Fluid Statics Lecture Notes

Summary of fluid mechanics fundamentals, including fluid properties, viscosity, surface tension, and pressure measurement techniques as outlined in the lecture.

Fluid Mechanics

The study of the physical behavior of fluids and fluid systems, the laws governing their behavior, and the action of forces on fluids resulting in flow patterns.

Fluid

A substance sub-divided into liquid and gas; liquids accommodate the shape of their container, while gases fill the entire containing vessel.

Dimension

A name which describes the measurable characteristics of an object, such as Mass ($M$), Length ($L$), and Temperature ($t$).

Unit

An accepted standard for measuring a dimension.

Newton ($N$)

The unit of force defined as the force which, when applied to a mass of $1\,kg$, gives an acceleration of $1\,m/s^2$ ($F = \text{kg} \cdot \text{m/sec}^2$).

Pascal ($Pa$)

The pressure produced by a force of one $Newton$ uniformly applied over an area of $1\,m^2$ ($N/m^2$).

Joule ($J$)

The work done when the point of application of a force of $1\,Newton$ is displaced ($N\cdot m$).

Watt ($W$)

A unit representing a work equivalent of a $Joule$ done per second ($J/Sec$).

Density (Mass Density)

The ratio of the mass of a fluid to its volume, denoted by $"\rho"$ and expressed as $kg/m^3$. The density of water is $1000\,kg/m^3$.

Specific weight (Weight density)

The ratio between the weight of a fluid to its volume, denoted by $w$ and calculated as $w = \rho \times g$.

Specific volume

The volume of the fluid occupied by a unit mass, representing the reciprocal of Mass density ($1/\rho$).

Specific Gravity ($s$)

Defined as the ratio of the Weight density (or density) of a fluid to the Weight density (or density) of a standard fluid (water for liquids and air for gases).

Viscosity

The property of a fluid which offers resistance to the movement of one layer of the fluid over another adjacent layer.

Coefficient of dynamic viscosity ($\mu$)

The constant of proportionality between shear stress ($\tau$) and the velocity gradient ($du/dy$).

Poise

The unit of viscosity in the CGS system, equal to $\text{dyne-sec}/cm^2$. One $Ns/m^2$ is equal to $10\,\text{Poise}$.

Kinematic Viscosity ($\nu$)

The ratio between dynamic viscosity and the density of the fluid ($\nu = \mu / \rho$).

Stoke

The unit of kinematic viscosity in CGS, equal to $cm^2/sec$ or $10^{-4}\,m^2/sec$.

Newton's Law of Viscosity

States that the shear stress ($\tau$) on a fluid element layer is directly proportional to the rate of shear strain.

Newtonian fluids

Fluids that obey Newton's law of viscosity, where shear stress is directly proportional to the rate of shear strain.

Non-Newtonian fluids

Real fluids in which shear stress is not proportional to the rate of shear strain.

Ideal fluid

An imaginary fluid that is incompressible and has no viscosity.

Real fluid

A fluid possessing a viscosity; all fluids in actual practice are real fluids.

Ideal plastic fluid

A fluid in which shear stress is more than the yield value and shear stress is proportional to the rate of shear strain.

Surface Tension ($\sigma$)

The tensile force acting on the surface of a liquid in contact with a gas, behaving like a membrane under tension; expressed in $N/m$ or $Kgf/m$.

Capillarity

The phenomenon of rise or fall of a liquid surface in a small tube relative to the adjacent general level of liquid.

Capillary Rise

The rise of liquid surface in a tube, calculated by the expression $h = \frac{4\sigma \cos(\theta)}{\rho \times g \times d}$.

Vaporization

A change from the liquid state to the gaseous state occurring because of continuous escaping of molecules through the free liquid surface.

Vapour Pressure

The pressure at which a liquid is converted into vapours or the pressure accumulated vapours exert on the liquid surface.

Cavitation

The phenomenon of formation of vapour bubbles in low-pressure regions and their sudden collapsing in high-pressure regions, causing pitting and erosion of metallic surfaces.

Absolute Pressure

Pressure measured with reference to absolute vacuum pressure (absolute zero).

Gauge Pressure

Pressure measured with a pressure measuring instrument using atmospheric pressure as the datum (zero).

Vacuum Pressure

Pressure defined as being below the atmospheric pressure.

Atmospheric Pressure

The pressure at sea level at $15^0C$ equal to $101.3\,KN/m^2$ or a head of $760\,mm$ of mercury.

Manometer

Devices used for measuring the pressure at a point in a fluid by balancing the column of fluid by the same or another column of fluid.

Piezometer

The simplest form of manometer used for measuring gauge pressure, where the rise of liquid in the tube gives the pressure head ($P = \rho g h$).

Differential Manometer

Devices used for measuring the difference of pressure between two points in a pipe or in two different pipes.