basics of fluid flow - anadolu university 307/icerik/nov 20.pdf · basics of fluid flow types of...
Post on 05-May-2018
218 Views
Preview:
TRANSCRIPT
1
Basics of fluid flow
Types of flow
Fluid
Ideal/Real
Compressible/Incompressible
Flow
Steady/Unsteady
Uniform/Non-uniform
Laminar/Turbulent
Pressure/Gravity (free surface)
2
Basics of fluid flow (Chapter 4)
Basics of fluid flow, kinematics
Mechanics
Statics
Dynamics
Kinematics
Kinetics
Kinematics: deals with motion apart from considerations
of mass, force or energy
3
Basics of fluid flow
Path lines, streamlines and streak lines
Path line: the trajectory that a fluid particle would make as it moves
around with the flow
Streamline: line that shows the flow direction, local velocity vector is
tangent to the streamline at every point along the line at that instant
4
Basics of fluid flow
Types of flow
Steady flow: all fluid/flow properties at any point in the flow do not
change with time; however, conditions may be different at different
points.
Uniform flow: at every point in the flow, the velocity (in both magnitude
and direction) is identical at any given instant.
For steady flows:
5
Basics of fluid flow
One -, two -, and three- dimensional flows
This is the most general 3-D flow:
The flow is classified as 2-D if: The flow can be viewed as 1-D if:
6
Partial derivative
Differentiating a function of more than one variable with respect to a particular
variable, with the other variables kept constant:
the notation ∂f/∂t means the partial derivative of the function f with respect to t
∂f/ ∂t : partial derivative
df/dt : total derivative
For more info:
http://apollo.lsc.vsc.edu/classes/met380/Fingerhuts_notes/driv.pdf
7
Basics of fluid flow
Velocity and Acceleration, 4.12
Convective (spatial)
acceleration
at
Local (temporal)
acceleration
an
8
Basics of fluid flow
Flow rate and Mean velocity
Flow rate: the rate at which fluid
crosses a known surface
volume flow rate mass flow rate
The volume flow rate passing through
the element of area dA (in yz plane) is
dQ = u(cosθ)dA=udA’
volume flow rate is equal to the magnitude of the mean
velocity multiplied by the flow area at right angles to the
direction of the mean velocity
9
Basics of fluid flow
Flow rate and Mean velocity
The volume flow rate passing through
the element of area dA is
dQ = u·dA =udA´
the local time mean velocity, u, will vary across the
section for real fluid
A
AVudAQ
QAVudAmA
10
Basics of fluid flow
Reynolds Transport Theorem & Continuity
QVAVA 2211
Copyright © The McGraw-Hill Companies, Inc.
FIGURE 5-24
Bernoulli’s Equation
(Energy per unit weight)
12
Energy in Steady Flow (Chapter 5)
Energies of a Flowing Fluid (Euler’s Equation)
Kinetic Energy
Potential Energy
1/2mV2 V2/2g
Wz z
Pressure Head
p = γh p/γ
Unit: L
(Energy per unit
weight)
13
Derivation of the Bernoulli Equation
The forces acting on a fluid
particle along a streamline.
Steady, incompressible flow:
The sum of the kinetic, potential, and
flow energies of a fluid particle is
constant along a streamline during
steady flow when compressibility and
frictional effects are negligible.
Bernoulli
equation
The Bernoulli equation between any
two points on the same streamline:
Steady flow:
14
Energy in Steady Flow (Chapter 5)
Bernoulli’s Equation
Unit: L
(Energy per unit weight)
Basic assumptions:
•Inviscid & incompressible fluid
•Steady flow
•Applies along a streamline
• No energy added or removed from the
fluid along the streamline
Piezometric pressure
Copyright © The McGraw-Hill Companies, Inc.
FIGURE 5-22
16
Energy in Steady Flow, Pipe Flow
V
p/γ p/γ
V2/2g
Bring moving water to a halt, and it'll
drive a column of water up to exactly
the height from which water would flow
to gain that velocity.
Pitot Tube
(Measures stagnation
pressure)
Free stream dynamic
pressure
Free stream static
pressure
17
Energy in Steady Flow, Free surface flow
V
V2/2g
Bring moving water to a halt, and it'll
drive a column of water up to exactly
the height from which water would flow
to gain that velocity.
Pitot Tube
(Measures stagnation
pressure)
18
Example: Bernoulli’s principle, Pitot Tube
http://www.youtube.com/watch?v=dk39ffdWq_E
19
Example:
Spraying Water
into the Air
Example: Water Discharge
from a Large Tank
20
The hydraulic
grade line (HGL)
and the energy
grade line (EGL)
for free discharge
from a reservoir
through a
horizontal pipe
with a diffuser.
Hydraulic grade line (HGL), P/g + z The line that represents the sum of
the static pressure and the elevation heads.
Energy grade line (EGL), P/g + V2/2g + z The line that represents the
total head of the fluid.
Dynamic head, V2/2g The difference between the heights of EGL and HGL.
21
Energy in Steady Flow
Stagnation pressure, ideal fluid (5.4)
1 2
V
V1 = V, p2 is the
stagnation
pressure
22
Energy in Steady Flow
General Energy Equation, steady flow, incompressible fluid
For an incompressible fluid with γ = const. and α =1:
23
Energy in Steady Flow
General Energy Equation, steady flow, incompressible fluid
For an incompressible fluid with γ = const. and α =1:
If there is no machine between points 1 and 2:
If head loss is neglected:
Real fluid
Ideal fluid
24
Energy in Steady Flow
Power considerations in fluid flow, Derivation of Power Equation
Power: P = (Force) x (Velocity) Power: P = Energy / Time
P = FV (F =ΔpA)
P = (ΔpA)V (Δp = γh)
P = (γhA)V (Q = AV)
P = γhQ
P = (Energy/Weight) x (Weight/Time)
P = ΔpQ
head (h) γQ
P = h γQ
25
Energy in Steady Flow
Power considerations in fluid flow, Units of Power
P = γhQ
Horsepower = P = γhQ/550
( [Q] = cfs, [h] = ft, [γ] = pcf )
Power in BG units
Kilowatts = P = γhQ/1000
( [Q] = m3/s, [h] = m, [γ] = N/m3 )
Power in SI units
P = γhQ P: power put into flow by a pump,
then h = hpump
P: power lost because of friction,
then h = hL
Pump efficiency, η = (power output) / (power input)
http://www.waterencyclopedia.com/Po-Re/Pumps-Traditional.html
top related