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)
Explanations:
(a) Surface tension of liquids generally decreases with temperature.
(Answer: decreases)
Because, Surface tension of liquids generally decreases with temperature
As temperature increases, the kinetic energy of molecules also increases. This reduces the cohesive forces between molecules at the surface of the liquid, thereby lowering the surface tension.
(b) Viscosity of gases increases with temperature, whereas viscosity of liquids decreases with temperature.
(Answer: increases, decreases)
Because, Viscosity of gases increases with temperature, whereas viscosity of liquids decreases with temperature
- In gases, viscosity arises due to molecular collisions and the transfer of momentum. As temperature increases, molecules move faster, increasing the frequency of collisions and the viscosity.
- In liquids, viscosity depends on intermolecular forces. Higher temperatures weaken these forces, allowing molecules to slide past each other more easily, thus decreasing viscosity.
(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.
(Answer: shear strain, rate of shear strain)
Because, 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
- In solids, deformation is elastic, and the shearing force is directly proportional to the shear strain, according to Hooke’s Law.
- In fluids, deformation is continuous under shear stress, and the shearing force depends on the rate at which layers of the fluid move relative to each other, known as the rate of shear strain.
(d) For a fluid in a steady flow, the increase in flow speed at a constriction follows Bernoulli’s principle.
(Answer: Bernoulli’s principle)
Because, For a fluid in a steady flow, the increase in flow speed at a constriction follows Bernoulli’s principle
Bernoulli’s principle states that in steady, incompressible flow, the sum of pressure energy, kinetic energy, and potential energy per unit volume remains constant. When the flow speed increases at a constriction, the pressure decreases to maintain energy conservation.
(e) For the model of a plane in a wind tunnel, turbulence occurs at a greater speed for turbulence for an actual plane.
(Answer: greater)
Because, For the model of a plane in a wind tunnel, turbulence occurs at a greater speed for turbulence for an actual plane
Turbulence depends on the Reynolds number, which is proportional to the speed, characteristic length (e.g., wing span), and inversely proportional to the fluid's viscosity. For a smaller model in a wind tunnel, the characteristic length is reduced. To match the Reynolds number, the speed must be increased compared to the actual plane.
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