Unit 5: Solids and Fluid Dynamics — Short Questions

Cohesive forces
i. Cohesive forces are the attractive forces between molecules of the same substance. They are responsible for phenomena like surface tension in liquids
ii. Viscosity
Property of the fluid due to which it internally resists its flow is known as viscosity. Viscosity measures how much force is required to slide one layer of the liquid over its other layer.
Viscosity depends upon the nature of fluid and on its temperature. Increase in temperature of the Liquids decrease its viscosity. Its S.I unit is Nsm⁻². Increase in temperature increases the viscosity of gases.

A flow of fluid is said to be laminar when every particle that passes a particular point moves exactly along the same path, followed by particles which passed that point earlier. And the irregular or unsteady flow of the fluid is called turbulent flow. The fluid particles do not move on definite path in this type of flow.
Also there is a definite flow pattern in a laminar flow while in turbulent flow there is a constantly changing flow pattern.
The water, flowing gently from a narrow pipe and water flowing rapidly from a tap when it is fully turned on are the examples of streamline and turbulent flow respectively.

Since P = ρgh
ρ = density of the fluid
g = acceleration due to gravity
h = depth
As you go deeper into a fluid, the pressure increases because there's more fluid above pushing down due to gravity. The deeper you go, the more weight is pressing from above, causing the pressure to rise steadily with depth.

The pressure and speed of a fluid are related by Bernoulli's Principle, which states:
As the speed of a fluid increases, its pressure decreases, and vice versa. i.e. v ∝ 1/P
When a fluid moves faster, more of its energy is used for motion (kinetic energy), leaving less energy available for pressure.
So, in fast-flowing regions, the pressure drops while when the fluid slows down, less energy is used for motion, so pressure increases.

The flow rate of a fluid is directly related to both its cross-sectional area (A) and velocity (v)
Flow rate = A × v
By increasing the area or speed, the flow rate increases.
If the area is narrow (like in a nozzle), the fluid must speed up to keep the flow rate constant (equation of continuity).

Fluid velocity varies at different points in a hose with changing diameter. Applying the continuity equation:
A₁v₁ = A₂v₂ or Av = constant
When the hose narrows (smaller diameter), the fluid must speed up.
• When the hose has larger diameter, the fluid slows down.
This relationship holds for incompressible fluids.

According to Archimedes' Principle "An object floats if the buoyant force (equal to the weight of the displaced fluid) is greater than or equal to its own weight. If the object's weight is greater than the buoyant force, it sinks."

Archimedes' reportedly discovered his principle while taking a bath. He noticed that the water level rose as he got in and realized that the volume of water displaced was related to the volume of his body, leading to the formulation of what is now known as Archimedes' Principle.

Standing near a fast moving train has the danger of falling towards it. The speed of air between man and train is very high as compared to the speed of air behind the man. So according to Bernoulli's affect, the pressure of air between man and train is low as compared to the pressure of air behind the man. Hence greater pressure of air on the man from his rear skde may push him towards the train.

i. Currently, there are few practical uses for superfluids. Superfluid helium-4 serves as a coolant for high-field magnets. Both helium-3 and helium-4 are utilized in advanced particle detectors.
ii. Researching superfluidity also helps us learn more about superconductivity.
iii. Liquid helium is recognized for its great thermal conductivity and is used in cryogenic applications, including cooling superconducting magnets, scientific research, and medical uses.
iv. Additionally, it is employed in industry for leak testing and in the production of electronic and optical products.

Quantity Stress
Definition: Force applied per unit area of a material.
Formula: Stress=F/A
SI Unit: pascal (Pa) or N/m²

Quantity Strain
Definition: The ratio of change in length to original length (dimensionless).
Formula: Strain=ΔL/L
SI Unit: No unit (dimensionless)

Quantity Young's Modulus
Definition: Ratio of tensile stress to tensile strain is called Young's modulus
Formula: Y= tensile Stress/tensile Strain
SI Unit: pascal (Pa) or N/m²

"Anything, which can flow, is called fluid" Liquids and gases are categorized as fluids.
"The fluid whose density remains constant and whose viscosity is zero is known as ideal fluid." There is no real fluid, which is an ideal fluid. Both air and water are approximately ideal fluids at low pressures.

It is a term used to describe the internal frictional effects between different layers of flowing fluid.

"The tangential force per unit area required to maintain a unit relative velocity between its two layers, unit distance apart is called coefficient of viscosity". It is denoted by η.
Unit: Its SI units are N s m⁻² or kg m⁻s⁻¹.

The inter-atomic force present between the atoms of a substance is called cohesive force.

The drag force 'F' on a sphere of radius 'r' moving slowly with velocity v in a fluid of viscosity η is given by:
F = 6πηrv

An ideal fluid satisfies the following conditions:
(i) The fluid is non-viscous i.e. there is no internal frictional force between adjacent layers of fluid.
(ii) The fluid is incompressible i.e. its density is constant.
(iii) The fluid motion is steady.

Flow rate of a fluid may be mass flow rate or volume flow rate defined as below:
"Mass of the fluid flown per second is called its mass flow rate". It is found by the following formula:
Mass flow rate = ρAv
"Volume of the fluid flown per second is called its volume flow rate". Its formula is:
Volume flow rate = Av
During streamline flow of an ideal fluid these flow rates remain constant.

Flow rate of an ideal fluid during its streamline flow remains constant. The equation that expresses this fact is known as equation of continuity written as below:
Av = constant——(1)
Where A is the area of cross-section of the pipe and v is the speed of flow of the fluid.

Bernoulli's equation states that the sum of pressure P, the kinetic energy per unit volume 1/2 ρv² and potential energy per unit volume ρgh in a steady flow of an incompressible and non-viscous fluid remains constant at every point of its path.
i.e. P + 1/2ρv² +ρgh = constant

Speed and pressure of an ideal fluid during its streamlines flow as the following relation:
(i) The pressure will be low where the speed of fluid is high and vice-versa.
(ii) This fact is written in the form of following equation for a fluid flowing in horizontal pipe:
P + 1/2 ρv² = constant
(iii) Aerodynamic lift and swinging of a cricket ball are practical applications of this relation.

Chimney is made very tall because at the top speed of air is very large therefore, by Bernoulli's effect this pressure will become low. Therefore, the burnt gases and smoke will be discharged effectively.

No, the atoms, ions or molecules in a crystalline solid are not static but they are vibrating to and fro about their mean position.

The amorphous mean 'without structure i.e. no regular arrangement of molecules exist in amorphous solids.

The alternation produced in shape, length or volume, when an external force is applied is called deformation.

The ability of a body to return to its initial state after the removal of external force is called elasticity.

The point on the stress-strain curve beyond which if stress is increased then permanent deformation occurs in the material is called yield point.

The substance which undergo plastic deformation until they break are called ductile substances e.g. Lead, Copper.

The substances which break just after the elastic limit is reached are brittle substance e.g. glass, high carbon steel.

When deformation becomes very large, the material typically experiences nonlinear behavior, this means the ratio of stress to strain, which is constant in the elastic region (small deformations), no longer holds. The material may undergo permanent deformation, and the relationship between stress and strain can become more complex, often described by plasticity.

When pure water falls on a glass plate, it spreads out because the adhesive forces between water and glass are stronger than the cohesive forces within water. This causes the water to "wet" the glass. Mercury forms small globules because the cohesive forces between mercury atoms are much stronger than the adhesive forces between mercury and glass. So mercury does not wet the glass.

According to Bernoulli's theorem, pressure remains constant in ideal, non-viscous flow.
In reality, fluid has viscosity so energy loss due to friction with pipe walls, leading to a gradual pressure drop even in a pipe of uniform radius.

Airplane wings are rounded on top and flat on the bottom to create a pressure difference. Air moves faster over the curved top which reduces pressure (by Bernoulli's principle), while slower air below exerts high pressure due to this pressure difference aeroplane lifts up in air.

Difference of Three types fluids
• Ideal Fluid: A hypothetical fluid with no viscosity and no compressibility. It flows without resistance.
• Real Fluid: Actual fluids like water or air that have viscosity, and compressibility. They experience energy loss due to friction.
• Superfluids: Superfluidity is the property of a fluid where they have zero viscosity or are frictionless. A substance exhibiting this property is superfluids.
• Existence in real world only real fluids exist in everyday life.
• Superfluids exist under special laboratory conditions.

The study of superfluids is very important in low-temperature physics because it provides direct insight into quantum mechanics at a macroscopic level. Superfluids (like liquid helium-4 below 2.17 K) exhibit phenomena such as:
• Zero viscosity: They can flow without losing energy, defying classical physics.
• Quantized vortices: Rotation in a superfluid happens in discrete steps, revealing quantum effects in fluid motion.
• Bose-Einstein condensation: Superfluidity is linked to particles occupying the same quantum state, a key concept in quantum physics.