FLUID STATIC3/1

FLUID STATIC

OBJECTIVESGeneral Objective :To know, understand and apply pressure measurement using piezometer, barometer, bourdon gauge and manometers. Specific Objective :At the end of the unit you should be able to : explain the concept of pressure measurement using piezometer. solve problems related to piezometer. explain the concept of pressure measurement using barometer. solve problems related to barometer. sketch, label and explain the working principle of bourdon gauge explain the concept of pressure measurement using manometers. solve problems related to the use of simple manometer. solve problems related to the use of differential manometer. U!IT 3FLUID STATIC3/ solve problems related to the use ofinverted differentialmanometer.

3"#$%ESSU%E &EASU%E&E!T3"' $IE(O&ETE% ! "ressure Tube # $igure%.1: "iezometer inside a pipeA "iezometer is used for measuring pressure inside a vessel or pipe in whichli&uid is there. A tube may be attached to the walls of the container !or pipe# inwhich the li&uid resides so that li&uid can rise in the tube. 'y determining theheight to which li&uid rises and using the relation p1 ( gh, gauge pressure ofthe li&uid can be determined. )t is important that the opening of the device is tobe tangential to any fluid motion, otherwise an erroneous reading will result. Although the "iezometer tube is a very simple and accurate pressure measuringdevice,it has several disadvantages. )t is only suitable if the pressure in thecontainer !pipe or vessel# is greater than the atmospheric pressure !otherwiseair wouldbesucked into system#,andthe pressure to bemeasured mustberelatively small so that the re&uired height of column is reasonable. Also, thefluid in the container in which the pressure is to be measured must be a li&uidrather than a gas.INPUTINPUTFLUID STATIC3/% E)a*ple 3"'A pressure tube is used to measure the pressure of oil ! mass density,%* +,- m kg # in a pipeline. )f the oil rises to a height of 1. above the centre of the pipe, what is the gauge pressure in

* m Nat that point. !gravity ( /.01 m/s2#S+l,ti+n t+ E)a*ple 3"'"utting %* +,- m kg = andm h. 1 =1e know that,gh p =2o, . 1 01 . / +,- = p

* 33 . 4 m kN p =FLUID STATIC3/, 3"- BA%O&ETE%S $igure %.:5ercury 'arometerA 'arometer is a device used for measuring atmospheric pressure. Asimple'arometer consistsof atubeof morethan%-inch!4+-mm# longinserted into an open container of mercury with a closed and evacuated end atthe top and open tube end at the bottom and with mercury extending from thecontainer up into the tube. 2trictly, the space above the li&uid cannot be a truevacuum. )t contains mercury vapour at its saturated vapour pressure, but this isextremely small at room temperatures !e.g. -.14% Pa at -oC#. The atmosphericpressure is calculated from the relationpatm(ghwhereis the density offluid in the barometer. There are two types of 'arometer6 5ercury 'arometerand Aneroid 'arometer.FLUID STATIC3/3 E)a*ple 3"-7escribe with a sketch, one method of measuring atmospheric pressure.S+l,ti+n t+ E)a*ple 3"- 8acuum !zero pressure#5ercury sp.wg, 9mp p ApA$igure %.%A 5ercury 'arometer in its simplest form consists of a glass tube, about 1mlong and closed at one end, which is completely filled with mercury and inverted in abowl of mercury!$igure %.%#. Avacuumforms at the topof the tube andtheatmosphericpressureactingonthesurfaceofthemercuryinthebowl supportsacolumn of mercury in the tube height, h.E)a*ple 3"31hat istheatmosphericpressureinN/m2if thelevel of mercuryina'arometer!$igure %.%# tube is 4+- mmabove the level of the mercury in the bowl. :iven thespecific gravity of mercury is 1%.+ and specific weight of water is % %* 1- 01 . / m N . S+l,ti+n t+ E)a*ple 3"3)f A is a point in the tube at the same level as the free surface outside, the pressure pAat A is e&ual to the atmospheric pressure p at the surface because, if the fluid is at rest,pressure is the same at all points at the same level.hFLUID STATIC3/+ The column of mercury in the tube is in e&uilibrium under the action of the force dueto pA acting upwards and its weight acting downwards6 there is no pressure on the topof the column as there is a vacuum at the top of the tube.2o,A column of area pA water of weight specific mercury of weight specific = ah A pm A = or h pm A = "utting h ( 4+- mm ( -.4+ mm1hile water of weight specific mercury of gravity specificm =

%* 1- 01 . / + . 1% m Nm = $rom h pm A = 2o

%* 4+ . - 1- 01 . / + . 1% m N pA =

* % . 1-1 m kN =FLUID STATIC3/4 3"3 BOU%DO! GAUGE $igure %., 'ourdon :auge is used to measure pressure differences that are more than 1. bar.The pressure to be measured is applied to a curved tube, oval in cross section. "ressureapplied to the tube tends to cause the tube to straighten out, and the deflection of theend of the tube is communicated through a system of levers to a recording needle. Thisgauge is widely used for steam and compressed gases. The pressure indicated is thedifference between that communicated by the systemto the external !ambient#pressure, and is usually referred to as the gauge pressure. The pressure sensing element is a tube of oval cross;section bent to acircular shape.