MODULE III_FM.pptx

1. MODULE III
MET203 MECHANICS OF
FLUIDS

2. SYLLABUS
• Control volume analysis of mass, momentum and energy,
Equations of fluid dynamics: Differential equations of mass,
energy and momentum (Euler’s equation), Navier-Stokes
equations (without proof) in cartesian co-ordinates. Dynamics
of Fluid flow: Bernoulli’s equation, Energies in flowing fluid,
head, pressure, dynamic, static and total head, Venturi and
Orifice meters, Notches and Weirs (description only for
notches and weirs). Hydraulic coefficients, Velocity
measurements: Pitot tube and Pitot-static tube.

3. CONTROL VOLUME ANALYSIS OF MASS
• The conservation of mass relation for a closed system
undergoing a change is expressed as
msys = constant or
dmsys/dt = 0, which is the statement that the mass of the
system remains constant during a process.
• For a control volume (CV), mass balance is expressed in rate
form as
Conservation of mass: m in – m out = dmCV /dt
• where min and mout are the total rates of mass flow into and out
of the control volume, respectively, and dmCV/dt is the rate of
change of mass within the control volume boundaries. In fluid
mechanics, the conservation of mass relation written for a
differential control volume is usually called the continuity
equation.

5. COUNTINUITY EQUATION IN THREE DIMENSIONS

8. THE MOMENTUM EQUATION

9. THE ENERGY EQUATION

10. EQUATIONS OF MOTION

11. EULER’S EQUATION OF MOTION

14. BERNOULLI’S EQUATION FROM EULER’S EQUATION

15. BERNAULLI’S EQUATION FOR REAL FLUID

16. STATIC, DYNAMIC, AND STAGNATION PRESSURES
• The Bernoulli equation states that the sum of the flow, kinetic,
and potential energies of a fluid particle along a streamline is
constant. Therefore, the kinetic and potential energies of the fluid
can be converted to flow energy (and vice versa) during flow,
causing the pressure to change. This phenomenon can be made
more visible by multiplying the Bernoulli equation by the
density,
• Each term in this equation has pressure units, and thus each term
represents some kind of pressure

17. • The stagnation pressure represents the pressure at a
point where the fluid is brought to a complete stop
isentropically.
• When static and stagnation pressures are measured at
a specified location, the fluid velocity at that location
is calculated from

18. • P is the static pressure (it does not incorporate any dynamic
effects); it represents the actual thermodynamic pressure of the
fluid. This is the same as the pressure used in thermodynamics
and property tables.
• ρV2/2 is the dynamic pressure; it represents the pressure rise
when the fluid in motion is brought to a stop isentropically.
• ρgz is the hydrostatic pressure term, which is not pressure in a
real sense since its value depends on the reference level selected;
it accounts for the elevation effects, i.e., fluid weight on pressure.
(Be careful of the sign—unlike hydrostatic pressure rgh which
increases with fluid depth h, the hydrostatic pressure term rgz
decreases with fluid depth.)
• The sum of the static, dynamic, and hydrostatic pressures is called
the total pressure.
• Therefore, the Bernoulli equation states that the total pressure
along a streamline is constant. The sum of the static and dynamic
pressures is called the stagnation pressure, and it is expressed as

19. • Each term in this equation has the dimension of length and
represents some kind of “head” of a flowing fluid as follows: •
P/ ρg is the pressure head; it represents the height of a fluid
column that produces the static pressure P.
• V2/2g is the velocity head; it represents the elevation needed
for a fluid to reach the velocity V during frictionless free fall.
• z is the elevation head; it represents the potential energy of the
fluid. Also, H is the total head for the flow. Therefore, the
Bernoulli equation is expressed in terms of heads as: The sum
of the pressure, velocity, and elevation heads along a
streamline is constant during steady flow when compressibility
and frictional effects are negligible

20. PRACTICALAPPLICATIONS OF BERNAULLI’S
EQUATION

21. VENTURIMETER

26. ORIFICE METER (ORIFICE PLATE)

30. PITOT TUBE

33. PITOT-STATIC PROBE
• The Pitot-static probe consists of a slender double-tube aligned
with the flow and connected to a differential pressure measuring
device such as manometer
• The inner tube is fully open to the flow at the nose and thus
measures the stagnation pressure (point ‘1’) while the outer tube
is sealed at the nose, but has the holes on the circumference of the
outer wall for measuring the static pressure (point ‘2’).
• Neglecting frictional effects in, Bernoulli’s equation can be
applied for the point ‘1 and 2’ to obtain the average flow velocity
• This equation is also known as Pitot formula. The volume flow
rate can be obtained by multiplying the cross-sectional area to
this velocity

34. (a) A Pitot probe measures stagnation pressure at the nose of the probe, while
(b) a Pitot-static probe measures both stagnation pressure and static pressure,
from which the flow speed is calculated.

35. • The Pitot-static probe is a simple, inexpensive and highly
reliable device because it has no moving parts.
• Moreover, this device can be used for velocity/flow rate
measurements for liquids as well as gases.
• When this device is used for gases, it is expected that velocity
is relatively high to create a noticeable dynamic pressure
because gases have low densities.

36. NOTCHES AND WEIRS

37. CLASSIFICATION OF NOTCHES AND WEIRS

39. HYDRAULIC COEFFICIENTS