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If ρ1=ρ2 a=b
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Two pipes containingthe same fluid of densityρ = 1000 kg m-3 areconnected using adifferential manometer.
What is the pressure between the two pipes ifthe manometer containsfluid of relatie density13.!"
2
EXAMPLE 2.5 - DIFFERENTIAL MANOMETER
Fluid density, ρ
C
Manometric fluid density, ρman
h = 0.5 m
h a= 1.5m
hb= 0.75 m
E
A
B
D
Fluid density, ρ
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PA- PB = ρ1g(b-a) + gh(ρman - ρ1)
= 9.81x103(0.75-1.5)+ 0.5(13.6 x 9.81x103 – 9.81 x 103)
= 9.81 x 103 (-0.75+0.5 x 12.6)
= 54.4 x 103 N/m2
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A dierential an!eter "!ntainin# er"$r% i& "!nne"ted t!
t'! (i(e& A and ). T*e (i(e A "!ntain& a li+$id !f &(e"i,"#rait% 1. and t*e !t*er (i(e )/ "!ntain& !il !f &(e"i,"#rait% 0.5. If t*e (re&&$re bet'een t*e t'! (i(e& i& 1.2 105 N32/ deterine t*e dierent in er"$r% leel&/ .
EXAMPLE 2.4 - DIFFERENTIAL MANOMETER
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In h! "#g$%!&
P' = PA + ρ(#)$#*g (5) + ρ+gg(x)
P', = PB + ρ-#(g(1.5 + x)
B$ P' = P', (am! h%#'na !!)
h$ PA + ρ(#)$#*g (5) + ρ+gg(x) = PB + ρ-#(g(1.5 + x)
#!n PA - PB = 1.2 105 N32
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Used for measuring pressure differences betweenpoints along a pipe.
Differential Manometer
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• The #$#-tube manometer has the disadantage that the change in height of
the li%uid in both sides must be read. This can be aoided by making thediameter of one side ery large compared to the other. &n this case the side
with the large area moes ery little when the small area side moe
considerably more.
8
2.4. ADAN6E7 TO T8E INERTEDDIFFERENTIAL MANOMETER
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• 'ssume the manometer is arranged as aboe to measure the pressure
difference of a gas of (negligible density) and that pressure difference is
p1-p*. &f the datum line indicates the leel of the manometric fluid when
the pressure difference is +ero and the height differences when pressure is
applied is as shown, the olume of li%uid transferred from the left side to
the right = +* (d* / )
• 'nd the fall in leel of the left side is
( ) *
*
*
*
*
1
1/d+=0/12)0/d2(+=
sideleftof area
moedolume=+
9
2.4. ADAN6E7 TO T8E 9:;-T:)EMANOMETER
2 4 6 7 O
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• We know from the theory of the #$# tube manometer that the height
different in the two columns gies the pressure difference so,
• if is ery much larger than d then (d/)* is ery small so p1 p* = ρg+*
• 4o only one reading need to be taken to measure the pressure difference.
( )( )
p - p g(+ + )
g + d / +
g+ d /
1 2 1 2
2
2 2
2
21
= ρ +
= ρ +
= ρ +
10
2.4. ADAN6E7 TO T8E 9:;-T:)EMANOMETER
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<$i 1 6MT 5>
T*e left le# !f a :-t$be er"$r% an!eter i& "!nne"ted t! a (i(e line"!ne%in# 'ater/ t*e leel !f er"$r% ?&(e"i," #rait% [email protected] in t*e le#bein# 40 " bel!' t*e "entre !f (i(e line and t*e ri#*t le# i& !(en t!at!&(*ere. T*e leel !f er"$r% in t*e ri#*t le# i& 5 " ab!e t*at int*e left le# and t*e &(a"e ab!e er"$r% in t*e ri#*t le# "!ntain&)enene ?&(e"i," #rait% 0. t! a *ei#*t !f @0 ". Find t*e (re&&$re
in t*e (i(e.
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In ,#$re/ B$id A i& 'ater and B$id ) i& er"$r%. C*at 'ill be
t*e dieren"e in leel *1 if t*e (re&&$re at X i& 10 N32
and *2 = 1.5 .
<:I 1 6MT 5> Mar"* 201