Fluid Mechanics Quiz 1 Examples

What is the meaning of the term specific gravity?

density of the fluid in question per (compared to) the density of water. SG = ρ/ρ_water

What are pathlines?

the actual path traversed by a given fluid particle.

What are streaklines?

the locus of particles that have earlier passed through a described point.

Given an example of a field representation of a continuum vector property.

where u, v, and w represent V_x, V_y, V_z

What is a fluid? Illustrate the difference between a fluid and a solid.

A fluid has the ability to move and deform continuously when a shear stress is applied and therefore a fluid cannot resist shear stress. A solid, on the other hand, has the ability to resist shear stress by a static deflection.

What is the difference between absolute (dynamic) viscosity and kinematic viscosity?

Absolute viscosity (μ): the measure of a fluids resistance to flow when an external force is applied. Kinematic viscosity: the resistive flow of a fluid under the weight of gravity alone. ν = μ/ρ (note: ν in these eqs. is Greek letter nu)

What is experimental uncertainty?

Accounts for the fact that no experiment is conducted with perfect conditions and as a result will always have some amount of error or "noise."

Illustrate the difference between cylindrical and Cartesian coordinate system.

Cartesian = V(x,y,z) Cylindrical = V(r,θ,Z) Polar = V(r,θ,Φ)

What is the difference between compressible and in-compressible flow?

Compressible has Mach# >0.3 In-compressible has Mach# <0.3

Name 3 conservation laws which describe the physics of fluid motion.

Conservation of mass Conservation of momentum Conservation of energy

Give an example of a field representation of a continuum property.

Density: ρ ≡ ρ(x,y,z,t)

Give two examples of body forces.

Gravity, magnetic forces, electric forces Body forces act though the entire body of the control volume.

What is the root of the SI system? Name the equation and the units obtained thereof.

Mass (M): Kilogram (kg) Length (L): Meter (m) Time (T): Second (s) Temperature (Θ): Kelvin (K)

What are the following terms: A system? A control volume? A control surface?

System (Closed system): quantity of matter or region in space chosen for study where the mass of the matter or region remains fixed and cannot leave the system. Control Volume: a defined volume in space chosen for study where the mass can flow/change with time. Control Surface: the surface that encloses the control volume.

Pair the following terms: infinitesimal and control volume versus integral and differential.

Infinitesimal → differential approach Control volume → integral approach

What is the difference between internal and external flows?

Internal Flows: Flow completely bounded by solid surfaces, such as a pipe or duct, are mostly viscous, and the wall layers grow to meet in the core of the duct. External Flows: flow of an unbounded fluid over a surface such as an aircraft wing. Partly viscous and partly inviscid.

What is the difference between viscous and inviscid flows?

Inviscid flow: Lacks the effects of viscosity because no relative velocity difference between two flow layers because they are traveling at the same velocity. Viscous flow: when two fluid layers move relative to each other, a friction force develops between them and the slower layer tries to slow down the faster layer. Viscous flow is greatest at surfaces which is where no-slip condition occurs.

What is the difference between Laminar and Turbulent flows?

Laminar flow: flow that occurs when a fluid flows in parallel layers, with no disruption between the layers. Internal Laminar Flow (Pipe flow/Duct Flow): Reynolds number <2100 External Laminar Flow: Reynolds number <5x10⁵ Turbulent flow: any pattern of fluid motion characterized by chaotic changes in pressure and flow velocity. Internal Turbulent Flow (Pipe flow/Duct Flow): Reynolds number >2100 External Laminar Flow: Reynolds number >5x10⁵ Reynolds #: Re = VD/ν v = Greek letter nu

What are the No Slip Condition and No Temperature Jump Condition?

No Slip Condition: When a fluid flow is bounded by a solid surface, molecular interactions cause the fluid in contact with the surface to seek momentum and energy equilibrium with that surface. In other words, the flow takes on the zero velocity of the surface. No Temperature Jump Condition: Temperature of Fluid at Boundary/wall ≡ Temperature of Boundary/Wall

What is the difference between normal and shear stress?

Normal stress: stress which acts normal to the plane (surface area) to which a force has been applied. Shear stress: stress which acts parallel to the plane (surface area) to which a force has been applied.

What is the ideal gas equation of state?

PV = mRT → Pv = RT → P/ρ = RT → P = ρRT P = pressure v = specific volume m = mass of gas R = gas constant T = absolute temperature (K) V = volume

Vector Analysis?

Page 35 in FE Reference Handbook

Give two examples of forces acting on control surfaces.

Pressure and viscous forces at points of contact, drag forces. Body forces and surface forces. Surface forces act on the control surface.

Dimensional homogeneity requires specifying primary dimensions. Name one basic system of dimensions.

SI System

Define the speed of sound and Mach number.

Speed of sound (a): the rate of propagation of sound waves through a fluid. a = √(kRT) , k = c_p/c_v Mach number: the ratio of the speed of a body to the speed of sound in the surrounding medium.

What are the differences between the Lagrangian and Eulerian viewpoints in describing fluid motion?

The Eulerian frame of reference can be described as a window through which we watch a flow; the coordinates are fixed and the flow passes by. Therefore, a fixed instrument placed in the flow takes an Eulerian measurement. In contrast to this, Lagrangian frame of reference follows the moving position of individual particles.

To classify continuum fluid mechanics the certain term are used.

The limiting volume δV must be ≥ 10⁻⁹ mm³

Give 2 examples on the effects of surface tension.

The movement of water in soil is due to surface tension effects. Rain-x applied to a windshield acts to reduce the surface tension of the water with the glass to allow the water to bead off the windshield. Wetting and non-wetting Hydrophoic and Hydrophilic

If the flow is three-dimensional and unsteady, write one property in functional form to describe the flow field.

V(x,y,z,t) ≡ iu(x,y,z,t) + jv(x,y,z,t) + kw(x,y,z,t) where u, v, and w represent V_x, V_y, V_z

What is viscosity? Describe an experiment to measure viscosity.

Viscosity is a quantitative measure of a fluids resistance to flow and it determines the fluid strain rate that is generated by a given applied shear stress. Experiment: take two glass jars and fill one with water and one with corn syrup. Drop a marble of the same dimensions in each. The marble in the corn syrup will take longer to reach the bottom so the viscosity is greater.

Describe a continuum. Under what circumstances can fluids be treated as a continuum?

Where fluid properties are considered to be continuous in space. So even though gas molecules have a relatively large amount of space between them, we can take it to be continuous and homogeneous so long as the limiting volume is greater than or equal to 10⁻⁹ mm³.

What are streamline?

a line everywhere tangent to the velocity vector

What are Timelines?

a set of fluid particles that form a line at a given instant.