Question

Fill in the blanks using the word(s) from the list appended with each statement: 

(a) Surface tension of liquids generally ... with temperatures (increases / decreases) 

(b) Viscosity of gases ... with temperature, whereas viscosity of liquids ... with temperature (increases / decreases) 

(c) For solids with elastic modulus of rigidity, the shearing force is proportional to ... , while for fluids it is proportional to ... (shear strain / rate of shear strain) 

(d) For a fluid in a steady flow, the increase in flow speed at a constriction follows (conservation of mass / Bernoulli’s principle) 

(e) For the model of a plane in a wind tunnel, turbulence occurs at a ... speed for turbulence for an actual plane (greater / smaller).

Answer 1

Complete Answers

• (a) Surface tension of liquids generally decreases with temperature
• (b) Viscosity of gases increases with temperature, whereas viscosity of liquids decreases with temperature
• (c) For solids with elastic modulus of rigidity, the shearing force is proportional to shear strain, while for fluids it is proportional to rate of shear strain
• (d) For a fluid in a steady flow, the increase in flow speed at a constriction follows conservation of mass
• (e) For the model of a plane in a wind tunnel, turbulence occurs at a smaller speed for turbulence for an actual plane

(a) Surface Tension vs Temperature

Higher temperature → more molecular kinetic energy → weaker cohesive forces → decreases

(b) Viscosity Behavior

Gases: Molecules collide more → momentum transfer ↑ → increases
Liquids: Cohesion weakens → layers slide easier → decreases

(c) Solids vs Fluids

Solids (Hooke's Law): \(F \propto\) shear strain (deformation)
Fluids (Newton's Law): \(F \propto\) rate of shear strain (velocity gradient)

(d) Flow Speed at Constriction

Continuity equation: \(A_1v_1 = A_2v_2\)
Small \(A_2\) → large \(v_2\) → conservation of mass
(Bernoulli gives pressure-velocity relation, not speed increase cause)

(e) Wind Tunnel Model vs Actual Plane

Model is smaller → lower Reynolds number → turbulence at smaller speed
\(Re = \frac{\rho v L}{\eta}\), smaller \(L\) → smaller \(v\) for same \(Re\)

Quick Reference Table

Statement	Correct Fill-in
(a) Surface tension	decreases
(b) Gases / Liquids viscosity	increases / decreases
(c) Solids / Fluids force	shear strain / rate of shear strain
(d) Speed increase	conservation of mass
(e) Model turbulence	smaller