Question

Bernoulli's equation relates

• A. heat and work
• B. stress and strain
• C. diffusion and temperature
• D. pressure and velocity

Hint:

When fluid flows through a constriction (such as a venturi tube), the velocity increases, causing the static pressure to drop. This is a direct application of Bernoulli's principle.

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
The question asks about the physical quantities that are related by Bernoulli's equation in fluid mechanics.

Step 2: Key Formula or Approach:
For an incompressible, frictionless (inviscid) fluid flowing along a streamline, Bernoulli's equation is expressed as:
\[ P + \frac{1}{2} \rho v^2 + \rho g h = \text{constant} \]
where:
\( P \) is the static pressure of the fluid,
\( \rho \) is the fluid density,
\( v \) is the flow velocity,
\( g \) is the acceleration due to gravity, and
\( h \) is the elevation relative to a reference plane.

Step 3: Detailed Explanation:

• Conservation of Energy: Bernoulli's equation is a statement of the principle of conservation of energy for flowing fluids.
It relates the static pressure energy, kinetic energy (related to velocity), and potential energy (related to height).

• Pressure and Velocity Relationship: In a horizontal flow system where elevation (\( h \)) is constant, the equation simplifies to:
\[ P + \frac{1}{2} \rho v^2 = \text{constant} \]
This demonstrates that an increase in the velocity of a fluid occurs simultaneously with a decrease in static pressure, establishing a direct relationship between pressure and velocity.

• Analysis of Other Options:
-

Heat and work (Option A) are related by the First Law of Thermodynamics.
-

Stress and strain (Option B) are related by Hooke's Law in elasticity.
-

Diffusion and temperature (Option C) are related via the Arrhenius equation for diffusivity.


Step 4: Final Answer:
Thus, Bernoulli's equation relates pressure and velocity, which corresponds to Option (D).