Respuesta :
2/Blood flows at an average speed of 0.40 m/s in a horizontal artery of radius 1.0 cm. The average pressure is 1.4 × 104N/m2 above atmospheric pressure (the gauge pressure).
The gauge pressure of the blood is the difference between the absolute
blood pressure and the atmospheric pressure.
- The gauge pressure of the blood as it moves past the constriction is approximately 3·7 × 10³ N/m
Reasons:
The given parameters are;
Radius of the blood vessel, r₁ = 1.0 cm = 0.01 m
Average speed of the blood, v₁ = 0.40 m/s
Average pressure of blood, P = 1.4 × 10⁴ N/m²
The radius of the constriction, r₂ = 0.30 cm = 0.003 m
Density of blood, ρ = 1,050 kg/m³
The velocity of the blood past the constriction is given as follows;
The continuity equation is; v₁ × A₁ = v₂ × A₂
A₁ = π × r₁²
A₁ = π × (0.01 m)² = 0.0001·π m²
A₂ = π × (0.003 m)² = 0.000009·π m²
[tex]\displaystyle v_2 = \mathbf{\frac{v_1 \times A_1}{A_2}}[/tex]
[tex]\displaystyle v_2 = \frac{0.4 \ m/s \times 0.0001 \cdot \pi \ m^2}{0.000009 \cdot \pi \ m^2} = 4. \overline 4 \ m/s[/tex]
The speed of the blood after the constriction, v₂ = [tex]\mathbf{4. \overline 4}[/tex] m/s
Dynamic pressure due to speed of fluid is given by the formula;
[tex]\displaystyle P = \mathbf{\frac{\rho \cdot v^2}{2}}[/tex]
Therefore;
[tex]\displaystyle \frac{\rho \cdot v_2^2}{2} = \frac{1,050 \ kg/m^3 \times (4.\overline 4 \ m/s)^2}{2} = 10370. \overline{370} \ Pa[/tex]
[tex]\displaystyle \frac{\rho \cdot v_1^2}{2} = \frac{1,050 \ kg/m^3 \times (0.4\ m/s)^2}{2} = 84 \ Pa[/tex]
According to Bernoulli's equation, for blood vessel section at the same level, we have;
- [tex]\displaystyle P_1 + \frac{\rho \cdot v_1^2}{2} = \mathbf{P_2 + \frac{\rho \cdot v_2^2}{2}}[/tex]
Which gives;
[tex]\displaystyle P_2 = P_1 + \frac{\rho \cdot v_1^2}{2} - \frac{\rho \cdot v_2^2}{2}[/tex]
[tex]\displaystyle P_2 = 1.4 \times 10^4 + 84 -10370. \overline{370} \approx 3,713.6296[/tex]
P₂ ≈ 3,713.6296 N/m²
- The gauge pressure of the blood as it moves past the constriction, given to two significant figures P₂ ≈ 3,700 N/m² = 3.7 × 10³ N/m²
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https://brainly.com/question/13018949
