Book

Question 1

What is a fluid, and how does it differ from a solid?

Answer 1

A fluid flows under shear stress, unlike a solid that resists it. Liquids have a fixed volume but no shape, while gases fill their container.

Question 2

What is the primary difference between fluid mechanics and solid rigid-body mechanics in terms of description?

Answer 2

Solid mechanics tracks individual particles (position, velocity, acceleration), while fluid mechanics deals with the motion of a continuum, not individual particles.

Question 3

What is the Eulerian description in fluid mechanics?

Answer 3

It describes the properties of the fluid (e.g., velocity, pressure) at specific points in space over time.

Question 4

How does the Eulerian description differ from the Lagrangian description?

Answer 4

Eulerian focuses on fixed points in space, while Lagrangian tracks individual fluid particles over time.

Question 5

What is the continuum assumption in fluid mechanics?

Answer 5

Fluids are treated as continuously divisible, with properties like pressure and velocity well-defined at every point.

Question 6

Why is the mean free path of fluid particles significant for the continuum assumption?

Answer 6

The mean free path must be much smaller than the system’s physical dimensions for the continuum assumption to hold.

Question 7

What happens if the mean free path is not negligible compared to physical dimensions?

Answer 7

The continuum assumption breaks down, and microscopic approaches like molecular flow theory are required.

Question 8

What are the five basic variables in fluid mechanics?

Answer 8

Velocity, pressure, temperature, density, and internal energy.

Question 9

Why do we need two thermodynamic properties to determine the state of a fluid?

Answer 9

Two properties (e.g., pressure and temperature) are sufficient to determine all other thermodynamic properties.

Question 10

What additional unknown variables appear in turbulent flows?

Answer 10

In turbulent flows, fluctuations in velocity, pressure, and other properties introduce more unknowns.

Question 11

Why is the energy equation not needed in incompressible fluid flow?

Answer 11

For incompressible flow, temperature and density are constant, so energy changes are not required to describe the system.

Question 12

What is pressure in a static fluid?

Answer 12

Pressure is the normal compressive force per unit area acting on a surface in a fluid at rest.

Question 13

What is hydrostatic pressure?

Answer 13

Hydrostatic pressure is the isotropic pressure in a fluid at rest, used in thermodynamics.

Question 14

How does pressure behave in a moving fluid?

Answer 14

In moving fluids, pressure may vary in different directions due to viscosity effects.

Question 15

What is viscosity?

Answer 15

Viscosity measures a fluid’s resistance to shear when in motion.

Question 16

What is the difference between viscous and ideal flow?

Answer 16

Viscous flow includes friction, while ideal flow assumes no friction or turbulence.

Question 17

How is shear stress (𝜏) in a fluid defined?

Answer 17

𝜏=μ ∂y/∂u, where 𝜇 is viscosity and ∂𝑢/∂𝑦 is the velocity gradient.

Question 18

What are the units of viscosity?

Answer 18

Viscosity is measured in poise (dyne-sec/cm2) or N·s/m2 (SI units).

Question 19

How does temperature affect the viscosity of liquids and gases?

Answer 19

The viscosity of a liquid decreases with increasing temperature, while the viscosity of a gas increases with increasing temperature. Temperature changes influence the molecular interactions within the fluid, making liquids flow more easily and gases experience greater resistance.

Question 20

What is the Newtonian relationship in fluid mechanics?

Answer 20

The Newtonian relationship is the linear relationship between shear stress (𝜏) and velocity gradient (∂𝑢/∂𝑦). Fluids that follow this relationship are called Newtonian fluids.

Question 21

What are Newtonian fluids?

Answer 21

Newtonian fluids have a linear relationship between shear stress and velocity gradient. Examples include water, air, and most gases.

Question 22

What are non-Newtonian fluids?

Answer 22

Non-Newtonian fluids do not follow a linear relationship between shear stress and velocity gradient. Their behavior depends on factors like strain rate or prior working.

Question 23

What is a thixotropic fluid?

Answer 23

Thixotropic fluids have shear stress that depends on prior working or straining. An example is printer’s ink.

Question 24

What is a plastic fluid?

Answer 24

A plastic fluid behaves as a solid until a yield stress is reached. After yielding, it flows like a viscous fluid. Examples include greases and sludges.

Question 25

What are dilatant fluids?

Answer 25

Dilatant fluids flow easily at low strain rates but become more solid-like as the strain rate increases. Quicksand is an example.

Question 26

What is an ideal fluid, and why is it significant in fluid mechanics?

Answer 26

An ideal fluid has no viscosity and no internal friction, meaning it does not generate shear stresses or energy losses. While no fluid is truly ideal, ideal flow is a useful approximation in certain regions, like aerodynamic flows over surfaces.

Question 27

What is laminar flow?

Answer 27

Laminar flow occurs when a fluid flows in smooth, parallel layers with no mixing between them.

Question 28

What is turbulent flow?

Answer 28

Turbulent flow is chaotic, with random fluctuations in velocity and mixing of fluid particles. Dye in turbulent flow spreads into threads and clouds, rapidly dispersing.

Question 29

What is the Mach number, and how is it used to classify flow?

Answer 29

The Mach number (𝑀) is the ratio of the fluid speed (𝑉) to the local speed of sound (𝑎): 𝑀=𝑉/𝑎. Flow is classified as subsonic (𝑀<1) or supersonic (𝑀>1) based on this ratio.

Question 30

What is steady flow in fluid mechanics?

Answer 30

Steady flow occurs when the velocity and thermodynamic properties at every point in space do not change with time, even if individual particles move through different regions.

Question 31

How can 𝑀<1 and 𝑀>1exist on the same body simultaneously?

Answer 31

The local sonic speed and fluid speed vary over the body, due to variations in temperature and pressure, allowing subsonic (𝑀<1) and supersonic (𝑀>1) flow regions to coexist.

Question 32

What is the boundary layer in external flow?

Answer 32

The boundary layer is the thin region near a body where the fluid develops a shear layer due to viscosity, with velocity gradually increasing from zero at the surface to the free stream. It can be laminar or turbulent.

Question 33

What causes the wake behind a body in external flow?

Answer 33

The wake is caused by the separation of the boundary layer from the surface of the body, leading to turbulence and low pressure. This results in drag forces due to the wake.

Question 34

How is pressure defined in fluid mechanics?

Answer 34

Pressure is defined as the stress, or surface force per unit area:
𝑝=limΔ𝐴→0 Δ𝐹/Δ𝐴=𝑑𝐹/𝑑𝐴. It measures the normal force exerted by a fluid on a surface.

Question 35

What challenge arises when defining pressure for an actual fluid at a small scale?

Answer 35

The continuum assumption conflicts with the use of differential quantities at very small scales. This is resolved by treating fluids as continuous at macroscopic scales for practical applications.

Question 36

What forces act on a small fluid element in a liquid at rest?

Answer 36

In a liquid at rest, the forces acting are: Normal pressure forces from the surrounding fluid. Body forces, such as gravity, which acts in the negative 𝑦-direction. Since there is no relative motion, shear stress is zero, and the system is in equilibrium.

Question 37

What is the equation for pressure variation with height in a fluid of constant density?

Answer 37

The equation is: 𝑝2−𝑝1=−𝜌𝑔(𝑧2−𝑧1), where 𝜌 is the fluid density, 𝑔 is gravitational acceleration, and 𝑧2−𝑧1 is the height difference.

Question 38

How is the pressure variation expressed for an ideal gas?

Answer 38

For an ideal gas, the pressure variation with height is given by: 𝑑𝑝=−𝜌𝑔/𝑅𝑇 𝑑𝑧, where 𝑅 is the gas constant and 𝑇 is the temperature.

Question 39

What are the equations for pressure variation in the three coordinate directions in fluid statics?

Answer 39

In fluid statics: ∂𝑝/∂𝑥=0, ∂𝑝/∂𝑦=0, ∂𝑝/∂𝑧=−𝜌𝑔. This means pressure is constant in the horizontal directions (𝑥 and 𝑦) and decreases linearly with elevation in the vertical direction (𝑧).

Question 40

What is the expression for force on a horizontal plane surface submerged at depth ℎ?

Answer 40

For an inclined plane, the force is: 𝐹=𝑝_0𝐴+1/2 𝛾𝑤 sin𝜃(𝑦2_2−𝑦1_2), where 𝑤 is the width of the surface, 𝜃 is the angle of inclination, and 𝑦1 and 𝑦2 are the vertical limits of the surface.

Question 41

What is the expression for force on an inclined submerged plane surface?

Answer 41

For a horizontal surface, the force is: 𝐹=(𝑝_0+𝛾ℎ)𝐴, where 𝐴 is the area of the surface.

Question 42

How is the total surface force (𝐹) on a submerged body calculated?

Answer 42

The total surface force is calculated by integrating the pressure over the entire surface area: 𝐹=∫𝐴𝑝 𝑑𝐴, where 𝑝=𝑝_0+𝛾ℎ, 𝑝_0 is the surface pressure, 𝛾 is the specific weight, and ℎ is the depth.