Class notes
Principles of Water Engineering Study Notes - CVEN2501 - UNSW
- Course
- Institution
Full set of study notes for principles of water engineering and fluid mechanics.
[Show more]
Seller
Follow
callumfisher
Content preview
Fluid Mechanics StudyNotes
Fluid Properties
DIMENSIONAL ANALYSIS
• Any quantity can be expressed in terms of the four basic dimensions as
follows:
o Length (L)
o Mass (M)
o Time (T)
o Force (F)
• For complex quantities in water engineering it is often helpful to
consider them in terms of their equivalent dimensional units (i.e.
F=MLT-2)
FLUID DEFINITIONS
• A fluid is any substance that deforms and flows when subjected to a
shear stress (applied pressure)
• The following quantities can be measured for each specific fluid:
o Mass: Amount of material (kg)
o Weight: Force exerted by fluid due to gravity (N)
o Density (ρ): Mass per unit of volume (kg/m3)
o Unit Weight (γ): Gravitational force exerted by fluid per unit of
volume (γ=gρ)
o Relative Density: Comparative density to water
o Specific Volume: Volume per unit of mass (1/ρ)
PRESSURE
• Pressure (Pa) is given as the normal force applied to a surface divided
by its area
• Absolute pressure is observed relative to absolute zero
• Gauge pressure is pressure recorded relative to atmospheric pressure
(101.3kPa at room temperature)
IDEAL GASES
• An ideal gas that has negligible volume and collision energy losses
follows the rule of PV=nRT
• Gases also follow the rule of P=ρRT where ‘P’ is absolute pressure
ELASTICITY AND COMPRESSIBILITY
• The Bulk Modulus of Elasticity (E) of a fluid is the ratio of pressure
change to the resulting fractional change in volume
• For gases ‘E’ is proportional to:
o E=p for isothermal processes
, o E=kp for adiabatic processes (the retention of heat energy
makes it more difficult to compress the gas)
• There are two formulas for sonic velocity:
o c=sqrt(E/ρ) for a liquid or solid
o c=sqrt(kRT) under adiabatic gas conditions
VISCOSITY
• Dynamic viscosity is the level of fluid flow in response to a shear
stress
• Highly viscous materials will flow extremely slowly even under high
shear stresses
• Shear stress = Viscosity*(Relative velocity)/(Flow Width)
• The viscosity of a fluid is highly temperature dependant
• Kinematic viscosity of a fluid is the ratio of its dynamic viscosity and
its density (v=V/ρ)
SURFACE TENSION
• The net inward intermolecular force between fluid molecules at the
surface leads to the creation of a membrane-like flat plane at that fluid
surface
• This tension arises due to an excess of pressure within the liquid
• For a curved surface, this pressure differential is calculated by equating
the equivalent forces:
o ‘pa2’ upwards
o ‘4σa2sin(θ/2)’ downwards
o Hence p=2σ/r
• Cohesion is the intermolecular forces between like particles
• Adhesion is the intermolecular forces between unlike particles such as
glass and water
• If adhesion exceeds the cohesion, the solid surface will be ‘wetted’
(small contact angle) and vice versa (large contact angle)
• Capillarity is the phenomenon of a fluid being carried up a narrow tube
due to adhesive forces and surface tension
• The capillary rise of a tube can be calculated be equating forces:
o ‘2πrσ’ upwards surface tension
o ‘πr2hγ’ downwards gravitational force
, o h=2σ/(γr)
VAPOUR PRESSURE
• Within a liquid, a certain amount of molecules will evaporate from a
free surface at every finite temperature and induce a vapour pressure
• Vapour pressure always increases with temperature
• Boiling of a liquid occurs when its vapour pressure is greater or equal
to the atmospheric temperature (e.g. water has a vapour pressure of
101.3kPa at 100 degrees Celsius, hence it boils)
• Cavitation occurs when a fluid flows at such a high velocity that its
pressure is low enough to equal the corresponding vapour pressure –
causing the liquid to rapidly evaporate
Hydrostatics
PRESSURE IN A STATIC FLUID
• Pressure is calculated as a limit of F/A as area becomes infinitesimally
small
• Weight force of a ‘parcel’ of fluid is given as: G=γ*δx*δy*δz
• The force exerted upon the fluid in each plane can be calculated by
multiplying the limit pressure minus its specific weight by the area
affected
• Pressure within a fluid increases with depth (decreases with height)
at a rate of γ*Pa/m
• Pressure within a static fluid does not vary with any movement along
the xz-plane in accordance with Pascal’s Law
MEASUREMENT OF PRESSURE
• A Piezometer column is a thin tube allowing for a liquid to rise without
overflowing which calculates gauge pressure from the height of the
piezometric head (p=γh)
• Manometers are narrow U-tubes that calculates pressure based off
the height difference from a predetermined datum (p=ρfgz+ρMgy)
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller callumfisher. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $9.49. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
77254 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 14 years now