Water hammer 1.- Input data
Speed of sound in water
Operating pressure and flowrate pop = 13.8 bar Q= %ipe data (aterial dn =
635.9
"3#*
c speed of sound !"#s$
c
+, 15+.,
"
&= ρ =
.1/,9 1,,,
c=
1+38.
%ipe di"ensions di = %ipeI"p)S:intdnsc* ,.4+
""
%ipeI"p)S;*ic'nessdnsc*
8.18
""
%ipe section area =
%a %a 'g#" "#s
bar 3.- )elerit2
a=
.- u7iliar2 ariables
s=
!& # ρ $,.5
in
s ul' "odulus and densit2 of water &= ,68+ bar ρ = 1,,, 'g#"
s=
ρ
8
Steel pipe elasticit2 "odule t = ,59394
di =
K
=
& water bul' "odulus !%a$ ρ water densit2 !'g#"$
)arbon Steel
sc* = 0=
c
!pi!$#+$
c
√(
1+
K
d ⋅
E t
s
)
a celerit2 !wae elocit2$ !"#s$ c speed of sound !"#s$ d inside pipe dia"eter !""$ s "ini"u" wall t*ic'ness !""$ & water bul' "odulus !bar$ c # !1 / !&# t$ < !d#s$ $!,.5$ a= c=
1+38.
"#s
.1/,9
%a
.1/11
%a %a
d=
,.,4
"
&= t =
=
,.,33
"
d=
,.4+
""
s=
8.18
""
a=
186.9
"#s
>luid elocit2 =
Q#
Q=
,.1466
= =
,.,33 5.+4
"3#s " "#s
ul' "odulus of water &=
.1/,9
%a
Steel elasticit2 "odulus t = .1,/,6
'p#c"?
&=
,68+
bar
t =
.,6/11
%a %a
t =
.1/,6
bar
&=
,68+
bar
t =
.,6/11
%a %a
t =
.1/,6
bar
+.- @elocit2 c*ange
4. )ritical ti"e
Initial elocit2 i =
(a7i"u" oer- pressure or under5.+4
>inal elocit2 f =
"#s
,.,,
"#s
@elocit2 c*ange ∆ = f - i
"#s
∆ =
-5.+4
"#s
pressure are obtained w*en t*e s*utoff ti"e C∆τC is less or eDual to t*e critical ti"e C τcC
τc = 5.- %ressure incre"ent due to water
0=
*a""er produced b2 a sudden s*utoff.
a= τc =
;*e pressure incre"ent can be calculated wit* Aou'os'2 elasticit2 t*eor2 b2 a Sudden S*utoff CSSC *SS = a= ∆ =
!- a < ∆ $ # g 186.9 "#s -5.+4 "#s
*= *SS =
418
"
4,.+
bar
6.- ;otal ;otal pressure de eloped b2 a sudden s*utoff
2 L ⋅
τ c
=
8.- %ressure i *a *a""er prod S*utoff CBSSC >or a s*utoff t critical ti"e t be used. h NSS =h SS ⋅
a
τ c ∆τ
*BSS presure i
<0#a 15+
"
186.9
"#s
.+
s
Sudden S*ut *SS %ressure S*utoff !Aou' τc )ritical ti"
∆τ : @aler clo
(ic*aud h NSS
=
h NSS
=
h NSS
=
a ⋅ ∆v g h NSS h NSS
2 ⋅ L ⋅ ∆v
@ale closing
g ⋅ ∆τ ∆v
g ⋅
⋅
2 ⋅ L ∆τ
a ⋅ ∆v g ⋅
∆τ =
⋅
2 ⋅ L a ⋅ ∆τ
%ressure ncre *BSS = *SS =
= h SS
2 ⋅ L =h SS ⋅ a ⋅ ∆τ 2 ⋅ L 1 =h SS ⋅ ⋅ a ∆τ
τc = ∆τ = *BSS =
with
ptotSS =
pop / *SS
pop =
13.8
bar
*SS =
4,.+
bar
ptotSS =
8+.
bar
τ c =
2 ⋅ L a
h NSS =h SS ⋅τ c ⋅ h NSS =h SS ⋅
τ c ∆τ
1
9. %ressure d s*utoff in t*e
∆τ
ptotBSS = pop = *BSS = ptotBSS =
Ee. cFc 3,.,1.,1+
cre"ent due to water uced b2 a Bot Sudden (ic*ad i"e greater t*an t*e e (ic*aud relation can
h NSS
=
2 ⋅ L ⋅ ∆v g ⋅ ∆τ
h NSS =h SS ⋅
ncre"ent in a Bon ff incre"ent in a Sudden
s'2$ e sing ti"e
τ c ∆τ
AouFos'2 hSS
=
τ c =
a ⋅ ∆v g
2 ⋅ L a
i"e 5.,
s
"ent !BSS$ *SS
bar s s bar
eloped due to ale i"e interal ∆τ G τc pop / *BSS 13.8
bar
33.+
bar
+4.
bar
t =
,59394
&=
,68+
bar s ul' "odulus and densit2 of water bar
Water hammer [2] Tyler, page 228 (a7i"u" pressure deeloped in a water pipeline wit* a pressure CpC if a ale is closed nearl2 instantl all stoped at t*e sa"e instant. %ipe data is CsteelC CdnC Csc*C C0C. ;*e water flow rate is CQC. H*at is t*e ale closes in a ti"e C ∆τCK 1. :ata SI ;2ler data in ne7 !;*is page below$ Operating pressure and flowrate p= 13.8 bar "3#s Q= ,.1464 %ipe data (aterial )arbon steel dn = 8 in sc* = 0=
+, 15+.,
@ale closing ti"e ∆τ =
5.,
" s
%ipe di"ensions di = %ipeI"p)S:intdnsc* di =
,.4+
s= s=
""
%ipe section = !pi!$#+$luid elocit2 = Q# Q= ,.1464
3.-Speed of s c
=
c speed of so & water bul' ρ water densi c &=
ρ = c=
"3#s
=
,.,33
"
=
5.+4
"#s
%ipeI"p)S;*ic'nessdnsc*
8.18
""
5.- %ressure incre"ent due to water *a""er produced b2 a sudden s*utoff.
6.- (a7i"u" pressure deeloped due to 8.- %ressure i a sudden s*utoff *a""er prod s*utoff.
;*e pressure incre"ent can be calculated
p"a7 =
pop / *
wit* Aou'os'2 elasticit2 t*eor2
pop = *= p"a7 =
13.8 4,.5
bar bar
8+.
bar
p"a7 =
11.8
h
− =
a Δv g ⋅
* pressure incre"ent "wcJ a wae elocit2 "#sJ ∆ speed ariation "#sJ final - initial ∆ =
!- a < ∆ $ # g
a= ∆ = f = i =
184.5 f - i , 5.+4
psi
4. )ritical ti"e
critical ti"e t be used. ∆ P =
2 ⋅ L ⋅
g ⋅ ∆
∆% presure in 0 pipe lengt*
g acceleration of grait2 "#s? ;*e pressure c*ange C*C is *=
>or a s*utoff t
"#s "#s "#s "#s
(a7i"u" oer- pressure or underpressure are obtained w*en t*e
∆ speed c*a g acceleratio
s*utoff ti"e C ∆τC is less or eDual to t*e critical ti"e C τcC
∆τ s*utoff ti"
τ c
=
2 ⋅ L
a
∆% = *= 0=
∆ = g= *=
-5.+4 9.81 418
"#s "#s? "wc
*=
4,.5
bar
τc = 0= a= τc =
<0#a 15+ 184.5 .+
a= ∆τ = ∆% =
" "#s s
ne7 ne7 . ;2ler data p= ,, dn = 8 sc* = +, 0= 5,,,
psi in ft
Q= τ =
8,, 5
gp" s
'= ρ =
3,,,,, 1,,,
psi 'g#"
=
3,,,,,,,
psi
:ata SI p= dn = sc* = 0=
;2ler results 13.8 8 +, 15+
Q= ,.144 τ = 5 ul' "odulus of water '= ,68+ '= ,68 %ipe elasticit2 "odule = ,68+8 =
,68+3
bar in " "3#s s bar (pa bar (pa
5.- )elerit2 a= )alculated al a= 6.- %ressure i *a""er prod *= )alculated al *= 8. %ressure d s*utoff in t*e p"a7 =
g=
9.8,665
di =
,.4+
""
s=
8.18
""
)alculated al p"a7 =
"#s?
Hater *a""er J ;2ler page 8 (a7i"u" pressure deeloped in a water pipeline wit* a pressure CpC if a ale is closed nearl2 instantl all stoped at t*e sa"e instant. %ipe data is CsteelC CdnC Csc*C C0C. ;*e water flow rate is CQC. H*at is t*e ale closes in a ti"e C:tCK 1. :ata SI ;2ler data in ne7 !;*is page below$ Operating pressure and flowrate p= 13.4895 bar Q= ,.1466556 "3#s %ipe data (aterial )arbon steel dn = 8 in sc* = +, 0= 15+ "
%ipe section = !pi!$#+$
3.-Hater spee
c speed of so & water bul' r water densi c &= r= c=
@ale closing ti"e . >luid elocit2 :t = 5 s = Q# %ipe di"ensions Q= ,.1466556 "3#s di = %ipeI"p)S:intdnsc* = ,.,386 " di = ,.4+ "" = 5.+4,6+, "#s s= %ipeI"p)S;*ic'nessdnsc* s= 8.18 ""
5.- %ressure incre"ent due to water *a""er produced b2 a sudden s*utoff. ;*e pressure incre"ent can be calculated wit* Aou'os'2 elasticit2 t*eor2
* pressure incre"ent "wcJ a wae elocit2 "#sJ : speed ariation "#sJ : = final - initial g acceleration of grait2 "#s? ;*e pressure c*ange C*C is *= !- a < : $ # g a= 184.+46+35+5 : = f - i f = , i = 5.+4 : = -5.+4 g= 9.8,665 *= 418.+ *= 4,.+5
6.- (a7i"u" pressure deeloped due to 8.- %ressure i a sudden s*utoff *a""er prod s*utoff. p"a7 = pop / * >or a s*utoff t pop = 13.8 bar critical ti"e t *= 4,.5 bar be used. p"a7 = 8+. bar p"a7 = 11.8 psi 4. )ritical ti"e
"#s "#s "#s "#s "#s "#s? "wc bar
(a7i"u" oer- pressure or underpressure are obtained w*en t*e s*utoff ti"e C:tC is less or eDual to t*e critical ti"e CtcC
tc = 0= a= tc =
<0#a 15+ 184.5 .+
:% presure i 0 pipe lengt* : speed c* g acceleratio :t s*utoff ti" :% = *= 0= a= :t = :% =
" "#s s
ne7 ne7 . ;2ler data p= dn = sc* = 0= Q= t= '= r= =
,, 8 +, 5,,, 8,, 5
psi in ft gp" s
3,,,,, psi 1,,, 'g#" 3,,,,,,, psi
:ata SI p= 13.4895 dn = 8 sc* = +, 0= 15+ Q= ,.1466556 t= 5 ul' "odulus of water '= ,68+.8 '= ,68.+8 %ipe elasticit2 "odule = ,68+8 = ,68+.8 di =
;2ler results bar in " "3#s s bar (pa bar (pa
,.4+ ""
5.- )elerit2 a= )alculated al a= 6.- %ressure i *a""er prod *= )alculated al *= 8. %ressure d s*utoff in t*e p"a7 = )alculated al
s= g=
9.8,665 "#s?
8.18 ""
p"a7 =
Ee. cFc 3,.,1.,1+
or pu"ps disc*arging into t*e line are *e "a7i"u" pressure deeloped if
und in water
+.- )elerit2
K
a
ρ
und !"#s$ "odulus !%a$ t2 !'g#"$ !& # ρ $,.5 .1/,9 1,,, 1+38.
=
c
a
K d 1 + ⋅ E t s
1483.2
=
K d 1 + ⋅ E s t
a celerit2 !wae elocit2$ !"#s$ c speed of sound !"#s$
%a
d inside pipe dia"eter !""$
'g#" "#s
s "ini"u" wall t*ic'ness !""$ & water bul' "odulus !bar$ c # !1 / !&#t$ < !d#s$ $!,.5$ a= c= &= t =
1+38. .1/,9
"#s %a
.1/11
%a
d= s= a=
,.4+ 8.18 184.5
"" "" "#s
∆ P = cre"ent due to water uced b2 a Bot sudden
∆% = *= τc =
*
bar
.+
s s
i"e greater t*an t*e
∆τ =
5.,
e (ic*aud relation can
∆% =
33.36
v
=
h⋅
2 ⋅ L
a ⋅ ∆τ
=
h⋅
τ c ∆τ
bar
9. %ressure deeloped due to ale s*utoff in t*e ti"e interal ∆τ G τc
∆τ =
5
p"a7 =
pop / *
pop =
13.8 33.+
bar bar
+4.1
bar
683.8
psi
s
h=
nge n of grait2 "#s? e interal !s$
*= p"a7 = p"a7 =
< * < 0 # !a < ∆τ$ 4,.5 bar 15+., "
2
a⋅ a ⋅ ∆v g
∆ P =
∆ P =
cre"ent !"wc$ !"$
h⋅
∆ P =
a⋅∆ g ∆v
g
⋅
2 ⋅ L ⋅ g ⋅
∆% = 0= ∆ = ∆τ =
184.5 5., 33.+
184.9 lue
∆% = ∆% =
"#s s bar
"#s
184.5 "#s cre"ent due to water ced b2 a sudden s*utoff. 4,.5 bar lue 4,.5 bar eloped due to ale i"e interal ∆τ G τc ++.4
ul' "odulus of water '= ,,,
%ipe elasticit2 "odule = ,68+8 bar
bar Note 1
Bote 1.
lue
;2ler error +4.1
bar
bar
+8+ / ,, = 68+ !psi$ = +4.16 !bar$
Carlos J. Cruz. Rev.15.01.2012
or pu"ps disc*arging into t*e line are *e "a7i"u" pressure deeloped if
d of sound
+.- )elerit2
und !"#s$ "odulus !%a$ 2 !'g#"$ !& # r $,.5 .,4/,,9 %a 1,,, 'g#" 1+38.,3 "#s
a celerit2 !wae elocit2$ !"#s$ c speed of sound !"#s$ d inside pipe dia"eter !""$ s "ini"u" wall t*ic'ness !""$ & water bul' "odulus !bar$
cre"ent due to water uced b2 a Bot sudden i"e greater t*an t*e e (ic*aud relation can
a= c= &= t = d= s= a=
c # !1 / !&#t$ < !d#s$ $!,.5$ 1+38.,3,+5 "#s ,68+8,,, %a .,68+/,11 %a ,.4+ "" 8.18 "" 184.5 "#s
:% = *= tc = :t = :% =
*
bar s s bar
9. %ressure deeloped due to ale s*utoff in t*e ti"e interal :t G tc :t = 5 s cre"ent !"wc$ !"$ nge n of grait2 "#s? e interal !s$
p"a7 = pop = *= p"a7 = p"a7 =
pop / * 13.4895 33.3544,4 +4.1+44 683.81344+
bar bar bar psi
< * < 0 # !a < :t$ 4,.+5 bar 15+.,, " 184.+8 "#s 5.,, s 33.+ bar
184.9 "#s lue 184.+46+ "#s cre"ent due to water ced b2 a sudden s*utoff. 4,.5 bar lue 4,.+51535 bar eloped due to ale i"e interal :t G tc ++.64 bar lue
ul' "odulus of water '= ,,, bar %ipe elasticit2 "odule = ,68+8 bar Bote 1. ;2ler error
+4.1+4 bar
+8+ / ,, = 68+ !psi$ = +4.16 !bar$
)arlos A. )ruL. Ee.15.,1.,1
a=
⋅ L
∆ P =
∆τ ∆% =
⋅
2 ⋅ L a ⋅ ∆τ
⋅ L
τ ∆v
τ < 0 < ∆ # !g < ∆τ$ 15+., "#s 5.+4 s 5., s
2 ⋅ L ⋅ ∆v g ⋅ ∆τ * < < 0 # !a < ∆τ$
*=
418.+
"
0= a=
15+., 184.5
" "#s
∆τ =
5.,
∆% = ∆% =
3+,. 33.+
s " bar
√(
1+
3+,. 33.+
" bar
a=
c
√(
1+
K d ⋅
E t s
)
Pehmco water-hammer [3], page 7.21 1. :ata Operating pressure and flowrate pop = 15 "wc pop = Q= Q= %ipe data (aterial dn =
"
=
M@0N
"
,.,,
"3#s
3. (aterial data ul' "odulus and densit2 of water '= ,,, bar
in bar
ρ = 1,,, %ipe elasticit2 "odule p = 48+5
0= 4, " @ale closing ti"e ∆τ = ;c . %ipe di"ensions and section de = %ipeI"pP:%%8,:e7t:n M@0N
""
s = %ipeI"pP:%%8,;*ic'ness:n%B
s= di =
M@0N
""
di =
M@0N
""
4.- %ressure incre"ent due to water *a""er produced b2 a sudden s*utoff.
48+.53 +. >luid elocit2 =
'g#" bar (%a
Q=
,.,,,
"3#s
= =
M@0N M@0N
" "#s
8.- (a7i"u" pressure deeloped due to a sudden s*utoff !Aou'os'2$ pop / *Aou'
pop =
1.5
bar
− a ⋅ ∆v
*Aou' =
M@0N
bar
g
%"a7Aou' =
M@0N
bar
calculated wit* Aou'os'2 elasticit2 t*eor2
*Aou' pressure incre"ent Aou'os'2 a wae elocit2 "#sJ ∆ speed ariation "#sJ final - initial ∆ = g acceleration of grait2 "#s? ;*e pressure c*ange C*C is *Aou' = !- a < ∆ $ # g
M@0N 9. )ritical ti"e (a7i"u" oer- pressure or underpressures are obtained w*en t*e
"
Q#
%"a7Aou' =
>or t*is case t*e pressure incre"ent can be
h Jou k =
M@0N
bar l#s
1,
de =
d=
1.+4
P:% %8,
%B
%ipe section = !pi!$#+$
s*utoff ti"e C ∆τC is less or eDual to t*e critical ti"e C τcC
a= ∆ = f = i =
M@0N f - i , M@0N
"#s "#s "#s "#s
∆ = g= *Aou' =
M@0N 9.81
"#s "#s?
τc =
M@0N
"wc
a=
τ c = 0=
2 ⋅ L a <0#a 4, M@0N
" "#s
*Aou' =
M@0N
bar
τc =
ppro7i"ate bul' "odulus
.,/,9
&=
,,,
%a
9.8,665
=
.,3/11
=
.,3/,6
bar
ir 1.+R1,5 %a !adiabatic bul' "odulus$ ir 1.,1R1,5 %a !constant te"perature bul' "odulus$
g=
s
Steel elasticit2 "odulus = .95/,4
Hater .R1,9 %a !alue increases a t *ig*er pressures$ &=
M@0N
"#s?
Hater bul* "odulus Hater &= .,6/,+ &= ./,9 &= ,,,
Ee. cFc 3,.,1.,1+
5.-Speed of sound in water c
K
=
d inside pipe dia"eter !""$
ρ
c speed of sound !"#s$ & water bul' "odulus !%a$ ρ water densit2 !'g#"$ !& # ρ $,.5 c &= ρ =
./,9 1,,,
c= 6.- )elerit2
a
=
a celerit2 !wae elocit2$ !"#s$ c speed of sound !"#s$
1+83.
c
K d 1 + E p ⋅ s
%a 'g#" "#s
s "ini"u" wall t*ic'ness !""$ & water bul' "odulus !bar$ c # !1 / !&# p$ < !d#s$ $!,.5$ a= c= &= p =
1+83. .,/,9
"#s %a
d=
4.8/,8 M@0N
%a ""
s= a=
M@0N M@0N
"" "#s
psi %a bar
'p#c"? %a bar
P:% elasticit2 "odulus %) p = 8,,, p =
4.8/,8
p =
48+5
'p#c"? %a bar
Slurry hammer [8] :ata Operating pressure and flowrate
Hater "wc
L
./,9
bar l#s
ρL =
1,,,
Q=
1.+4
Q=
,.,,
"3#s
pop =
15
pop =
@ale closing ti"e
∆τ = %ipe data (aterial dn =
,.,
P:% %8,
%B 0=
1, 4,
in bar "
P
4.8/,8
%a
)v =
,.+
-
ρs =
18,,
'g#"
ρL =
1,,,
'g#"
Slurr2
S
1.14/11 !)opper$
%a
)elerit2 of slurries
Slurr2 celerit2 calculation ! ! ! !)#ρs$ / !! a=
D. , 8J page 3+,
C 1 − C + ρ ρ = E ⋅ C 1 − C + v
am 2
v
s
L
L
v
E S
v
⋅ E ⋅ + E D E ⋅ e L
L
P
)v =
,.+
ρs =
18,,
ρL =
1,,,
P
4.85/,8
L
./,9
am2
)elerit2 of an *eterog.
S
1./11
)v
Solids concentration ol.
:
M@0N
ρs
Solids densit2
e
M@0N
ρL
Hater densit2
a=
M@0N
P
lastic "odulus pipe "at.
L
lastic "odulus of liDuid
S
lastic "odulus of solids %ipe dia"eter
:
e
%ipe wall t*ic'ness
%ressure incre"ent for *eterogeneous slur22 due to suddenl2 ale s*ut-off In engineering practice t*e initial *a""er pressure can usuall2 be used to substitute t*e slurr2 *a""er pressure D. 33 page 3++
P =
am ⋅ um 0 ⋅ ρ L ⋅ ρ S
(1 − C V ) ⋅ ρ S + C V ⋅ ρ L
%
slurr2 *a""er pressure
%aJ
am
celerit2 of "i7ture !slurr2$
"#sJ
um0
elocit2 of"i7ture !slurrr2$ before ale closure
"#sJ
ρL
liDuid densit2
'g#"J
ρS
solids densit2
'g#"J
)V
@olu"e concentration
-J
%=
a" < u", < ρ0 < ρS # ! !1 - ) @$ < ρS / )@ < ρ0 $
am =
M@0N
"#s
um0 =
M@0N
"#s
ρL =
1,,,
ρS =
18,,
)V =
,.+ M@0N M@0N
%= %=
%a bar
(a7i"u" pressure deeloped due to a sudden s*utoff %"a7Aou' = pop / % %op = %=
1.+4 M@0N
bar bar
%"a7Aou' =
M@0N
bar
Ee. cFc 3,.,1.,1+
%ipe di"ensions and section %a
de =
'g#"
de =
%ipeI"pP:%%8,:e7t:n
M@0N
""
s = %ipeI"pP:%%8,;*ic'ness:n%B
s= di =
s
di =
M@0N
""
%ipeI"pP:%%8,:int:n%B
=
M@0N !pi!$#+$
""
d= =
M@0N M@0N
>luid elocit2 = Q=
Q# ,.,,,
=
M@0N
"
=
M@0N
"#s
" "
"3#s
-)$ # !ρ0$$ $<0 $ # !1 - ) / 0#s < ) / 0 < : # !% < e$$ $,.5
'g#" 'g#" %a
%ipe P:%
%a
0iDuid Hater
%a
Solids copper
"" "" "#s
9J
c
a=
1+ a=
k E
⋅
( DR − 2 )
c # ! 1 / !'#$ < !:E-$ $,.5
a wae elocit2 ) speed of sound ' water bul' "odulus pipe elasticit2 "odulus :E di"ension Eatio c= '=
+66, 3,,,,,
fps psi
%@) 1+5+ =
+,,,,,
psi
% 3+,8 =
115,,,
psi
a$ ∆ = (aterial :E = )elerit2 a= c= &= = :E = a=
fps %@) 1+5+ 5
c # ! 1 / !'#$ < !:E-$ $,.5
+66, 3,,,,, +,,,,, 5 1,91
fps psi psi fps
Surge pressure a < ∆@ # !.31
b$ ∆ = (aterial :E = )elerit2 a= c= &= = :E = a=
% 3+,8 11
fps
c # ! 1 / !'#$ < !:E-$ $,.5
+66, 3,,,,, 115,,, 11 9+
fps psi psi fps
Surge pressure a < ∆@ # !.31
;e*"co
C + 1 − C ρ ρ E ⋅ C 1 − C + v
am 2
=
v
s
L
L
v
E S
v
⋅ E E ⋅ D + E ⋅ e L
L
P
am2
)elerit2 of an *eterogeneous fluid
)v
Solids concentration b2 olu"e
ρs
Solids densit2
ρL
Hater densit2
P
lastic "oduli of pipe "aterial
L
lastic "odulus of liDuid
S
lastic "odulus of solids
λ T
tension stress on t*e pipe wall %ipe dia"eter %ipe wall t*ic'ness
: e D. , 8J page 3+,
8J
*ttp##tec*.scic*ina.co"8,8#scie#fileup#%:>#982e,334.pdf
%ressure incre"ent for *eterogeneous slur22 due to suddenl2 ale s*ut-off
P =
am ⋅ um 0 ⋅ ρ L ⋅ ρ S
(1 − C V ) ⋅ ρ S + C V ⋅ ρ L
P =
a ⋅ v ⋅ ρ w ⋅ ρ s
(1 − C v ) ⋅ ρ s + C v ⋅ ρ w
1,J *ttp##www.plasticpipe.org#pdf#c*apter,6.pdf :esign of % %iping S2ste"s )*apter 6 page 161
;e"porar2 surge pressures % pipes can safel2 tolerate t*e co""onl2 obsered "a 7i"u" pea' te"porar2 surge pressure of twice t*e stead2 state condition.
Eepetead c2clel loads 0ong-ter" strengt* of % pipes is not adersel2 affected b2 repeated c2clic load. ;*us % pipes are er2 fatigue resistant.
Occasional surge pressures
Eecurring surge pressures
Begatie pressures
:esign principles
Occasional surge pressures
P t ot= P sustained+ P surge P t ot ≤ 2 ⋅ PRtemerature _ co mp en s at ed Eecurring surge pressures
P tot
≤ 1.5 ⋅ PRtemerature _compe nsated
J
;2ler %ower generation calculations reference ;2ler . Pic's. %.. ditor ;*e (craw-Pill ngineering reference guide series 1985 Hater-*a""er in liDuid pipelines. %age 8
3J
%roductos %)) ;e*"co S.. 7a"ple page 4.1
+J
Peat ans "ass transfer nt*on2 >. (ills Irwin 1995
5J
Peat transfer A. %. Pol"an (craw-Pill 1989
6J
Water Hammer
*ttp##issuu.co"#roc'oic"#docs#catalogofinalte*"co
by Robert Pelikan April 1, 2005
4J
8J
*ttp##tec*.scic*ina.co"8,8#scie#fileup#%:>#982e,334.pdf
9J *ttp##www.plasticengineeredproducts.co"#"anufacturers#unibell#pubs#uni-tr-4.pdf
1,J
*ttp##www.plasticpipe.org#pdf#c*apter,6.pdf :esign of % %iping S2ste"s
