Consider 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 Reynold’s number.

E. In a steady flow two stream lines never intersect.

Choose the correct answer from the options given below :

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 is incorrect. Surface tension arises due to the cohesive forces between molecules. Molecules at the surface experience an imbalance of forces since they are not surrounded by similar molecules on all sides, causing them to pull inward, which results in surface tension. It is not about extra energy but the difference in forces.

B. As the temperature of liquid rises, the coefficient of viscosity increases.

• This is incorrect. For liquids, the coefficient of viscosity decreases with an increase in temperature. As temperature rises, the molecules move faster, making it easier for them to flow past each other, reducing viscosity.

C. As the temperature of gas increases, the coefficient of viscosity increases.

• This is correct. For gases, the coefficient of viscosity increases with temperature because the kinetic energy of molecules increases, leading to more frequent collisions and higher resistance to flow.

D. The onset of turbulence is determined by Reynold’s number.

• This is correct. The Reynolds number (Re) is used to predict the flow regime of a fluid. If Re exceeds a critical value (typically around 2000-4000 depending on the situation), the flow transitions from laminar to turbulent.

E. In a steady flow two streamlines never intersect.

• This is correct. In steady flow, streamlines represent the paths followed by fluid particles, and since the flow velocity is consistent at any given point, two streamlines cannot intersect.