Civil 202
Types of movement within a fluid
Static (at rest), flowing (fluid is moving)
Type of fluid flow according to space
Uniform (fluid doesn't change with distance), Varied/non-uniform (fluid changes with distance)
Type of fluid flow according to time
Steady (fluid doesn't change with time), Unsteady (fluid changes with time)
Type of fluid orientations
Linear & Rotational
Boundary Conditions for fluids
Pipe flow, Open Channel / Free Surface flow
Types of flow patterns
Laminar (fluid moves smoothly on predictable paths), Turbulent (fluid moves randomly)
Types of speed of information transfer for fluids
Subcritical (liquids) or subsonic (gases): fluid velocity is lower than information celerity & Supercritical (liquids) or supersonic (gases): fluid velocity higher than information celerity
Froude's number
Fr = v / (gl)^1/2
Reynold's number
Re = pVL/u
Reynold's scale
Nv = 1 / NL
Froude's scale
Nv = (NL)^1/2
Bar to pascal conversion:
1 mbar = 100Pa
1 bar = 100,000 Pa
1 Pa = 0.001 kPa
Q = ∫ V n dA , what does dA = ?
dA = 2 pi r dr
average velocity formula
v = Q / A
Explain velocity in terms of mass conservation
velocity: ∂u/∂x > 0 & velocity: ∂v/∂y < 0
mass is conserved due to the volume: v shrinks or stretches to ensure equilibrium (shown by equations) where density = constant
specific weight symbol
γ = gamma
specific volume symbol and equation:
v = 1 / density
specific gravity symbol:
s, where it is relative to density
Ideal gas law?
P / rho = Rs T
where Rs = gas constant (8.31) and T = absolute Temp
Absolute Pressure at sea level?
P abs = 101.3kpa
Compressivility of liquids equation:
- dp = Ev dv/v
where Ev = bulk modulus and dp = change in Pressure
Pabs equation:
Pabs = Pgauge + Patm
where Pabs can = 0 & Pgauage can be (-)
Trapezoidal load force formula:
Fx = F1x1 + F2x2
& F = PA
Velocity & acceleration dimensions:
V = L/T & A = L/T^2
Area & Volume dimensions:
A = L^2 & V = L^3
Density and Viscosity dimensions:
Density = ML^-3 & Viscosity = M/LT
Energy dimesnion:
Energy = ML^2/T^2
HGL notes:
HGL = P/rho g + Z
- in the flow
- starts from EGL
- always at free surface
EGL notes:
EGL = total head (horizontal line) = above datum
Bernoulli Equation notes:
- finding H = head
- things can equal 0 depending on question
- Patm = Pg = 0
- add on CL
- Q = VA
Continiuity equation:
A1v1 = A2v2
- d can be used instead
Dimensional Analysis criteria:
- Geometric (L)
- Fluid Analysis: rho or density
- External factors / kinetic (F or velocity or g or a)
Dimensional Analysis equations:
pi1 = Φ (pi2, pi3, pi4...)
pi1 = a * bi * cj * dk
- solve for pi's
- use same middle of table
- start at 0 then a = what dimensions
- M T L order
find velocity?
- sub in x and y values
a local = ?
a local = ∂u/∂t
a local = sqrt of i^2 + j^2
steady or unsteady a?
if a = 0 and no t == steady
streamlines?
∫ each term and sub in values
- equal to 0 to find +C term
What is the Darcy-Weisbach equation?
It is used to measure pipe friction losses for tublent flow.
where hs = fLV^2/2gD
Reynolds number for laminar and turbulent flow?
Re < 2000 = laminar flow
Re > 4000 = turbulent flow
Within the Bernoulli equation, what does each variable calculate?
- P/rhog = pressure head
- v^2/2g = velocity head
- z = elevation
What is the first law of thermodynamics? And the equation?
States that the rate of heat added to a system plus the rate of work done on the system is equal to the time rate of change of the total energy within a system.
From the Bernoulli equation, what are the formulas for HGL and EGL?
EGL = v^2/2g
HGL = P/rho g
What are the important principles to apply when solving hydrostatic problems?
- Assume uniform pressure distribution in spaces filled with gas
- In a continuous static fluid, pressure is the same even at different elevations in the same fluid
- Use (P = Po + rho g h) to find pressures at different elevations in the same fluid
Sum of pressure equation:
Pressure absolute = Pressure gauage + Pressure atmospheric
Pressure units:
Pa, where 1 Pa = 1 N/m^2
1 bar = 100kPa
Absolute Pressure is:
always positive, and when P atmospheric is 101.325kPa, then it is defined as an absolute Pressure
An atmospheric pressure assumed to be 0 is?
Gauge Pressure
Newton's viscosity law?
Shear stress in a fluid is proportional to rate of change of velocity.
formula: tao = (viscosity coefficient)du/dy
mass conservation:
outflow - inflow, where m = rho V A = rho Q
What happens at a smooth turbulent zone?
- Occurs at lower Re, smoother pipe walls
- σ >> e where(σ = the height between e and the laminar boundary)
- Turbulence does not interact with wall
- Shielded by laminar sub-layer
- Roughness has no impact
This is the bottom curved line in the flow graph
What happens at the transitional turbulent zone?
- Turbulence interacts with pipe wall
- Not full interaction
- σ same order size as e
- Effect increases with increasing Re
- Interaction starts earlier for rougher pipes
- Most real pipe flow in this zone
Summary: pipe roughness starts to stick through laminar sub layer => influences flow => larger re => pushes laminar sub layer down further => bigger interaction with pipe roughness
What happens at the rough turbulent zone?
- Full turbulence interaction with pipe wall
- no laminar sub layer
- σ ~ 0
- Very high Re
- f not a function of Re
This is represented in the left side of the flow graph, from the left of the dashed "R" line
Cavitation Mechanism info:
- Lowest pressure occuras at pump suction end (where water enters the pump)
- Vapour bubbles move with water to high pressure zones of pump
- Vapour bubbles implode causing localised pressure spikes
- Over time pump material gets worn away
Consequences of Cavitation:
- Noise
- Uneven operation
- Reduced efficiency
- Internal damage to pump = expensive
Cavitation evaluation risk is done by...
- NPSH (Net positive suction head)
- always given in absolute pressure
How/where do energy losses occur within a system
At local disturbances such as;
- Entrances
- Exits
- Joints
- Bends
- Changes in diameter
(also known as minor/secondary losses)
venturi meter vs orifice plate
The discharge coefficient becomes useful when comparing the Venturi Meter to a very similar device called an Orifice Meter. This is a lowcost alternative to the Venturi Meter, in which the constriction is achieved by inserting a plate with a hole in its centre. The sudden expansion downstream of the plate creates significant turbulence and energy losses.
Why is f not constant?
• Most turbulent headloss takes place at pipe wall
• Influenced by the laminar sub-layer
- Flow near wall slowed down by friction
- Causes laminar flow next to wall
- Shields turbulence from pipe wall