AIIMS 2004 Physics Bernoulli’s Principle MCQ Question

To understand the question regarding the increase in blood pressure due to narrowing of arteries in old age, we need to delve into the principles of fluid dynamics, specifically Bernoulli's principle.

Explanation of the Correct Answer: C) Bernoulli’s Principle

Bernoulli’s Principle states that for an incompressible fluid flowing in a streamline, the total mechanical energy along a streamline is constant. This principle highlights the relationship between the pressure, velocity, and height of a fluid.

The equation for Bernoulli's principle is given by:

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

Where:

• $P$ = pressure of the fluid
• $\rho$ = density of the fluid
• $v$ = velocity of the fluid
• $g$ = acceleration due to gravity
• $h$ = height above a reference point

In the context of blood flow in arteries:

1. As arteries narrow (due to factors such as aging or plaque buildup), the cross-sectional area decreases.
2. According to the principle of conservation of mass (continuity equation), if the cross-sectional area decreases, the velocity of the blood must increase to maintain a constant flow rate. This is given by:

$$A_1 v_1 = A_2 v_2$$

Where $A_1$ and $A_2$ are the cross-sectional areas of the artery at two points, and $v_1$ and $v_2$ are the corresponding velocities.

1. As the velocity $v$ increases, the kinetic energy term $\frac{1}{2} \rho v^2$ increases. To maintain the constant total mechanical energy (as per Bernoulli's equation), the pressure $P$ must decrease. However, in the case of a narrowing artery, the blood is often under more pressure due to the heart's pumping force. Therefore, the body compensates by increasing the overall blood pressure to ensure adequate blood flow, leading to an increase in blood pressure despite the local decrease in pressure due to increased velocity.

Clarification of Incorrect Options

A) Pascal’s Law: This law states that a change in pressure applied to an incompressible fluid is transmitted undiminished throughout the fluid. While it applies to fluid pressure in general, it does not explain the relationship between velocity and pressure in the context of blood flow in narrowed arteries.

B) Stoke’s Law: This law describes the force of viscosity acting on spherical objects moving through a viscous fluid. It is more relevant to the motion of small particles in a fluid rather than the dynamics of blood flow in arteries.

D) Archimedes’ Principle: This principle states that any object submerged in a fluid experiences an upward buoyant force equal to the weight of the fluid displaced. It relates to buoyancy and is not applicable to the dynamics of blood flow in arteries.

Conclusion

In summary, the increase in blood pressure in narrowed arteries in older individuals can be effectively explained using Bernoulli's principle. The relationship between the pressure and velocity of blood as it flows through constricted areas leads to an increase in overall blood pressure to ensure sufficient blood circulation. Understanding these fluid dynamics principles is crucial for grasping cardiovascular health in the context of aging.