Mechanical Properties of Fluids

Vocabulary practice flashcards covering fluid statics, fluid dynamics, Bernoulli's principle, viscosity, Stokes' law, terminal velocity, surface tension, and capillarity from Class XI Physics.

Fluid

A substance that can flow, lacks a fixed shape of its own, and deforms continuously under even very small shear stress to take the shape of its container.

Hydrostatics

The branch of physics that deals with the study of fluids at rest.

Hydrodynamics

The branch of physics that deals with the study of fluids in motion.

Pressure

A scalar quantity defined as the normal force acting per unit area ($P = \frac{F}{A}$), having the SI unit Pascal ($\text{Pa} = 1\,\text{N/m}^2$) and dimensions $[\text{ML}^{-1}\text{T}^{-2}]$.

Atmosphere (atm)

A common unit of pressure defined by the average atmospheric pressure at sea level, equal to $1.013 \times 10^5\,\text{Pa}$.

Density ($\rho$)

A positive scalar quantity defined as the mass per unit volume of a substance ($\rho = \frac{m}{V}$), with dimensions $[\text{ML}^{-3}]$ and SI unit $\text{kg\,m}^{-3}$.

Relative Density (Specific Gravity)

A dimensionless, positive scalar quantity defined as the ratio of the density of a substance to the density of water at $4\,^\circ\text{C}$ ($1.00 \times 10^3\,\text{kg\,m}^{-3}$).

Hydrostatic Paradox

The principle stating that the pressure exerted by a liquid column at a given depth depends only on the vertical height of the liquid and not on the shape, base area, or volume of the container.

Atmospheric Pressure ($P_{\text{atm}}$;)

The pressure exerted by the weight of the column of air above a given surface, equal to $1.013 \times 10^5\,\text{Pa}$ at sea level.

Gauge Pressure ($P_g$)

The pressure measured relative to atmospheric pressure ($P_{\text{gauge}} = P_{\text{absolute}} - P_{\text{atm}}$). It is positive when above atmospheric pressure and negative (suction) when below it.

Absolute Pressure ($P_{\text{abs}}$;)

The total pressure at a point in a fluid, calculated as the sum of atmospheric pressure and gauge pressure ($P_{\text{abs}} = P_{\text{atm}} + \rho gh$).

Barometer

An instrument designed to measure atmospheric pressure, typically balancing atmospheric pressure against a $76\,\text{cm}$ column of mercury ($\text{Hg}$).

Torr

A unit of pressure equivalent to $1\,\text{mm of Hg}$, named after Torricelli, where $1\,\text{torr} = 133\,\text{Pa}$.

Bar

A meteorological unit of pressure equal to $10^5\,\text{Pa}$.

Open Tube Manometer

A U-tube device containing a fluid (oil for low pressure differences, mercury for large ones) used to measure the gauge pressure of a gas or fluid in an enclosed system.

Pascal's Law

The law stating that pressure applied to an enclosed incompressible fluid at rest is transmitted equally and undiminished in all directions to every point of the fluid and the vessel walls.

Hydraulic Lift

A hydraulic machine based on Pascal's law where a small force applied on a smaller piston of area $A_1$ generates an upward force $F_2 = F_1 \left(\frac{A_2}{A_1}\right)$ on a larger piston of area $A_2$, providing a mechanical advantage of $\frac{A_2}{A_1}$.

Hydraulic Brakes

A braking system utilizing Pascal's law to transmit pressure applied at a master cylinder equally through brake fluid to wheel cylinders, providing equal, magnified, and balanced braking forces on all wheels.

Buoyant Force

The upward force exerted by a fluid on an object partially or completely submerged in it, which opposes the object's weight and makes it feel lighter.

Archimedes' Principle

The principle stating that the buoyant force exerted on a body partially or totally immersed in a fluid is equal to the weight of the fluid displaced by the immersed part ($F_B = \rho V g$).

Law of Floatation

The law stating that an object will float in a fluid when the total weight of the object is equal to the weight of the fluid displaced by its submerged portion.

Streamline Flow

Steady fluid motion in which every fluid particle follows exactly the same path as the particle preceding it, possessing identical speed and direction at any given point.

Streamline

A curve whose tangent at any point indicates the instantaneous direction of fluid velocity at that point during steady flow. Streamlines never cross each other.

Tube of Flow

A tubular region bounded by a bundle of streamlines such that fluid particles passing across any cross-section have identical velocities.

Laminar Flow

Orderly, steady fluid flow in which adjacent fluid layers slide smoothly over each other along parallel paths without macroscopic mixing.

Turbulent Flow

Disordered, fluctuating, and chaotic fluid flow occurring when fluid speed exceeds a critical threshold, resulting in irregular eddy currents and mixing.

Ideal Fluid

A hypothetical fluid model characterized by steady flow, incompressibility (constant density), non-viscous behavior (zero internal friction), and irrotational flow (no angular rotation of elements).

Equation of Continuity

The mathematical expression of mass conservation for an incompressible fluid flowing steadily through a pipe of varying cross-section: $A_1 v_1 = A_2 v_2$ or $Av = \text{constant}$.

Bernoulli's Principle

The principle stating that along any streamline in steady, non-viscous, incompressible fluid flow, the total mechanical energy per unit volume is conserved: $P + \frac{1}{2}\rho v^2 + \rho gh = \text{constant}$.

Torricelli's Law

The law stating that the speed of efflux of an ideal liquid exiting a small orifice at depth $h$ beneath the free surface of an open tank is equal to the speed acquired by an object in free fall: $v = \sqrt{2gh}$.

Dynamic Lift

The net upward force exerted on an object moving through a fluid as a consequence of differing fluid velocities and resultant pressure differences across opposite surfaces.

Magnus Effect

The generation of lateral dynamic lift on a spinning sphere or cylinder moving through a fluid due to velocity and pressure differentials created between its opposite sides.

Aerofoil

A streamlined body cross-section engineered so that air flows faster over the convex upper surface than beneath the flat lower surface, producing lower pressure above and generating upward dynamic lift.

Atomiser (Sprayer)

A device that utilizes Bernoulli's principle by passing high-speed air across the top of an open vertical tube, creating low pressure that draws liquid upward into the airstream to form a fine spray.

Viscosity

The property of a fluid that represents its internal frictional resistance to relative motion between adjacent fluid layers.

Coefficient of Viscosity ($\eta$)

The ratio of shearing stress to strain rate ($\eta = \frac{\text{shearing stress}}{\text{strain rate}}$) in a fluid, with SI unit poiseuille ($\text{Pl}$), alternative units $\text{N}\cdot\text{s}\cdot\text{m}^{-2}$ or $\text{Pa}\cdot\text{s}$, and dimensions $[\text{ML}^{-1}\text{T}^{-1}]$.

Viscosity Measurement Apparatus

A laboratory method to determine $\eta$ by measuring the steady horizontal terminal velocity of a metal block sliding across a thin liquid film of known thickness under a known gravitational tension.

Stokes' Law

The physical law stating that the retarding viscous force opposing a small spherical body of radius $r$ moving at uniform velocity $v$ through a fluid of viscosity $\eta$ is given by $F = 6\pi\eta rv$.

Terminal Velocity

The constant maximum velocity attained by a body falling through a viscous fluid when the downward gravitational force is completely balanced by the sum of the upward buoyant and viscous forces ($a = 0$).

Terminal Velocity Free-Body Equilibrium

The force diagram showing that terminal velocity is reached when upward viscous drag ($F_V$) plus buoyant force ($F_B$) equals downward weight ($mg$), resulting in zero net force.

Intermolecular Binding Energy of a Liquid

The total energy required to overcome the attractive forces of all surrounding liquid molecules and completely separate a single molecule from the liquid.

Cohesive Forces

The intermolecular forces of mutual attraction between molecules of the same liquid substance.

Adhesive Forces

The intermolecular forces of mutual attraction between liquid molecules and molecules of an adjacent solid boundary surface.

Surface Tension ($S$)

The property of a liquid's free surface by which it behaves like a stretched elastic membrane tending to minimize surface area, defined as the force per unit length ($\text{N\,m}^{-1}$) acting perpendicular to a line on the surface.

Surface Energy

The extra potential energy possessed by molecules at the surface of a liquid relative to interior molecules, defined as the work done per unit area to create new surface area.

Surface Energy Wire-Frame Model

A physical setup comprising a rectangular wire frame with a movable slider of length $l$ displaced by distance $x$ against surface tension force $F$ to measure work done in increasing film area ($W = S \Delta A$).

Excess Pressure Inside a Liquid Drop

The difference between internal and external pressure across the single liquid-air interface of a spherical drop of radius $r$, given by $P_i - P_o = \frac{2S}{r}$.

Excess Pressure Inside a Soap Bubble

The pressure difference across the two concentric liquid-air interfaces of a soap bubble of radius $r$, given by $P_i - P_o = \frac{4S}{r}$.

Angle of Contact ($\theta$)

The angle formed between the tangent to the liquid-vapor interface and the solid-liquid boundary inside the liquid at the three-phase contact line.

Wetting vs. Non-Wetting Contact Behavior

The surface contact phenomenon where strong adhesive forces cause acute angles of contact and liquid spreading (wetting), whereas strong cohesive forces cause obtuse angles of contact and bead formation (non-wetting).

Capillarity

The phenomenon of the spontaneous rise or depression of a liquid inside a narrow cylindrical tube (capillary tube) immersed vertically in the liquid due to surface tension and contact angle.