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