1. Introduction, fluid properties (1.1, and handouts) · VVR 120 Fluid Mechanics 1. Introduction,...

VVR 120 Fluid Mechanics

1. Introduction, fluid properties (1.1, and handouts)

• Introduction, general information

• Course overview

• Fluids as a continuum

• Density

• Compressibility

• Viscosity

Exercises: A1


Applications of fluid mechanics

• Societal supply of safe energy and water by gas and fluids in pipes and channels

• Energy production (oil, hydropower, nuclear energy, natural gas)

• Environmental engineering and water treatment (channels, basins, filtering)

• Industrial process technology (relationship temperature, pressure, and energy)

• Protection against climate extremes/catastrophes (flooding, harbours, wind forces)

• Biomedical engineering

• Ecological evolution of species (predator-prey)


Major ”Fluid mechanics” employers

• SWECO

• Thyréns

• WSPgroup

• Skanska

• Eon, VA SYD

• Community offices

• Governmental, Naturvårdsverket


Fluid mechanics

• Fluid properties (2)

• Hydrostatics (3)

• Basic equations (6)

• Pipe flow (5)

• Flow around submerged

bodies (1)

• Channel flow (3)

• Repetition (2)


FLUID AS A CONTINUUM

• A fluid is considered to be a continuum in which there

are no holes or voids velocity, pressure, and

temperature fields are continuous.

• Validity criteria: Smallest length scale in a flow >>

average spacing between molecules composing the

fluid.


DENSITY ()

Mass/ unit volume (kg/m3)

Density decreases normally with increasing temperaturewater = (T,S,p)

i.e., dependent on

- Temperature

- Salt content ( 1000 + 0.741S, S in per mille;

S = 3.5% in ocean = 1026 kg/m3)

- Pressure (but only a small variability)


OTHER DEFINITIONS• Weight = mass gravity acceleration

(W = mg, [N = kgm/s2]) (Eqn. 1.4)

• Weight density (or specific weight)= density gravity acceleration(w = g, [N/m3 = kg/(m2s2)]) (Eqn. 1.6) (Note w = γ in exercises)

• Specific volume = reciprocal of density( = 1/, [m3/kg])

• Relative density (or specific gravity), s, is the density normalized with the density of water at a specific temperature and pressure (normally 4C and atmospheric pressure):s = R.d. = /water (often = /1000) (Eqn. 1.7)

• Power P [W = J/s = kgm2/s3 = Nm/s]; P = T ω (T = torque, ω = angular velocity [rad/s, 360o = 2rad]; V = ω r (V = velocity, r = radius)


Example – density. The specific weight of

water at ordinary temperature and pressure is

9.81 kN/m3. The specific gravity of mercury is

13.56. Compute the density of water and the

specific weight and density of mercury.


COMPRESSIBILITY

• All fluids can be compressed by application of pressure

elastic energy being stored

• Modulus of elasticity describes the compressibility

properties of the fluid and is defined on the basis of

volume


• Modulus of elasticity:

E=-dp/(dV/V1) [Pa]

• For liquids, region of engineering interest is when V/V1 1

• Ewater ~ 2109 Pa (function of temperature)

E

p

V

V


A1 What pressure must be applied to

water to reduce its volume 1 % ?


Example – compressibility. At a depth of 8 km in

the ocean the pressure is 81.8 MPa. Assume that

the specific weight of sea water at the surface is

10.05 kN/m3 and that the average volume

modulus of elasticity is 2.34*109 N/m2 for the

pressure range.

A) What will be the change in specific volume

between that at the surface and at that depth?

B) What will be the specific volume at that depth?

C) What will be the specific weight at that depth


IDEAL FLUID

A fluid in which there is no friction

REAL FLUID

A fluid in which shearing forces always exist

whenever motion takes place due to the fluid’s

inner friction – viscosity.


VISCOSITY

• Viscosity is a measure of a fluid’s “inner friction” or

resistance to shear stress.

• It arises from the interaction and cohesion of fluid

molecules.

• All fluids posses viscosity, but to a varying degree. For

instance, syrup has a considerably higher viscosity than

water.


DEFINITION OF DYNAMIC VISCOSITY -

Shearing of thin fluid film between two plates. The upper plate has

an area A.

• Experiments have shown that for a large number of fluids:

F ~ AV/h (if V and h not too large)

• Linear velocity profile V/h = dv/dy

y


• Introduction of the proportionality constant , named

dynamic viscosity, gives Newton’s viscosity law shear

force:

[Pas or kg/ms]

• = / [m2/s] - Kinematic viscosity

• No-slip condition – water particles adjacent to solid

boundary has zero velocity (observational fact)

dy

dv

h

V

A

F

(Eqn. 4.1-4.2) N/m2


μ (Pa·s)


Implication of viscosity: a fluid cannot sustain a shear

stress without deformation


Implications of Newton’s law:

• , independent of pressure (in contrast to solids)

• no velocity gradient no shear stress

Restriction of Newton’s law:

• law only valid if the fluid flow is laminar in which viscous

action is strong


• Laminar flow: smooth, orderly motion in which fluid

elements appears to slide over each other in layers (little

exchange between layers).

• Turbulent flow: random or chaotic motion of individual

fluid particles, and rapid mixing and exchange of these

particles through the flow

Turbulent flow is most common in nature.


Newtonian – non-Newtonian fluidsExamples non-Newtonian fluids:

Plastics, blood, suspensions, paints, foods

ii dy

du ,

Shear vs. rate of strain re-

lations for non-Newtonian

fluids:

Bingham plastic

n>1: Shear-thickening fluid,

n<1: Shear-thinning fluid

n

dy

du)(


Example – density. The specific weight of water at ordinary temperature and pressure is 9.81 kN/m3. The

specific gravity of mercury is 13.56. Compute the density of water and the specific weight and density of

mercury.


A1 What pressure must be applied to water to reduce its volume 1 % ?


Example – compressibility. At a depth of 8 km in the ocean the pressure is 81.8 MPa.

Assume that the specific weight of sea water at the surface is 10.05 kN/m3 and that

the average volume modulus of elasticity is 2.34*109 N/m2 for the pressure range.

A) What will be the change in specific volume between that at the surface and at that

depth?

B) What will be the specific volume at that depth?

C) What will be the specific weight at that depth

1. Introduction, fluid properties (1.1, and handouts) · VVR 120 Fluid Mechanics 1. Introduction,...

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