Chapter 2 - Part 1 Pressure

7/27/2019 Chapter 2 - Part 1 Pressure

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CHAPTER 2

Part 1:PressurePart 1:Pressure

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Fluid Statics Fluid Statics deals with problems

associated with fluids at rest.

In fluid statics, there is no relativemotion between adjacent fluid layers.

Therefore, there is no shear stress inthe fluid tr in to deform it.

The only stress in fluid statics isnormal stress

Normal stress is due to pressure

Variation of pressure is due only to the

weight of the fluid fluid statics is onlyrelevant in presence of gravity fields.

Applications: Floating or submergedbodies, water dams and gates, liquidstorage tanks, etc. 2


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Pressure Pressure is defined as anormal

force exerted by a fluid per unitarea.

Unit of pressure is N/m2, which iscalled pascal (Pa).

P = F/A

Since the unit Pa is too small forpressures encountered in practice,

kilopascal(1 kPa = 103 Pa) and

megapascal(1 MPa = 10

6

Pa) arecommonly used.

Other units includebar,atm,

kgf/cm2

, lbf/in2

=psi.3


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Pressure at a PointPressure ?

Indicating the normal force per unitarea at a given point acting on agiven plane within the fluid mass ofinterest.

ow t e pressure at a po nt var eswith the orientation of the planepassing through the point ?

In fluid at rest, pressure at any pointis the same at all direction.

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The pressure at a point in a fluid atrest, or in motion, is independent ofthe direction as long as there are noshearing stresses present.

Pressure at any point in a fluid is thesame in all directions.

Pressure has a magnitude, but not aspecific direction, and thus it is ascalar quantity.

The result is known asPascals lawnamed in honor ofBlaise Pascal(1623-1662).

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Absolute, gauge, andvacuum pressures

Actual pressure at a give point

is called the absolute pressure.

Most pressure-measuring

devices are calibrated to read

,

therefore indicate gauge

pressure,

Pgauge= Pabs - Patm.

Pressure below atmospheric

pressure are called vacuum

pressure, Pvac= Patm - Pabs. 6


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Absolute, gauge, and

vacuum pressures

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Atmospheric Pressure, Patm

* Pressure due to weight of airabove it.

* Standard value (1 atm =)

10.35 mH2O water (34 ftH2O)

760 mmHg

14.7 si

101.3 kN/m2

can be measured by P = gh

* Fluid pressure at free surfaceis equal to atmosphericpressure.

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Gauge Pressure, Pg

* Measured using pressure gauge.

* Can be positive (above atm pressure) ornegative (below atm pressure)

* Gauge negative pressure is referred tosuction pressure ofvacuum pressure.

ero pressure means e pressure sequal to atmospheric pressure.

* Gauge pressure units:

N/m2

gaugepsig

kPa gauge

barg

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Pressure Head of Fluid

* Pressure head of fluid is a pressure and it isinterpreted as the height of a column offluid of specific weight required.

* A basic equation is a relationship amongpressure, density and depth. P = gh

* Consider an element of fluid as shownbelow.

dA : cross sectional area of element : fluid density

P : pressure

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In equilibrium;

Upward Force = Downward Force

(P + dP) dA = PdA + mg

dPdA = mg

But;

m = v (v = element volume = dAdh)

dPdA = vg = gdAdh

dP = gdh

Integrated it;

P2 - P1 = g (h2 - h1)

=2

1

2

1

h

h

P

PdhgdP

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But;

h2 - h1 = h

Then

P2 - P1 = g h

If h1 = 0 and P1 = 0 (atmospheric pressure), then

P2 = gh

Based on the above equation, pressure isproportional to depth ( P h ) regardless of shapeof container.

O In pressure head, the above equation become

and its unit is in e.g.; mmHg or mmH20

21 pph

=

12

Specific weight


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Variation of Pressurewith Depth

Pressure in a fluid at rest is

independent of the shape of the

container.

Pressure is the same at all points on

a horizontal plane in a given fluid.

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Absolute pressure (atm)

on diver at 100 ft?

( ),2 3 21

998 9.81 1003.28

1

gage

kg m mP gz ft

m s ft

atm

= =

Scuba Diving and HydrostaticPressure

100 ft

1

Danger of emergency

ascent?

,2 ,2

. .

101.3252.95 1 3.95

abs gage atm

kPaP P P atm atm atm

= + = + =

2

1 1 2 2

1 2

2 1

3 . 9 54

1

P V P V

V P a tm

V P a tm

=

= =

Boyles lawIf you hold your breath on ascent, your lungvolume would increase by a factor of 4,would result in embolism and/or death.

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Example;

Change a pressure of 350 kN/m2 gauge into pressure

head of water and mercury.

Water

OHmsmxmkg

mNx

g

Ph

water

223

23

68.35/81.9/1000

/10350===

ercury

Hgmsmxmkg

mNx

g

Ph

mercury

62.2/81.9/13600

/1035023

23

===

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Transmission of Fluid Pressure

* If a fluid remaining constant in the horizontal direction,the pressure applied to a confined fluid increases thepressure throughout by the same amount. This iscalled Pascals Law.

* The transmission of fluid pressure throughout astationary fluid is the principle upon which manyhydraulic devices are based.

P1 = P2

Note : The pressure force exerted by the fluid is

always normal to the surface at the

specified points

11

222211 F

A

AFpAFpAF ===

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Pascals Law

Pressure applied to aconfined fluid

increases the pressure

throughout by the

same amount.

In picture, pistons areat same height:

Ratio A2/A1 is called

ideal mechanical

advantage

1 2 2 21 2

1 2 1 1

F F F AP P

A A F A= = =

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Example;Example;

Dimension of hydraulic jack is shown in figure below.

If a force of 100 N applied onto the jet handle,determine a maximum force F2 would be support.

Free Body Diagram of handle

100 N x 33 cm - F1 x 3 cm = 0

F1 = (100 N x 0.33 m/0.03 m) = 1100 N

100 N

F1

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Pressure at small piston (left site);

Based on transmission principle;

26

2

1

1

1m/N10x22.6

4

d

N1100

A

FP =

==

Therefore;

kN22.124

dx10x22.6APF

2

6

222===

19

P1 = P2 = 6.22 x 106

N/m2


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ExampleExample;;

Oil with a specific gravity of 0.9 is used

in a hydraulic apparatus as shown in

figure below. If a gauge indicate that a

pressure of 2.15 bar, determine thevalue of W so that the system is in

equilibrium condition.

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At x x

2

2325

'

/232658

)2)(/81.9)(/1000(9.0/1015.2

mN

msmmkgmNx

ghPP oilgaugex

=

+=

+=

AreaxessureForce Pr=

Based on transmission principle;

Px = Px' = 232658 N/m2

N66.730916

)2(4

xm/N232658 22

=

=

kg30.74507

s/m81.9

N66.730916W

2==

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Chapter 2 - Part 1 Pressure