Question

Consider the following statements: 
A. Surface tension arises due to extra energy of the molecules at the interior as compared to the molecules at the surface of a liquid. 
B. As the temperature of liquid rises, the coefficient of viscosity increases. 
C. As the temperature of gas increases, the coefficient of viscosity increases. 
D. The onset of turbulence is determined by Reynolds number. 
E. In a steady flow, two streamlines never intersect.
Choose the correct answer from the options given below:

• A. A, B, C Only
• B. A, D, E Only
• C. B, C, D Only
• D. C, D, E Only

Hint:

When analyzing fluid dynamics, remember that Reynolds number is crucial for determining the nature of flow (laminar or turbulent).

Answer 1

The Correct Option is D

Let's analyze each statement:

A. Surface tension arises due to extra energy of the molecules at the surface as compared to the molecules at the interior of a liquid.
The molecules at the surface experience a net inward force due to cohesive forces from the liquid below. This gives the surface molecules extra energy, leading to surface tension. Thus, statement A is incorrect.

B. As the temperature of a liquid rises, the coefficient of viscosity decreases.
This is because the cohesive forces between liquid molecules decrease with increasing temperature, making it easier for the liquid to flow. Thus, statement B is incorrect.

C. As the temperature of a gas increases, the coefficient of viscosity increases.
In gases, viscosity arises due to the transfer of momentum between gas molecules. At higher temperatures, the gas molecules move faster, leading to more frequent and effective collisions and thus increased momentum transfer. Thus, statement C is correct.

D. The onset of turbulence is determined by the Reynolds number.
The Reynolds number is a dimensionless quantity that characterizes the flow regime: low Reynolds numbers indicate laminar flow, while high Reynolds numbers indicate turbulent flow. Thus, statement D is correct.

E. In a steady flow, two streamlines never intersect.
Streamlines represent the direction of fluid flow at a given instant. If streamlines intersected, it would imply that a fluid particle at that point would have two different velocities simultaneously, which is not possible in steady flow. Thus, statement E is correct.

Final Answer:
The correct statements are C, D and E.

The final answer is $ \boxed{C, D \text{ and } E \text{ only}} $.

Answer 2

Step 1: Analyze each statement carefully.

Statement A: Surface tension arises due to extra energy of the molecules at the interior as compared to the molecules at the surface of a liquid.
This statement is incorrect because surface tension arises due to extra energy of the surface molecules (not the interior ones). Molecules at the surface experience unbalanced forces and thus have higher potential energy compared to those in the interior.

Statement B: As the temperature of liquid rises, the coefficient of viscosity increases.
This statement is incorrect. For liquids, as temperature increases, the intermolecular forces weaken and the coefficient of viscosity decreases.

Statement C: As the temperature of gas increases, the coefficient of viscosity increases.
This statement is correct. For gases, higher temperature means faster-moving molecules, leading to more momentum transfer and hence higher viscosity.

Statement D: The onset of turbulence is determined by Reynolds number.
This statement is correct. Reynolds number is a dimensionless quantity that helps predict flow patterns—laminar or turbulent—in fluids. When it exceeds a critical value (≈ 2000), turbulence begins.

Statement E: In a steady flow, two streamlines never intersect.
This statement is correct. If streamlines were to intersect, it would imply that a fluid element has two velocities at one point, which is physically impossible.

Step 2: Choose the correct set of statements.
From the analysis, statements C, D, and E are correct.

Final Answer:
\[ \boxed{C, D, E \text{ only}} \]