Fluid Mechanics Unit 1

Glossary

Every term used in Unit 1, in plain words. Type to search.

Absolute pressure
Pressure measured from a perfect vacuum. Absolute pressure equals gauge pressure plus atmospheric pressure.
Amorphous solid
A solid whose molecules are fixed in place but disordered, such as glass.
Archimedes’ principle
An object in a fluid is pushed up by a force equal to the weight of the fluid it displaces.
Atmospheric pressure
The pressure of the air around us, about 101.3 kPa at sea level.
Bernoulli's equation
p + ½ρV² + ρgz = constant along a streamline, for steady, incompressible, nearly frictionless flow with no pump or turbine.
Boundary
The real or imaginary surface between a system and its surroundings.
Bulk modulus
How hard a substance is to compress, K = −dp ÷ (dV/V), in Pa.
Buoyant force
The upward push a fluid exerts on an object placed in it, equal to the weight of the fluid the object pushes aside.
Capillary action
Liquid rising or falling in a narrow tube or gap because of surface tension and the attraction between the liquid and the wall.
Cavitation
Vapour bubbles forming where liquid pressure falls to its vapour pressure, then collapsing violently.
Closed system
Energy can cross its boundary, mass cannot.
Coefficient of contraction
C_c, the ratio of the narrowest jet area to the opening's area. About 0.62 for a sharp-edged hole. C_d = C_c × C_v.
Coefficient of velocity
C_v, the ratio of the actual jet velocity to the ideal velocity √(2gh); it accounts for energy losses. About 0.97 to 0.98 for a sharp-edged hole.
Contact angle
The angle a liquid surface makes where it meets a solid wall. Below 90° the liquid wets the wall; above 90° it does not.
Continuum hypothesis
Treating a fluid as continuous by assigning to every point the average property of a small representative volume around it.
Control mass
A fixed amount of matter followed as it moves; no mass crosses its boundary. The tool for analysing a closed system.
Control surface
The boundary of a control volume.
Control volume
A region in space chosen for analysis, which may be fixed, moving or deforming. Mass may cross its boundary; it is the usual tool for open systems.
Crystalline solid
A solid whose molecules sit in an ordered, repeating arrangement, such as metals, salt and ice.
Density
Mass per unit volume, ρ = m ÷ V, in kg/m³.
Dimension
The kind of a physical quantity, such as mass, length or time.
Dimensional homogeneity
Every term in a correct equation has the same dimensions.
Discharge coefficient
C_d, the ratio of actual to ideal flow through an opening; about 0.6 for a sharp-edged hole.
Dynamic viscosity
μ, a fluid's resistance to shearing: shear stress divided by shear rate, in Pa·s.
Electrical input power
Power drawn by the motor, shaft power divided by motor efficiency.
Energy grade line slope
Energy lost to friction per unit length of channel; the S in Manning's equation. Equal to the bed slope only in uniform flow.
Eulerian description
Describing flow by watching fixed points in space.
Fluid
A substance that deforms continuously under an applied shear stress, however small. At rest an ordinary fluid cannot sustain shear stress; in motion it resists shearing through viscous stress. Liquids and gases are fluids.
Fluid dynamics
The study of fluid motion together with the forces and energy involved.
Fluid element
A small volume of fluid, such as dx dy dz, used to write balance equations.
Fluid kinematics
The study of fluid motion without considering the forces causing it.
Fluid mechanics
The study of fluids at rest and in motion and the forces they exert.
Fluid particle
A tiny amount of fluid, holding many molecules, treated as a point that moves with the flow.
Fluid statics
The study of fluids at rest.
Free surface
The surface of a liquid open to the air or another gas.
Gauge pressure
Pressure measured above atmospheric pressure.
Hydraulic power
Power given to the fluid by a pump, P = ρgQH, in W.
Hydraulic radius
Flow area divided by wetted perimeter, R_h = A ÷ P, in m.
Hydraulics
The practical, experiment-based engineering of liquid flow in pipes, channels and machines.
Hydrodynamics
The study of liquid motion from the equations of motion. Historically focused on ideal fluids; today it also includes viscous flow.
Hydrostatic pressure
Pressure in a fluid at rest caused by the weight of the fluid above, p = ρ g h.
Ideal fluid
An imagined fluid with no viscosity, often also incompressible.
Isolated system
Neither mass nor energy can cross its boundary.
Kinematic viscosity
ν = μ ÷ ρ, in m²/s.
Knudsen number
Mean free path divided by a characteristic length, Kn = λ ÷ L. Continuum holds below about 0.01.
Lagrangian description
Describing flow by following individual fluid particles.
Laminar flow
Smooth flow in orderly layers.
Linear elastic solid
A solid whose stress is proportional to its strain, τ = Gγ in shear, and which returns to shape when unloaded.
Mass flow rate
Mass passing a section per second, ṁ = ρAV, in kg/s, where V is the average velocity normal to the section.
Mean free path
The average distance a molecule travels between collisions; about 68 nm for air at sea level.
Newtonian fluid
A fluid whose shear stress is proportional to its rate of shear strain, such as water, air and most oils.
No-slip condition
A fluid touching a solid surface moves with that surface; its speed relative to the wall is zero.
Non-Newtonian fluid
A fluid that does not follow τ = μ du/dy, such as paint, ketchup, blood and toothpaste.
Open system
Mass and energy can cross its boundary.
Pascal (Pa)
SI unit of pressure, 1 N/m².
Pascal’s law
Pressure added to an enclosed fluid is passed on equally to every part of the fluid and the walls of its container.
Pathline
The path one fluid particle takes over time.
Pressure
Normal force per unit area, p = F ÷ A, in Pa.
Representative volume (δV*)
The smallest volume over which a property averages steadily. It depends on the fluid and the accuracy needed; about 10⁻¹⁸ m³ as an order of magnitude for air at standard conditions.
Reynolds number
Re = ρVL ÷ μ, the ratio of inertia to viscous effects; it tells whether a flow is laminar or turbulent.
Shaft power
Power delivered to the pump shaft, hydraulic power divided by pump efficiency.
Shear modulus
G, the stiffness of a solid in shear, in Pa.
Shear stress
Force acting along a surface divided by the area, τ = F ÷ A, in Pa.
Slip flow
Gas flow with Kn between about 0.01 and 0.1, where the continuum model needs corrections at walls.
Solid mechanics
The study of how solids deform and carry load.
Specific gravity
Density of a substance divided by the density of water. Steel is about 7.85, so it is 7.85 times denser than water.
Specific weight
Weight per unit volume, ρg, in N/m³.
Streakline
The line joining all particles that passed through one fixed point, such as a line of smoke.
Streamline
A line everywhere tangent to the velocity at one instant. In steady flow pathlines, streaklines and streamlines coincide.
Surface tension
The pull that makes a liquid surface act like a stretched sheet, measured in N/m. Water is about 0.073 N/m at room temperature.
Surroundings
Everything outside the system that can interact with it.
System
The part of the universe chosen for study.
Terminal velocity
The steady speed a falling object reaches when drag and buoyancy balance its weight.
Torque
A force times its perpendicular lever arm, in N·m. Same dimensions as energy, different meaning.
Torricelli's law
Ideal speed of a jet leaving a tank, v = √(2gh).
Turbulent flow
Chaotic flow with swirling eddies that mix the fluid.
Unit
The agreed size used to measure a dimension, such as kilogram, metre or second.
Vapour pressure
The pressure at which a liquid starts to boil at a given temperature; about 2.3 kPa for water at 20 °C.
Viscoelastic
Behaving partly like an elastic solid and partly like a viscous fluid, such as pitch or silly putty.
Viscosity
Internal friction of a fluid, its resistance to flowing. Dynamic viscosity μ is measured in pascal seconds (Pa·s).
Viscous shear stress
The shear stress a moving fluid develops because its layers slide past each other; for a Newtonian fluid τ = μ du/dy.
Volume flow rate
Volume passing a section per second, Q = A × V, in m³/s.
Water hammer
A pressure surge when flowing liquid is stopped suddenly, as when a tap is shut fast.