Fluids Statics

Fluids staticsThe general rules of statics (as applied in solid mechanics) apply to fluids at rest. From earlier we know that:

• a static fluid can have no shearing force acting on it, • any force between the fluid and the boundary must be acting at right angles to the boundary. • The forces on any fluid particle are the result of gravity and pressure only. ( we are neglecting surface tension and assuming that no electromagnetic forces act on the fluid)

The pressure has the following three characteristics.1. The pressure of a fluid always acts perpendicular to the wall in

contact with the fluid.

The normal stress and shear stressat the surface of a fluid element. For fluids at rest, the shear stress is zero and pressure is the only normal stress.

Pascal Law

Pressure acting on a minute triangular prism

2. The values of the pressure acting at any point in a fluid at rest are equal regardless of its direction.

3. The fluid pressure applied to a fluid in a closed vessel is transmitted to all parts at the same pressure value as that applied (Pascal’s law).

Hydraulic press

The Basic Equations of Fluid Statics

• Pressure-Height Relation

Hydrostatics

Pressure in liquid

p = tekanan absolut

Pressure Variation in a static Fluid

• Compressible Fluid: Ideal Gas

Need additional information, e.g., T(z)

for atmosphere

Pressure Variation in a Static Fluid

In the sea level surface p0, 0 and z0 = 0. • po = 101,303 Pa (14.696 lb/in2) = lapse rate (koefisien muai untuk

udara) = 0,00650 K/m. For U.S Standard AtmosphereTo = 15oC = 288.15 K (59oF or

518.67oR)

Troposphere

Rg

o T

zpp

01 Per. 2.27

Per. 2.26

Pressure Variation in a Static Fluid

Stratosphere

Temperature constant

T=Tc=216,7 K=319,1 R

Zc=11 km (36000ft)

Pc=22600 Pa (3,28 lb/in2)

c

c

RTzzg

cepp

Stratosphere

Per 2.24

• Ionosphere

DISCONTINUM FLUID

Pressure Variation in a static Fluid

Pressure Measurement

Barometers

A barometer is a device for measuring atmospheric pressure. A simple barometer consists of a tube more than 30 inch (760 mm) long inserted in an open container of mercury with a closed and evacuated end at the top and open tube end at the bottom and with mercury extending from the container up into the tube.

Pressure Gauges

There are two types pressure measurement :

1. Tube gauges : a. piezometer tube b. manometer tube

2. Mechanical gauge : bourdon manometer

Pressure Measurement

1. Tube gauges

a. piezometer tube

This method can only be used for liquids (i.e. not for gases) and only when the liquid height is convenient to measure (just positive pressure). It must not be too small or too large and pressure changes must be detectable.

1ghpA

b. Manometers

Pressure Measurement

Manometers - Various forms1. Simple U - tube Manometer : a. positive, b negative2. Deferential Manometer 3. Inverted Differential U - tube Manometer4. Micrometers Manometer a. U - tube with one leg enlarged, b Two leg enlarged U - tube Manometer, c. Inclined U - tube Manometer

A somewhat more complicated device for measuring fluid pressure consists of a bent tube containing one or more liquid of different specific gravities

Simple U Tube Manometer

a. Positive pressure

CB pp

112 ghghpp

pppp

manDA

CDDABA

atmosfireaD ppp

112 ghghp

gaugepressure

manA

Simple U Tube Manometer

b. Negative pressure

atmosfereCD ppp

)(

)(

12

12

lmanA

lmanCA

ABACBC

ghghp

gagepressure

ghghpp

pppp

atmosfireaD ppp

Measurement Of Pressure Difference Using a "U"-Tube Manometer

If the "U"-tube manometer is connected to a pressurized vessel at two points the pressure difference between these two points can be measured.

blmanlla pgLghghgLpp

Deferential Inverted U - tube Manometer

gHpp 21

Katup yg berfungsi membuang gas saat sebelum dilakukan pengukuran

Two fluids U-tube with one leg enlarged Micromanometer

Small differences in pressure in gases are often measured with a manometer of the form shown in the figure.

gHpp 21

HhdD

ghgHpp ,

21

21

Two fluids U-tube Micromanometer

ghpp 21

Inclined Micromanometer

gHpp 21

The sensitivity to pressure change can be increased further by a greater inclination of the manometer arm; alternatively the density of the manometer fluid may be changed.

Advance and Limitation Manometer

The manometer in its various forms is an extremely useful type of pressure measuring instrument, but suffers from a number of limitations.

• While it can be adapted to measure very small pressure differences, it can not be used conveniently for large pressure differences - although it is possible to connect a number of manometers in series and to use mercury as the manometer fluid to improve the range. (limitation)

• A manometer does not have to be calibrated against any standard; the pressure difference can be calculated from first principles. ( Advantage)

• Some liquids are unsuitable for use because they do not form well-defined menisci. Surface tension can also cause errors due to capillary rise; this can be avoided if the diameters of the tubes are sufficiently large - preferably not less than 15 mm diameter. (limitation)

• A major disadvantage of the manometer is its slow response, which makes it unsuitable for measuring fluctuating pressures.(limitation)

• It is essential that the pipes connecting the manometer to the pipe or vessel containing the liquid under pressure should be filled with this liquid and there should be no air bubbles in the liquid.(important point to be kept in mind)

• Fluid that is measured cannot mixture or reaction with manometer fluid

Mechanical Gauge

• Bourdon Gauge