thermo fluids me 439
TRANSCRIPT
Thermo Fluids – ME 439
Arab Academy for Science, Technology
and Maritime Transportation
Dr. Ahmed Khalifa Mehanna
Assistant Professor
Room No: 223
Course Assistant Lecturer:
Eng. Persis Boushra
Lecture 3:
Fluid Statics or (Fluids at Rest)
Thermo Fluids – ME 439
Fluid Statics
Pressure Definition
Hydrostatic Pressure in a Liquid
Pressure at a point
Variation of Pressure with Depth
Hydrostatic Pressure Distribution
Examples
Pressure Measurement Devices
Outline
Fluid Statics deals with problems associated with
fluids at rest.
In fluid statics, there is no shear stress in the fluid
trying to deform it.
The only stress in fluid statics is the normal stress
Normal Stress is due to pressure,
Variation of pressure is due only to the weight of the fluid,
Applications of fluid statics:
Pressure measurement with hydrostatics, Floating or
submerged bodies, water dams and gates, liquid storage
tanks, etc.
Fluid Statics
Pressure is defined as a
normal force exerted by a
fluid divided by the area
that the force acts over and
therefore has units of F/A .
It can be a result of an
applied force (for example
pumping) or hydrostatic
(weight of a column of
fluid).
Pressure Definition
Unit for pressure is the Pascal (Pa), which equal (N/m2 or kg/m.s2).
1 bar = 105 Pa = 0.1 MPa = 100 kPa
1 atm = 101,325 Pa
1 atm = 101.325 kPa
1 atm = 1.01325 bars
Pressure Units
P = g hP = F/A i.e: m*g/ABut m=V
P= V g / A = g (V/A)P = g h
The pressure at a given depth in a static liquid is a result of the weight of the liquid
acting on a unit area at that depth plus any pressure acting on the surface of the
liquid.
The pressure due to the liquid alone (i.e. the Gauge Pressure) at a given depth
depends only upon the density of the liquid ρ and the distance below the surface of
the liquid h.
Hydrostatic Pressure in a LiquidPressure
Hydrostatic pressure in a liquid
can determined using the
following equation:
P = ρ g h
Where
P = Pressure;
(N/m2, or Pa, or kg/m.s2)
ρ = Density of liquid (kg/m3)
g = The gravitational gravity,
constant (9.807 m/s2)
h = Depth at which the
pressure is measured (m)
Hydrostatic pressure in a water column at
(ρ =1000 kg/m3) is indicated below:
Hydrostatic Pressure in a Liquid
Barometer – an instrument that measures pressure
Mercury barometer
Measuring Pressure
vacuum
A Bh
Atmospheric Pressure P = PA = PB = Hg g h
Mean sea-level pressure: P = 1.01325x105 Pa = 101.325 kPa
= 0.101325 MPa
= 1.01325 bars
= 1 atm
P = 1013.25 hecto Pa = 1013.25 hPa
Absolute Pressure: The actual pressure at a given position. It is measured
relative to absolute vacuum (i.e., absolute zero pressure).
Gage Pressure: Most pressure-measuring devices are calibrated to read zero in
the atmosphere, and so they indicate gage pressure. For example, an ordinary
pressure gauge reading of zero does not mean there is no pressure, it means
there is no pressure in excess of atmospheric pressure
Vacuum Pressure: Pressures below atmospheric pressure.
Pabs = Patm + Pgage
Patm = Pvac + Pabs
Absolute, Gage, and Vacuum Pressures
Absolute, Gage, and Vacuum Pressures
Absolute Pressure = True Pressure.
All given values for pressure are gage pressure except if :
(abs) is mentioned beside the unit.
Dealing with atmospheric pressure.
Dealing with vapour pressure.
Pabs = Patm + Pgage
• Pressure at any point in a fluid is the same in all directions.
• Pressure has a magnitude, but not a specific direction, and thus
it is a scalar quantity.
Pressure at a Point
Pabs = Patm + Pgage
Pgage = Pabs Patm
Patm = Pvac + Pabs
Pvac = Patm PabsPressure acts equally in all directions
Pascal’s low: The pressure at point is the same in all directions
and normal to surface.
Pressure at a Point: Pascal’s Law
Free-body diagram of a rectangular
fluid element in equilibrium.
The pressure of a fluid at rest increases
with depth (as a result of added weight).
When the variation of density with
elevation is known
Variation of Pressure with Depth
Pabs = Patm + Pgage
The pressure is the same at all points on a horizontal plane in a given fluid
regardless of geometry, provided that the points are interconnected by the
same fluid.
Points a, b, c, and d are at equal depths in water and therefore have identical
pressures. Points A, B, and C are also at equal depths in water and have
identical pressures higher than a, b, c, and d. Point D has a different pressure
from A, B, and C because it is not connected to them by a water path.
Hydrostatic Pressure Distribution
The quantity is called the specific weight of the fluid, with dimensions of
weight per unit volume. The quantity (P / ) is a length called the pressure head
of the fluid.
Hydrostatic Pressure Distribution in Oceans and Atmospheres
Evaluating Pressure Changes Through a Column of Multiple Fluids
ExampleBlood pressures is usually given as the ratio of the maximum
pressure to the minimum pressure. For example, atypical value
for this ratio for a human would be 120/70, where the pressures
are in mm Hg. What would these pressures be in pascals.
Solution:
P = ρ g h = h in Pa or N/m2 and = 133,326 in N/m3
For 120 mm Hg:
P = (133.326 * 103 N/m3) * (120/1000 m) ………... in pascal (Pa)
P = (133.326 * 103 ) * (0.12 ) / 1000 = 15.999 kPa
The pressure for 120 mm Hg is approximately 16 kPa
For 70 mm Hg:
P = (133.326 * 103 N/m3) * (70/1000 m) .………... in pascal (Pa)
P = (133.326 * 103 ) * (0.07 ) / 1000 = 9.333 kPa
The pressure for 70 mm Hg is 9.333 kPa
Pascal’s law: The pressure applied to a confined fluid increases the
pressure throughout by the same amount.
Lifting of a large weight
by a small force by the
application of Pascal’s
law.
The area ratio A2/A1 is
called the ideal
mechanical advantage of
the hydraulic lift.
ExampleA 0.3 m diameter pipe is connected to
20 mm diameter pipe and both are
rigidly held in place. Both pipes are
horizontal with pistons at each end. If
the space between the pistons is filled
with water, what force will have to be
applied to the larger piston to balance
a force of 90 N applied to the smaller
piston? Neglect the friction.
Thus
Or
Solution:
The Barometer
Atmospheric pressure is measured by a device called a barometer; thus, the
atmospheric pressure is often referred to as the barometric pressure.
A frequently used pressure unit is the standard atmosphere, which is defined as
the pressure produced by a column of mercury 760 mm in height at 0°C (Hg =
13,595 kg/m3) under standard gravitational acceleration (g = 9.807 m/s2).
The basic barometer.
The length or the
cross-sectional area of
the tube has no effect
on the height of the
fluid column of a
barometer, provided
that the tube diameter
is large enough to
avoid surface tension
(capillary) effects.
Pressure Measurement Devıces
F = P A = W
Mercury barometer
Mercury Barometer:
It is a method for measuring the local atmospheric
pressure. The mercury barometer consists of a glass tube
closed at one end with the open end immersed in a
container of mercury as shown in Figure. The tube is
initially filled with mercury (inverted with its open end
up) and then turned upside down (open end down) with
the open end in the container of mercury. The column of
mercury will come to an equilibrium position where its
weight plus the force due to the vapor pressure (which
develops in the space above the column) balances the
force due to the atmospheric pressure. Thus:
Patm = h+ Pvapor
For most practical purposes the contribution of the vapor pressure can be
neglected since it is very small (about: 0.16 Pa = 0.16 N/m² = 0.0000016 bar
= 0.000016 kgf/cm²). Therefore:
Patm = h
Where is the specific weight of mercury.
Piezometer Tube
Piezometer Tube:
It is the simplest type of manometer consists of a
vertical tube, open at the top, and attached to the
container in which the pressure is desired, as
shown.
Since manometers involve columns of fluids at
rest, the fundamental equation describing their
use is :
P = h + Po
Application of this equation to the Piezometer
tube of indicates Figure that the gage pressure PA
can be determined by a measurement of h1 ,
through the relationship:PA = 1 h1
where 1 is the specific weight of the liquid in the
container.
Note that:
Since the tube is open at the top, and the pressure Po set equal to zero, then
we are now using gage pressure.
Although the Piezometer tube is a very simple and accurate pressure
measuring device, it has several disadvantages:
1. It is only suitable if the pressure in the container is greater than
atmospheric pressure (otherwise air would be sucked into the system).
2. The pressure to be measured must be relatively small so the required
height of the column is reasonable.
3. The fluid in the container in which the pressure is to be measured must
be a liquid rather than a gas.
To overcome the disadvantages noted U-Tube manometer should be used.
U-tube manometer
U-Tube Manometer:It consists of a tube formed in U shape as
shown. The fluid in the manometer is called
the gage fluid.
The pressure at points A and (1) are the
same, and as we move from point (1) to (2)
the pressure will increase by 1 h1. The
pressure at point (2) is equal to the pressure
at point (3) - since the pressures at equal
elevations in a continuous mass of fluid at
rest must be the same - at the open end
where the gage pressure is zero, as we move
vertically upward the pressure decreases by
an amount 2 h2. So:
Therefore,PA + 1 h1 2 h2 = 0
PA = 2 h2 1 h1
Differential U-tube manometer
The U-tube manometer is used to measure the
difference in pressure between two containers or
two points in a given system.
Consider a manometer connected between
containers A and B as is shown in Fig. The
difference in pressure between A and B can be
found where the pressure at A is PA, which is
equal to P1,and as we move to point (2) the
pressure increases by 1 h1. The pressure at P2 is
equal to P3, and as we move upward to point (4)
the pressure decreases by 2 h2. Similarly, as we
continue to move upward from point (4) to (5)
the pressure decreases by 3 h3.
Finally, P5 = PB , since they are at equal elevations. Thus:
and the pressure difference is:
PA + 1 h1 2 h2 3 h3 = PB
PA PB = 2 h2 + 3 h3 1 h1
Differential U-tube manometer
Inclined-Tube Manometer:
It is used to measure small pressure changes. as shown in Figure, one
leg of the manometer is inclined at an angle .
So, the difference in pressure can be expressed as:
i.e.,
Inclined-tube Manometer
