × 2.6 × 10⁻⁴ m²
F = 4.86 N
Therefore, the additional outward force F is 4.86 N
