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CHAPTER 2

PRESSURE IN A

STATIC FLUID

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Recap: Pressure

The compressive force acting on a surfaceimmersed in a fluid is expressed as a forceper unit area and is termed pressure.

Thus, pressure is measured as force perunit area, and its units are N/m 2.

It is given the name Pascal (Pa). Typical atmospheric pressure is about 10 5

Pa.

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Variation of Pressure inVertical Direction

z

p A

A z z p

p

g z A

Force balance in verticaldirection gives:

g

z

p

A zg A z z

p

or,

,0

Since p does not vary in x and y directions,

gdz

dp

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Variation of Pressurein Horizontal Direction

x

p A A x x p

p

Horizontal force balance will give 0 x p

Therefore, pressure does not change ina horizontal plane.

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gh pgz p p

z p p

const gz p

gdzdp

00

0

so,

,0at

. or,

(Pa) 108.910

);m()(m/s8.9)(kg/m10(Pa)1035

2335

h p

hgh p p atm

Hydrostatic Pressure Variation

h

z

For water with a free surfaceexposed to atmosphere

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Example

What is the pressure at a depth of 10m in water?

What is the pressure at a depth of 10m in mercury?What is the pressure at a depth of 1

km in water?

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A Liquid Maintains its Level

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BAROMETER

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PRINCIPLE OF BAROMETER

The mercury barometer was first discovered bythe Italian Scientist Torricelli in 1643 and has beensince then known as the Torricelli barometer.

This barometer works by the level of the mercuryin the glass being balanced with the amount ofpressure in the atmosphere.

Under normal circumstances, the column ofmercury in the glass tube stands at a height ofabout 30 (29.92) inches (75 centimeters) whenmeasured at sea level.

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WHY MERCURY?

Mercury is used because of it's very highdensity, it is 13.6 times as dense as water. Theatmosphere on average holds up about 76cm

of mercury in a barometer... A sensible size. Ifyou used water, it would have to be 76 x 13.6cm at least in height.

Mercury doesn't evaporate very much. Awater barometer would constantly needrefilling.

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CAPILLARITY ACTION

It is the rise or fall of a liquid against gravity ina narrow space such as a thin tube or inporous materials such as paper.

This phenomenon is due to combined effect of

cohesion and adhesion of liquid particles.

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Capillary Action

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Capillary Action

ghr r 22

rgh

2

For water ( = 7.2X10 -2 N/m),r = 0.5 mm, the capillary rise

is 29 mm

h

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CAPILLARY

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Capillary Action

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Capillary Action

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Figure 1a. The pool of red colored wateron this countertop is held together bysurface tension and cohesion betweenthe water droplets.

Figure 1b. Capillary action causesthe water to "climb" up this papertowel.

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MANOMETERS MECHANICAL GAUGES

PRESSURE MEASUREMENT

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Simple Manometers Piezometer U-tube Manometer

Differential Manometers

MANOMETERS

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PIEZOMETER

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LIMITATIONS OFPIEZOMETER

1. Piezometers can measure gauge pressuresonly. It is not suitable for measuring negative

pressures.

2. Piezometers cannot be employed whenlarge pressures in the lighter liquids are to bemeasured since this would require very longtubes, which cannot be handled conveniently.

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U-TUBE MANOMETER

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DIFFERENTIAL MANOMETER

A differential manometer is a device thatmeasures the difference in pressure betweentwo places.

Differential manometers are also used tocompare the pressure of two differentcontainers. They reveal both which containerhas greater pressure and how large thedifference between the two is.

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Inclined Tube Manometer

Inclined-tube manometer is used to measuresmall pressure differences between twosystems .

The advantage of the inclined manometer isthat the differential reading scales along thetube can be made large compared to avertical manometer for a given pressuredifference, hence improving the accuracy inreading the scale.

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Inclined-Tube Manometer

Pressure p A

l

p A = gl sin

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Reducing Errors in Manometry

Change in density of gauge fluid

Density of water changes by 0.75 % as thetemperature changes from 10 0 C to 40 0 C.

Density of mercury changes by 0.5 % as thetemperature changes from 10 0 C to 40 0 C.

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Reducing Errors in Manometry

Capillary riserg

h

2

U-tube manometer with both legs ofsame dia is helpful

Cleanliness. Degreasing.