AIIMS 2007 Physics Bernoulli's Principle MCQ Question

Let's analyze the given question about the increase in blood pressure due to narrowing arteries in old age, linking it to fluid mechanics principles.

Explanation of the Correct Answer

Correct Answer: A) Pascal's Law

In fluid mechanics, Pascal's law states that when pressure is applied to a confined fluid, the pressure change occurs throughout the fluid uniformly in all directions. This principle is crucial in understanding how blood pressure operates in the cardiovascular system.

As arteries narrow due to factors like aging, the same volume of blood is forced through a smaller cross-sectional area. According to the principle of continuity in fluid flow, when the cross-section decreases, the velocity of the fluid must increase to maintain a constant flow rate. This can be expressed as:

$A_1 v_1 = A_2 v_2$

where:

• $A_1$ and $A_2$ are the cross-sectional areas of the artery before and after narrowing, respectively,
• $v_1$ and $v_2$ are the fluid velocities before and after narrowing, respectively.

As the cross-sectional area $A_2$ decreases, to keep $A_1 v_1 = A_2 v_2$ valid, $v_2$ (the velocity of blood flow) must increase. According to Bernoulli’s principle, an increase in fluid velocity leads to a decrease in pressure, but in this case, the body compensates for that by increasing the overall systemic blood pressure to ensure that essential organs continue to receive adequate blood supply.

Clarification of Other Options

B) Stoke's Law

• Incorrect: Stoke's law pertains to the force of viscosity acting on spherical objects moving through a fluid. It describes how the drag force $F_d$ experienced by a small spherical particle in a viscous fluid is given by:

$F_d = 6 \pi \eta r v$

where:

• $\eta$ is the viscosity of the fluid,
• $r$ is the radius of the sphere,
• $v$ is the velocity of the sphere.

This law does not directly relate to blood pressure or flow through arteries.

C) Bernoulli's Principle

• Incorrect: Although Bernoulli's principle does relate to fluid flow and pressure, it states that in a streamline flow, the total mechanical energy remains constant. The formula is given by:

$P + \frac{1}{2} \rho v^2 + \rho gh = \text{constant}$

where:

• $P$ is the pressure,
• $\rho$ is the fluid density,
• $v$ is the fluid velocity,
• $g$ is the acceleration due to gravity,
• $h$ is the height above a reference level.

While Bernoulli's principle explains the relationship between velocity and pressure, the increase in blood pressure due to narrowing arteries is primarily a result of Pascal's law and the body's compensatory mechanisms.

D) Archimede's Principle

• Incorrect: Archimede's principle deals with buoyancy and states that an object submerged in a fluid experiences an upward buoyant force equal to the weight of the fluid it displaces. It does not apply to the dynamics of blood flow in arteries.

Conclusion

In summary, as arteries narrow with age, the continuity of blood flow requires an increase in velocity, which, according to Pascal's law, necessitates a compensatory increase in blood pressure to maintain adequate circulation. This interplay of fluid dynamics is crucial for understanding cardiovascular health, especially in aging populations.