Mechanical Properties of Fluids

Fluid

A substance that flows

thrust

total force exerted by a liquid on a surface

pressure

thrust acting normally per unit area

specific gravity/relative density

ratio of the density of the substance to the density of water at 4 degrees celcius

Hydrostatic Paradox

The pressure exerted by a column of liquid depends on its height and not on the shape of the vessel

atm pressure

1.013 X 10^5 Pa

absolute pressure

the total or actual pressure P at a point is called absolute pressure

guage pressure

the difference between the actual pressure at a point and the atmospheric pressure

Buoyancy

the upward force acting on a body immersed in a fluid is called the buoyant force. This phenomenon is called buoyancy.

center of buoyancy

the force of buoyance acts through the center of gravity of the displaced fluid which called the center center of buoyancy

Archemedes Principle

the buoyant force is equal to the weight of the fluid displaced by the body and the upthrust acts through the center of gravity of the displaced fluid

Law of floatation

A body will float in a liquid if the weight of the liquid displaced by the immersed part of the body is equal to or greater than the weight of the body

fractional submerged volume of floating body

density of body/density of liquid

Viscosity

The frictional force that comes into play when a fluid is in motion and which opposes the relative motion between the different layers.

velocity gradient

the rate of change of velocity with distance in the direction of increasing distance

coefficient of viscosity(1 poise or 1dyne s cm^-2) (SI: poiseulle)

the tangential viscous force required to maintain a unit velocity gradient between its two parallel layers each of unit area

Stokes Law

When any object rises or falls through a fluid it will experience a viscous drag(F=6pi n rv)

terminal velocity

the maximum constant velocity acquired by a body while falling through a viscous medium is called a terminal velocity

poiseulle's formula

formula

Streamline flow

When a fluid moves in such a way that each particle of the liquid passing a given point mores in the same path and with the same velocity as its predecessor.

Streamline

The path of the tangent at any point showing the direction of the flow of the liquid.

tube flow

a collection of streamlines

Turbulent flow

When the path and velocity of a liquid particle change haphazardly.

Laminar flow

a liquid that flows in the form of layers sliding past each other

Critical Velocity

the limiting value of velocity up to which the flow of liquid is laminar, above which the flow is turbulent

Reynold's number

R<2000 - flow is laminar, R>3000 flow is turbulent, 2000-3000 - unstable

ideal fluid

An ideal fluid is non-viscous, incompressible, and its flow is steady and irrotational.

equation of continuity

during streamline flow of an ideal fluid, the product of area of cross section and the normal fluid velocity remains constant

Bernoulli's Principle

Pressure energy(PV), kinetic energy and potential energy per unit volume of an ideal fluid remains constant along a streamline

dynamic lift

the force that acts on a body by virtue of its motion through a fluid

cohesive force

force of attraction between identical molecules

adhesive force

force of attraction between molecules of different chemical identities

molecular range

maximum distance up to which a molecule can exert some force

Sphere of Influence

sphere drawn around a molecule of its molecular range

Surface tension

It is a property of which the free surface of a liquid at rest behaves like an elastic stretched membrane and tends to contract to occupy minimum surface area.

Surface energy

extra energy associated with the free surface(work done/increase in surface area)

capilarity

the phenomenon of rise of a liquid in a capillary tube in comparison to the surroundings.