FLUIDS 1

Continuum

The molecular nature of a fluid can be ignored and the fluid is treated as a continuum

Compressibility

The ability to change in volume in reaction to an increase in pressure

Viscosity

Stickiness of a fluid

Incompressible

The density of a fluid is essentially constant during a flow process (very low compressibility)

What is the cause of viscosity?

Caused by the internal resistance to relative motion between adjacent layers of fluids

No slip condition

A fluid in direct contact with a solid surface sticks to the surface

Viscous Shear Stress

Develops between two adjacent fluid layers to retard their relative motion

Newton's Law of Viscosity

For certain fluids, viscous shear stress is linearly proportional to the rate of change of velocity with respect to distance with the viscosity coefficient

Newtonian Fluid

Where the shear stress is linearly proportional to the velocity gradient

Specific Weight

Combination of gravitational acceleration and density

Surface Tension

The molecules at the liquid surface experiences both an inward pull and a pulling force along the liquid-gas interface. Hence the liquid tends to form a spherical shape to attain a minimum surface area for given volume. The liquid resembles a stretched elastic membrane

Capillary Effect

The rise and fall of a liquid in a small diameter tube inserted into the liquid

Cohesive Force

Forces between like molecules

Adhesive Force

Forces between unlike molecules

What does the capillary effect depend on?

Determined by the relative strength of cohesive and adhesive forces a liquid is subjected to at a solid-liquid interface. Rises if co<ad and falls if co>ad

Absolute Pressure

It is the actual pressure and it is measured relative to absolute vacuum (absolute zero pressure)

Gauge Pressure

It is the difference between the absolute pressure and the atmospheric pressure

Shear stress in a stationary fluid

No relative motion between fluid layers so the shear stress is zero. The normal stress is equal to the pressure in magnitude (acts in opposite direction)

Specific Gravity

A dimensionless ratio of the densities of two materials. Can be found by measuring the weight in and out of water.

Hydrostatic Force

The resultant force caused by the pressure loading of a liquid acting on submerged surfaces

Centre of pressure

The point of intersection of the line of action of Fr and the surface

Pascal’s Principle

Pressure transmitted, undiminished in a closed static fluid. The fluid pressure at all points, which are at the same height, in a connected body of an incompressible fluid at rest, is all the same.

Steady flow

Flow parameters at any point in the flow do not vary with time

Unsteady flow

The flow condition at a given point changes with time

Laminar flow

Smooth and orderly motion. Particles move in definite and observable paths

Turbulent flow

Chaotic motion. Particles travel in irregular paths with no observable pattern.

Reynold’s number

Dimensionless parameter that is the ratio of inertial force to viscous force. Boundary between laminar and turbulent flow (Re<2300 flow is laminar)

Streamlines

Curve on which the tangent at each point indicates the direction of fluid at that point

Streaklines

The line formed by a series of fluid particles which passed a certain point in the stream one after another

Pathlines

The trajectory of a particular fluid particle

Closed system

Mass CANNOT cross the boundary

Control volume (CV)

Mass CAN cross the boundary. It is also a selected region in space

Control surface

The real or imaginary surface that separates the volume from its surroundings

Volume flow rate

The volume of fluid going through a cross-sectional area per unit time

Mass flow rate

The amount of mass going through a cross sectional area per unit time

Newton’s Second Law of Motion

The momentum change per unit time in a body is equal to the force acting on the body

Momentum flux

Momentum carried by a fluid flow per unit time as it enters or leaves a CV

Angular momentum

the moment of linear momentum

Buoyancy

The upward force on an object produced by the surrounding fluid in which it is fully or partially immersed

What produces buoyancy?

Produced by the pressure difference of the fluid between the top and bottom of the object

Archimedes principle

The buoyancy force acting on a body immersed in a fluid is equal to the weight of the fluid displace by the body

Metacentre

The intersection point of the lines of action of the buoyancy force and line of symmetry

Static pressure

P, it is the actual pressure of the fluid (no dynamic effect)

Dynamic pressure

½ rho V*2, the pressure rise when the fluid in motion is brought to a stop in a frictionless manner

Hydrostatic pressure

rho gz, it’s value depends on where z=0 is taken. It accounts for elevation

Boundary layer

The near-wall region containing the slow moving fluid

Flow separation

At sufficiently high velocities, the fluid stream may detach itself from the surface of a body

Froude number

Determines whether a flow is subcritical (slow), critical or supercritical (fast). Subcritical if Fr<1, supercritical if Fr>1

Hydraulic jump

It is an abrupt change from a shallow high-speed flow to a deep low-speed flow of lower energy. Where mass is conserved, momentum principle is satisfied and mechanical energy is lost.