Chapter 2 Missing slides.pptx

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If ρ1=ρ2 a=b



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



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



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



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





Used for measuring pressure differences betweenpoints along a pipe.

Differential Manometer



• 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



• '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



• 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











<$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.



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

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Chapter 2 Missing slides.pptx