example 1 a u-tube manometer similar to that shown in below is used to measure the gauge pressure of...
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![Page 1: Example 1 A U-tube manometer similar to that shown in below is used to measure the gauge pressure of water (mass density ρ = 1000 kg /m 3 ). If the density](https://reader035.vdocuments.us/reader035/viewer/2022072114/56649dbe5503460f94ab1403/html5/thumbnails/1.jpg)
SIMPLE U-TUBE MANOMETER
Example 1A U-tube manometer similar to that shown in below is used to measure the gauge pressure of water (mass density ρ = 1000 kg /m3). If the density of mercury is 13.6 × 103kg /m3, what will be the gauge pressure at A if h1 = 0.45 m and D is 0.7 m above BC.
Mercury, Hg
Water
It is a manometer that has a fluid reservoir and the end open to atmosphere. It is common to have two different type of fluids within the manometer, one fluid in the reservoir, and another type of fluid within the U.
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SOLUTION :Considering
the pressure at left-hand limb;PB = Pressure, at A + Pressure due to depth, of fluid P
33 /106.13 mkgQ
33 /100.1 mkgP
mh 45.01
mh 7.02
= 1hp PA
= 1ghp PA
the pressure at right-hand limb;
Cp = Pressure Dp at D + Pressure due to depth 2h of liquid Q
Cp = 20 hQ
= 20 ghQ
Since CB pp
21 ghghp QPA
12 ghghp PQA
45.081.9100.17.081.9106.13 33 2/7.88976 mN
23 /1097.88 mN
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EXAMPLE 2.5
A U-tube manometer similar to that shown below is used to measure the gauge pressure of a fluid P of density ρ = 1000 kg/m3. If the density of the liquid Q is 13.6 × 103kg/m3, what will be the gauge pressure at A if h1 = 0.15 m and h2 = 0.25 m above BC. Take into consideration patm = 101.3 kN/m2.
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SOLUTIONPutting ,
ρQ = 13.6 310 ρP = 1000 kg/m3
h1 = 0.15 m h2 = 0.25 m
pressure at left-hand limb;
Bp = Pressure Ap at A + Pressure due to depth 1h of fluid P + Pressure due to
depth 2h of liquid Q
= 21 hhp QPA
= 21 ghghp QPA
pressure at right-hand limb;
Cp = Pressure Dp at D
Dp = Atmospheric pressure
Cp = atmp
CB pp
DQPA pghghp 21
21 ghghpp QPBA
25.081.9100015.081.91036.133.101
2/1.70835 mN2/84.70 mkN
,
Since
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ACTIVITY
The U-tube manometer measures the pressure of water at A which is below the atmospheric pressure. If the specific weight of mercury is 13.6 times that of water and the atmospheric pressure is 101.3 kN/m2, find what is the absolute pressure at A when h1 = 10 cm, h2 = 25 cm and the specific weight of water is 9.81×103N/m3.
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SOLUTION
21 hhpp mercuryairAB
2/3.101 mkNpp atmC
CB pp
atmmercuryairA phhp 21
21 hhpp mercuryairatmA
25.06.1398101.09810103.101 3 Ap
2/66965 mN
2/965.66 mkN
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SELF ASSESSMENT
2.3 Assuming that the atmospheric pressure is 101.3 kN/m2 find the absolute pressure at A in the figure below when
a) Fluid P is water, fluid Q is mercury ω = 13.6, a = 1 m and h = 0.4 m.
b) Fluid P is oil ω = 0.82, fluid Q is brine ω = 1.10, a = 20 cm and h = 55 cm.