Properties of Fluids for Fluid Mechanics. P M V Subbarao Associate Professor Mechanical Engineering Department IIT Delhi. Basic Steps to Design…………. Continuum Hypothesis.
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Properties of Fluids for Fluid Mechanics
P M V Subbarao
Associate Professor
Mechanical Engineering Department
IIT Delhi
Basic Steps to Design………….
For a static fluid
Shear Stress should be zero.
For A generalized Three dimensional fluid Element, Many forms of shear stress
is possible.
+Y
u=U
u=0
+X
+
tyx
tzx
txy
tzy
tyz
txz
Y
X
Z
Y
tyx
tzx
tyy
tzy
txy
txx
tyz
X
tzz
txz
txz
Z
First Law of Pascal
Proof ?
Fluid Statics for Power Generation
P M V Subbarao
Associate Professor
Mechanical Engineering Department
IIT Delhi
Steps for Design of Flow Devices………….
1st order Taylor series estimate for pressure variation over dz
For a static fluid, the pressure only varies with elevation z and is constant in horizontal xy planes.
Basic equation for pressure variation with elevation
Pressure variation equation can be integrated for γ(p,z) known.
For example, here we solve for the pressure in the atmosphere assuming ρ(p,T) given from ideal gas law, T(z) known, and g ≠ g(z).
Flue gas out
Air in
Zref,,pref
pA = pref +Dp
Hchimney
Tgas
Tatm
B
A
Zref,,pref
pA = pref +Dp
Hchimney
Tgas
Tatm
B
A
Pressure variations in Troposphere:
Linear increase towards earth surface
Tref & pref are known at Zref.
a : Adiabatic Lapse rate : 6.5 K/km
Reference condition:
At Zref : T=Tref & p = pref
Pressure at A:
Pressure variation inside chimney differs from atmospheric pressure.
The variation of chimney pressure depends on temperature variation along
Chimney.
Temperature variation along chimney depends on rate of cooling of hot gas
Due to natural convection.
Using principles of Heat transfer, one can calculate, Tgas(Z).
If this is also linear: T = Tref,gas + agas(Zref-Z).
Lapse rate of gas, agas is obtained from heat transfer analysis.
Pressure Measurement
Another Application of Fluid Statics
Pressure is an important variable in fluid mechanics and many instruments have been devised for its measurement.
Many devices are based on hydrostatics such as barometers and manometers, i.e., determine pressure through measurement of a column (or columns) of a liquid using the pressure variation with elevation equation for an incompressible fluid.
Enlarged Leg
Inverted U Tube
U Tube
Two Fluid
Inclined Tube
Right Limb fluid statics :
Left Limb fluid statics :
Point 3 and 2 are at the same elevation and same fluid
Gauge Pressure:
System Pressure
Gauge Pressure
Absolute Pressure
Atmospheric Pressure
Absolute zero pressure
Absolute, Gauge & Vacuum Pressures
Atmospheric Pressure
Vacuum Pressure
System Pressure
Absolute Pressure
Absolute zero pressure
Y
tyy
txx
X
tzz
Z
0
0
0
0
0
0
Shear stress(t): Tangential force on per unit area of contact
between solid & fluid