S3 Chapter 2 Fluid Pressure
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Transcript of S3 Chapter 2 Fluid Pressure
CHAPTER 2: FLUIDPRESSURE
PREPARED BY :
NOOR ASSIKIN BINTI ABD WAHAB
Learn more about
Fluids &
TODAY’S GOAL
PRESSURE
PRESSURE Pressure is defined as a normal force
exerted by a fluid per unit area. Units of pressure are N/m2, which is called a
pascal (Pa). Since the unit Pa is too small for pressures
encountered in practice, kilopascal (1 kPa = 103 Pa) and megapascal (1 MPa = 106 Pa) are commonly used.
Other units include bar, atm, kgf/cm2, lbf/in2=psi.
Pressure
Pressure is the force per unit area, where the force is perpendicular to the area.
p=A m2
Nm-2
(Pa)
NF
This is the Absolute pressure, the pressure compared to a vacuum.
pa= 105 Nm-2
1psi =6895Pa
The pressure measured in your tyres is the gauge pressure, p-pa.
Pressure
Pressure in a fluid acts equally in all directions
Pressure in a static liquid increases linearly with depth
p=increase in depth (m)
pressure increase
g h
The pressure at a given depth in a continuous, static body of liquid is constant.
p1p2
p3 p1 = p2 = p3
PressurePressure is the ratio of a force F to the area A over which it is applied:
Pressure ; Force F
PArea A
Pressure ; Force F
PArea A
A = 2 cm2
1.5 kg
2
-4 2
(1.5 kg)(9.8 m/s )
2 x 10 m
FP
A
P = 73,500 N/m2P = 73,500 N/m2
The Unit of Pressure (Pascal):
A pressure of one pascal (1 Pa) is defined as a force of one newton (1 N) applied to an area of one square meter (1 m2).
21 Pa = 1 N/mPascal:
In the previous example the pressure was 73,500 N/m2. This should be expressed as:
P = 73,500 PaP = 73,500 Pa
PRESSURE HEAD
P(A) static pressure of system Column of water supported by this pressure Pressure Head hp = p ρg
Fluid exerts forces in many directions. Try to submerse a rubber ball in water to see that an upward force acts on the ball.
• Fluids exert pressure in all directions. F
Pressure vs. Depth in Fluid
Pressure = force/area
; ; mg
P m V V AhA
Vg AhgP
A A
h
mgArea
• Pressure at any point in a fluid is directly proportional to the density of the fluid and to the depth in the fluid. P = gh
Fluid Pressure:
Independence of Shape and Area.Water seeks its own level, indicating that fluid pressure is independent of area and shape of its container.
• At any depth h below the surface of the water in any column, the pressure P is the same. The shape and area are not factors.
• At any depth h below the surface of the water in any column, the pressure P is the same. The shape and area are not factors.
PROPERTIES OF FLUID PRESSURE
The forces exerted by a fluid on the walls of its container are always perpendicular.
The fluid pressure is directly proportional to the depth of the fluid and to its density.
At any particular depth, the fluid pressure is the same in all directions.
Fluid pressure is independent of the shape or area of its container.
The forces exerted by a fluid on the walls of its container are always perpendicular.
The fluid pressure is directly proportional to the depth of the fluid and to its density.
At any particular depth, the fluid pressure is the same in all directions.
Fluid pressure is independent of the shape or area of its container.
Example 2. A diver is located 20 m below the surface of a lake ( = 1000 kg/m3). What is the pressure due to the water?
h = 1000 kg/m3
P = gh
The difference in pressure from the top of the lake to the diver is:
h = 20 m; g = 9.8 m/s2
3 2(1000 kg/m )(9.8 m/s )(20 m)P
P = 196 kPaP = 196 kPa
Atmospheric Pressure
atm
atm h
Mercury
P = 0One way to measure atmospheric pressure is to fill a test tube with mercury, then invert it into a bowl of mercury.
Density of Hg = 13,600 kg/m3
Patm = gh h = 0.760 m
Patm = (13,600 kg/m3)(9.8 m/s2)(0.760 m)
Patm = 101,300 PaPatm = 101,300 Pa
Absolute PressureAbsolute Pressure:Absolute Pressure: The sum of the pressure due to a fluid and the pressure due to atmosphere.Gauge Pressure:Gauge Pressure: The difference between the absolute pressure and the pressure due to the atmosphere:
Absolute Pressure = Gauge Pressure + 1 atmAbsolute Pressure = Gauge Pressure + 1 atm
hP = 196 kPa
1 atm = 101.3 kPa
P = 196 kPa1 atm = 101.3 kPa
Pabs = 196 kPa + 101.3 kPa
Pabs = 297 kPaPabs = 297 kPa
Pascal’s Law
Pascal’s Law: An external pressure applied to an enclosed fluid is transmitted uniformly throughout the volume of the liquid.
FoutFin AoutAin
Pressure in = Pressure outPressure in = Pressure out
in out
in out
F F
A A
Example 3. The smaller and larger pistons of a hydraulic press have diameters of 4 cm and 12 cm. What input force is required to lift a 4000 N weight with the output piston?
FoutFin AouttAin
; in out out inin
in out out
F F F AF
A A A
2
2
(4000 N)( )(2 cm)
(6 cm)inF
2; 2
DR Area R
F = 444 NF = 444 N
Rin= 2 cm; R = 6 cm
ABSOLUTE, GAGE, AND VACUUM PRESSURES
Actual pressure at a give point is called the absolute pressure.
Most pressure-measuring devices are calibrated to read zero in the atmosphere, and therefore indicate gage pressure, Pgage=Pabs - Patm.
Pressure below atmospheric pressure are called vacuum pressure, Pvac=Patm - Pabs.
Absolute, gage, and vacuum pressures
PRESSURE AT A POINT
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.
SCUBA DIVING AND HYDROSTATIC PRESSURE
PRESSURE MEASUREMENT 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.
PRESSURE Force exerted on a unit
area : Measured in kPa Atmospheric pressure at
sea level is 1 atm, 76.0 mm Hg, 101 kPa
In outer space the pressure is essentially zero. The pressure in a vacuum is called absolute zero.
All pressures referenced with respect to this zero pressure are termed absolute pressures.
Many pressure-measuring devices measure not absolute pressure but only difference in pressure. This type of pressure reading is called gage pressure.
Whenever atmospheric pressure is used as a reference, the possibility exists that the pressure thus measured can be either positive or negative.
Negative gage pressure are also termed as vacuum pressures.
MANOMETERS
U Tube
Enlarged Leg
Two FluidInclined Tube
Inverted U Tube
THE MANOMETER
1 2
2 atm
P P
P P gh
An elevation change of z in a fluid at rest corresponds to P/g.
A device based on this is called a manometer.
A manometer consists of a U-tube containing one or more fluids such as mercury, water, alcohol, or oil.
Heavy fluids such as mercury are used if large pressure differences are anticipated.
MUTLIFLUID MANOMETER
For multi-fluid systems Pressure change across a fluid
column of height h is P = gh. Pressure increases downward,
and decreases upward. Two points at the same elevation
in a continuous fluid are at the same pressure.
Pressure can be determined by adding and subtracting gh terms.
2 1 1 2 2 3 3 1P gh gh gh P
MEASURING PRESSURE DROPS
Manometers are well--suited to measure pressure drops across valves, pipes, heat exchangers, etc.
Relation for pressure drop P1-P2 is obtained by starting at point 1 and adding or subtracting gh terms until we reach point 2.
If fluid in pipe is a gas, 2>>1 and P1-P2= gh
THE BAROMETER
C atm
atm
P gh P
P gh
Atmospheric pressure is measured by a device called a barometer; thus, atmospheric pressure is often referred to as the barometric pressure.
PC can be taken to be zero since there is only Hg vapor above point C, and it is very low relative to Patm.
Change in atmospheric pressure due to elevation has many effects: Cooking, nose bleeds, engine performance, aircraft performance.
Measuring pressure (1)Manometers
h
p1 p2=pa
liquiddensity
x y
z
p1 = px
px = py
pz= p2 = pa
(negligible pressure change in a gas)
(since they are at the same height)
py - pz = gh
p1 - pa = gh
So a manometer measures gauge pressure.
Measuring Pressure (2)Barometers
A barometer is used to measure the pressure of the atmosphere. The simplest type of barometer consists of a column of fluid.
p1 = 0
vacuum
h
p2 = pa
p2 - p1 = gh
pa = gh
examples
water: h = pa/g =105/(103*9.8) ~10m
mercury: h = pa/g =105/(13.4*103*9.8) ~800mm