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Dr H Md Azamathulla

Lecturer,REDAC, USMhttp://redac.eng.usm.my/eah416/

EAH 221

july 28th

FLUID MECHANICSfor

CIVIL Engineers

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The expression is p1+m

(0.25m)

Here the term Ym(0.25)m is change in pressurebetween two points 1 and 2 due to change inelevation

Ym - specific weight of mercury (right leg ofmanometer) Expression for the Pr.. At point 3? P1+Ym(0.25m) Because the points 2 & 3 are on the sameelevation (same level) in the same fluid at rest. So pr.. Are equal.

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Now we will write expression for Pr.. At

point 4. P1+Ym(0.25m)-Ym(0.40m) See here sign decrease in pr.. Betweenpoints 3 & 4, so last term subtracted from

previous expression.

Now Pr.. at Point A? pA=P1+Ym(0.25m)-Ym(0.40m)

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Sg=13.54 Yw=9.81 KN/m3 Ym=Sg*g=13.54*9.81 KN/m3=132.8 KN/m3 p1=0=patm=0Pa

pA= 0+132.8*0.25-9.81*0.40

pA=29.28 kN/m2=29.28 Kpa

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Barometers

A barometer is a device formeasuring atmosphericpressure.

h=760 mm of mercury why not water or ethanol? is the vacuum on top reallyempty space?

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Manometers

A manometer is a device for measuringfluid pressure consisting of a bent tubecontaining one or more liquids of differentdensities.

A known pressure (which may be

atmospheric) is applied to one end of the

manometer tube and the unknown

pressure (to be determined) is applied tothe other end.

Differential pressure manometer measures onlythe difference between the two pressures.

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Manometer types

Simple U - tube manometer Inverted U - tube manometer U - tube with one leg enlarged Two fluid U - tube manometer Inclined U - tube manometer

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Simple U -

tube manometer

( )hagppX ++= 1

ghgapp mX ++= 2'

'XXpp =

( ) hgpp m = 21

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Inverted U -

tube manometer

( ) hgpp m= 21

( )hagppX += 1

ghgapp mX = 2'

'XXpp =

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U - tube with one leg enlarged

( )hgpp

m =

21

used for moreaccurate readings

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Two fluid U-tube manometer

used for more

accurate readings ofsmall pressure

differences

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Inclined U-tube manometer

used for more accurate readings of

small pressure differences

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Pressure measurement categories

Gravity based : barometer, manometer, dead weightpiston

Elastic deformation: Bourdon tube (metal & quartz),

strain gauge, optical beam displacement

Gas behavior : Gas compression (McLeod gage),thermal conductance (Pirani

gae), Moducular

impact

(Knudsen gage), ionization, air piston, thermalconductivity

Electric output: resistance (Bridgman wire gage),

diffused strain gage, piezoelectric, Linear variabledifferential transformer (LVDT)

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Bourdon tube device foe mechanical measurement

of high pressures

When pressurized internally , a curved tube with flattene

cross

Section will deflect outward.

The deflection can be measured by a linkageattached to a calibrated dial pointer,

An interesting variation of the fused quartz,

force-balanced bourdon tube

Whose spiral tube deflection is sensed optically andreturned to a zero reference state by a magnetic elemen

whose out put is proportional to the fluid pressure

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Dr H Md Azamathulla

Lecturer,REDAC, USMhttp://redac.eng.usm.my/eah416/

July 28th

FLUID MECHANICSfor

CIVIL Engineers

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Question: Pressure gage B is to measure the pressure at point A

in water flow.

If the Pressure at B is 87KPa , estimate the pressure at A in KPa.?

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If PB = 87 K Pa, PA =? water=9790 N/m3 ; Y mercury

=133100 N/m3

Y oil = 8720 N/m3

Proceed from A to B , down then up jumpingacross at the left mercury .. PA +9790(0.05)-133100(0.07)-8720(0.06)=87000 PA = 96.4 KPa

Question: Pressure gage B is to measure the pressure at point A

in water flow.

If the Pressure at B is 87KPa , estimate the pressure at A in KPa.?

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Hydrostatic forces on Plane Surfaces

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Figure shows, a plane panel of arbitraryshape completely submerged in a liquid.

The panel plane makes an arbitrary angle with horizontal free surface, so thatdepth varies over the plane surface.

If h

is depth to any element area dA of

the plate.

The pressure is hpp a +=

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To derive formulas involving the plateshape, establish an xy coordinate systemin the plane of the plate with the origin anits centroid, plus a dummy co-ordinate down from the surface in the plane of theplate.

Then the total hydrostatic force on one

side of the plate is given by

+=+== hdAApdAhppdAF aa )(

The remaining integral is evaluated by noticing

from figure that h= sinBy definition, the centroidal slant distance from the

surface to the plate is = dAACG

1

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Therefore, since

is constant along the plate,

above equation becomesAApdAApF

CGaa sinsin +=+=

Finally, unravel this is by noticing that CG Sin =hCG,the depth straight down from the surface to the platecentroid.

Thus

ApAhpaAhApFCGCGCGa

=+=+= )(

The force on one side of any plane submeged surface in a uniform

fluid

equals the pressure at the plate centroid times the plate area,

independent of the

Shape of the plate or the angle

at which slanted.

AIggCP +=

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HOME WORK

The gate shown in figure is 5 ftwide, is hinged at point B, rest

against a smooth wall at point A.

Compute (1) the force on the

gate due to sea water pressure,(2) the horizontal force P

exerted by the wall at point A,

and (3) the reactions at the

hinge B

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Free body diagram of GATE