fluid , civil

7/24/2019 Fluid , civil

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FLUID MECHANICSChapter 3: FLUID STATICSDr. Randa Hatamleh

Fall 2014


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Pressure Measurements

1. Barometer: measures atmospheric

Pressure = +

Pv = 2.4 x 10-6atm at 20 0C

The Aneroid Barometer

Has some advantages over a mercurybarometer because it is smaller and

allows data recording over time.


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Bourdon-Tube Gage

Low cost, reliable, easy to install,

and available in many different pressure ranges.

Accuracy of the gage can be lower than otherinstruments; and the gage can be damaged by excessive

pressure

Piezometer

Itis a vertical tube in which a liquid risesin response to a positive gage pressure.

simplicity, direct measurement, and accuracy.

Piezometer is limited to low pressures


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Example

What is the maximum gauge pressure of water that can

be measured by a Piezometer of height 1.5m? And if the

liquid had a relative density of 0.85 what would the

maximum measurable gauge pressure?


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Pressure Measurements Pressure

Measurements Manometer: is a device for measuring pressure by

raising or lowering a column of liquid. Manometers

use the relationship between pressure and head to

measure pressure


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The Piezometer tube Manometer

The simplest manometer is a tube, open at the top, which

is attached to the top of a vessel containing liquid at a

pressure (higher than atmospheric) to be measured.

This simple device is known as a Piezometer tube.

As the tube is open to the atmosphere the

pressure measured is relative to

atmosphereic so is gauge pressure


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Example

A manometer connected to a pipe indicates a negative

gauge pressure of 50mm of mercury. What is the absolute

pressure in the pipe in Newtons per square metre is theatmospheric pressure is 1 bar?

[93.3 kN/m2]


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The U Tube Manometer

U-Tube enables the pressure of both liquids and gases

to be measured U is connected as shown and filled with

manometric fluid.

Important points:

1. The manometric fluid density should be greater than of

the fluid measured. man>

2. The two fluids should not be

able to mix they mustbe immiscible.


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Pressure in a continuous static fluid is the same at any

horizontal level.

pressure at B = pressure at CpB= pC

For the left hand arm

pressure at B = pressure at A + pressure of height of liquid

being measured

pB= pA+ gh1

For the right hand arm

pressure at C = pressure at D + pressure of height ofmanometric liquid

pC= patmospheric+ mangh2


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We are measuring gauge pressure we can subtractpatmosphericgiving

pB= pCpA= man gh2- gh1

What if the fluid is a gas?

Nothing changes.

The manometer work exactly the same.

BUT:As the manometric fluid is liquid (usually mercury , oilor water) And Liquid density is much greater than gas,

man>> Ugh1 can be neglected,

and the gauge pressure given by pA= mangh2


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Example

Using a u-tube manometer to measure gauge pressure of

fluid density p = 700 kg/m3 , and the manometric fluid is

mercury, with a relative density of 13.6. What is the gauge

pressure if:

a) h1= 0.4m and h2= 0.9m?

b) h1stayed the same but h2= -0.1m?


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Manometer


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EXAMPLE 3.6

Water at 10C is the fluid in the pipe and mercury is the

manometer fluid. If the deflection h is 60 cm and L is 180

cm, what is the gage pressure at the center of the

pipe?


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EXAMPLE 3.6


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EXAMPLE 3.7


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Pressure difference measurement Using

a U-Tube Manometer. The U-tube manometer can be connected at both ends

to measure pressure difference

between these two points

pressure at C = pressure at D

pC= pD

pC= pA+ g ha

pD= pB+ g (hb+ h) + mang h


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pA + g ha= pB+ g (hb + h) + mang h

Giving the pressure difference

pA- pB= g (hb- ha) + (man- )g h

Again if the fluid is a gas man>> , then the terms involving

can be neglected,

pA- pB= mang h


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Example In the figure below two pipes containing the same fluid of

density = 990 kg/m3 are connected using a u-tubemanometer. What is the pressure between the two pipes if

the manometer contains fluid of relative density 13.6?


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EXAMPLE 3.8

A differential mercury manometer is connected to two pressure taps in

an inclined pipe as shown in Fig. 3.12. Water at 50F is flowingthrough the pipe. The deflection of mercury in the manometer is 1

inch. Find the change in piezometric pressure and piezometric head

between points 1 and 2.


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Example

a tank of oil with one side open to the atmosphere and the

other side sealed with air above the oil. The oil has a

specific gravity of 0.90.

Calculate the gage pressure at

points A, B, C, D, E, and F and

the air pressure in the right side

of the tank.


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Example

Find the location of the surface in the manometer The

distance h is the height of the liquid in the manomoter

above the heavier liquid in the tank.


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Example

Specific weight of fluid

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