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Transcript of Water Hamme
7/21/2019 Water Hamme
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17 Parcel , ITCC Project
KB-01,02
Water hammer
Design criteria :
H = 31.0 m Pump head
28.0 m Static head
L = 500.0 m Pipeline length
D = 250 mm Pipeline diameter = 0.250 m
t = 9.3 mm Pipe wall thickness = 0.0093 m
403.9 Total flow ( pump delivery capacity ) = 0.11220
Pipe material : 3289.25
1- water velocity in the pipe :
S = S = 3.14 x 0.250 x 0.250
0.04909--------------------- ------------------------------------------- =4 4
V =
V =0.11220
2.285!9 m " s--------- ---------------------- =.
H 0 =
# = m3 " h m3 " sec
# = V x S
3.14 x D2
m2
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2- Wave velocity :
a =1
-----------------------------------------------------
1
$D
)
a : Wave velocity ( m sec )
1!!! Water density
2E+009 %a compression elastisity modulus ( young"s modulus ) for water ( pa = nm#)$
2E+011 %a
g = %$&1 'cceleration of gravity
a =1
12!4.31 m"sec ----------------------------------------------------------------
1000 x ( 1 + 0.250 )2.1E+009 0.0093 x 2.1 E+11
3- eriod o! vi"ration :
& = 2 x L
& = 2 x 500.00
0.!8 sec ------------------ -------------------------- = a 12!4.3
#- Wave propa$ation :
%ta$e 1 : &epression wave
%ta$e 2 : &epression ret'rn wave
%ta$e 3 : i$h press're wave
%ta$e # : i$h press're ret'rn wave
5- )i*e o! clos're t :
e!erin$ to the previo's para$raph :
,t sta$es 1 and 2 o! wave propa$ation a depression persist at one side o! chec valve
so that the chec valve still open at these sta$es .
)his *ean : !$& sec
'ec(mmen)ati(n
r x ( * water
pipe
r = +g"m3
* water
=
* pipe
= Tension elastisity modulus ( young"s modulus ) for pipe material $( pa = nm # )
m"sec 2
& : eriod o! vi"ration
t = T =
,hie) ater #/m# VD se/ence ( (#erati(n hae t( tae the time ( res#(nse t( eiminateh)ra/ic hammer in the chie) ater sstem
7/21/2019 Water Hamme
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17 Parcel , ITCC Project
KB-03
Water hammer
Design criteria :
H = 31.0 m Pump head
32.0 m Static head
L = 420.0 m Pipeline length
D = 200 mm Pipeline diameter = 0.200 m
t = 8.2 mm Pipe wall thickness = 0.0082 m
1!4.4 Total flow ( pump delivery capacity ) = 0.04845
Pipe material :
1- water velocity in the pipe :
S = S = 3.14 x 0.200 x 0.200
0.03142 --------------------- -------------------------------------------
V =
V =0.04845
1.54226 m " s--------- ----------------------.
2- Wave velocity :
a =1
-----------------------------------------------------
1 $ )
a : Wave velocity ( m sec )
1!!! Water density
2E+009 %a compression elastisity modulus ( young"s modulus ) for water ( pa = nm#)$
2E+011 %a
g = %$&1 'cceleration of gravity
a =1
1286.!! m"sec ----------------------------------------------------------------
1000 x (1
+0.200
)2.1E+009 0.00/2 x 2.1 E+11
3- eriod o! vi"ration :
& = 2 x L
& = 2 x 420.00
0.65 sec ------------------ -------------------------- = a 1286.8
#- Wave propa$ation :
%ta$e 1 : &epression wave
%ta$e 2 : &epression ret'rn wave
%ta$e 3 : i$h press're wave
%ta$e # : i$h press're ret'rn wave
5- )i*e o! clos're t :
H 0 =
# = m3 " h m3 " sec
# = V x S
3.14 x D2
m2
r x ( * water
pipe
r = +g"m3
* water
=
* pipe
= Tension elastisity modulus ( young"s modulus ) for pipe material $( pa = nm# )
m"sec 2
& : eriod o! vi"ration
7/21/2019 Water Hamme
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17 Parcel , ITCC Project
KB-04
Water hammer
Design criteria :
H = 24.0 m Pump head
16.0 m Static head
L = 300.0 m Pipeline length
D = 150 mm Pipeline diameter = 0.150 m
t = !.1 mm Pipe wall thickness = 0.00!1 m96.5 Total flow ( pump delivery capacity ) = 0.02680
Pipe material :
1- water velocity in the pipe :
S = S =
3.14 x 0.150 x 0.150
0.01!6! --------------------- -------------------------------------------
V =
V =0.02680
1.51661 m " s--------- ----------------------.
H 0 =
# = m3 " h m3 " sec
# = V x S
3.14 x D2
m
2
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2- Wave velocity :
a =1
-----------------------------------------------------
1 $ D )
a : Wave velocity ( m sec )
1!!! Water density
2E+009 %a compression elastisity modulus ( young"s modulus ) for water ( pa = nm#)$
2E+011 %a
g = %$&1 'cceleration of gravity
a =1
1303.65 m"sec ----------------------------------------------------------------
1000 x (1
+0.150
)2.1E+009 0.001 x 2.1 E+11
3- eriod o! vi"ration :
& = 2 x L
& = 2 x 300.00
0.46 sec ------------------ -------------------------- = a 1303.6
#- Wave propa$ation :
%ta$e 1 : &epression wave
%ta$e 2 : &epression ret'rn wave
%ta$e 3 : i$h press're wave
%ta$e # : i$h press're ret'rn wave
5- )i*e o! clos're t :
e!erin$ to the previo's para$raph :
,t sta$es 1 and 2 o! wave propa$ation a depression persist at one side o! chec valve
so that the chec valve still open at these sta$es .
)his *ean : !$+ sec
'ec(mmen)ati(n
r x ( * water
x pipe
r = +g"m3
* water
=
* pipe
= Tension elastisity modulus ( young"s modulus ) for pipe material $( pa = nm # )
m"sec 2
& : eriod o! vi"ration
t = T =
,hie) ater #/m# VD se/ence ( (#erati(n hae t( tae the time ( res#(nse t( eiminate
h)ra/ic hammer in the chie) ater sstem
7/21/2019 Water Hamme
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17 Parcel , ITCC Project
KB-05
Water hammer
Design criteria :
H = 2!.0 m Pump head
15.0 m Static head
L = 220.0 m Pipeline length
D = 150 mm Pipeline diameter = 0.150 m
t = !.1 mm Pipe wall thickness = 0.00!1 m
116.6 Total flow ( pump delivery capacity ) = 0.03240
Pipe material :
1- water velocity in the pipe :
S = S = 3.14 x 0.150 x 0.150
0.01!6! ----- -- -- -- -- -- -- -- -- -- -- -- -- -- -- --- -- -- -- -- -- -- -- -- -- -- -- -- -- -- =
V =
V =0.03240
1.83352 m " s--------- ---------------------- =.
H 0 =
# = m3 " h m3 " sec
# = V x S
3.14 x D2
m2
7/21/2019 Water Hamme
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2- Wave velocity :
a =
1
----------------------------------------------------- 1
$D
)
a : Wave velocity ( m sec )
1!!! Water density
2E+009 %a compression elastisity modulus ( young"s modulus ) for water ( pa = nm#)$
2E+011 %a
g = %$&1 'cceleration of gravity
a =1
1303.65 m"sec ----------------------------------------------------------------
1000 x (1
+0.150
)2.1E+009 0.001 x 2.1 E+11
3- eriod o! vi"ration :
& = 2 x L
& = 2 x 220.00
0.34 sec ------------------ -------------------------- = a 1303.6
#- Wave propa$ation :
%ta$e 1 : &epression wave
%ta$e 2 : &epression ret'rn wave
%ta$e 3 : i$h press're wave
%ta$e # : i$h press're ret'rn wave
5- )i*e o! clos're t :
e!erin$ to the previo's para$raph :
,t sta$es 1 and 2 o! wave propa$ation a depression persist at one side o! chec valve
so that the chec valve still open at these sta$es .
)his *ean : !$,+ sec
'ec(mmen)ati(n
r x ( * water
pipe
r = +g"m3
* water
=
* pipe
= Tension elastisity modulus ( young"s modulus ) for pipe material $( pa = nm # )
m"sec 2
& : eriod o! vi"ration
t = T =
,hie) ater #/m# VD se/ence ( (#erati(n hae t( tae the time ( res#(nse t( eiminateh)ra/ic hammer in the chie) ater sstem
7/21/2019 Water Hamme
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17 Parcel , ITCC Project
KB-06Water hammer
Design criteria :
H = 28.0 m Pump head
20.0 m Static head
L = 280.0 m Pipeline length
D = 150 mm Pipeline diameter = 0.150 m
t = !.1 mm Pipe wall thickness = 0.00!1 m
119.5 Total flow ( pump delivery capacity ) = 0.03320
Pipe material :
1- water velocity in the pipe :
S = S = 3.14 x 0.150 x 0.150
0.01!6! ----------- ---------- --- ----------------- ----------------- ------
V =
V =0.03320
1.8!8!9 m " s--------- ---------------------- =.
2- Wave velocity :
a =1
-----------------------------------------------------
1 $
D)
a : Wave velocity ( m sec )
1!!! Water density
2E+009 %a compression elastisity modulus ( young"s modulus ) for water ( pa = nm#)$
2E+011 %a
g = %$&1 'cceleration of gravity
a =1
1303.65 m"sec ----------------------------------------------------------------
1000 x (1
+0.150
)2.1E+009 0.001 x 2.1 E+11
3- eriod o! vi"ration :
& = 2 x L
& = 2 x 280.00
0.43 sec ------------------ -------------------------- = a 1303.6
#- Wave propa$ation :
%ta$e 1 : &epression wave
%ta$e 2 : &epression ret'rn wave
%ta$e 3 : i$h press're wave
%ta$e # : i$h press're ret'rn wave
5 )i*e o! clos're t :
H 0 =
# = m3 " h m3 " sec
# = V x S
3.14 x D2
m2
r x ( * water
x pipe
r = +g"m3
* water
=
* pipe
= Tension elastisity modulus ( young"s modulus ) for pipe material $( pa = nm# )
m"sec 2
& : eriod o! vi"ration
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17 Parcel , ITCC Project
WH-01,04
Water hammer
Design criteria :
H = 2!.0 m Pump head
2!.0 m Static head
L = 390.0 m Pipeline length
D = 250 mm Pipeline diameter = 0.250 m
t = 9.3 mm Pipe wall thickness = 0.0093 m2!0.0 Total flow ( pump delivery capacity ) = 0.0!500
Pipe material :
1- water velocity in the pipe :
S = S = 3.14 x 0.250 x 0.250 0.04909--------------------- -------------------------------------------4 4
V =
V =0.0!500
1.52!93 m " s--------- ---------------------- =S 0.04909
H 0 =
# = m3 " h m3 " sec
# = V x S
3.14 x D2
m2
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2- Wave velocity :
a =1
-----------------------------------------------------
1 $ D )
a : Wave velocity ( m sec )
1!!! Water density
2E+009 %a compression elastisity modulus ( young"s modulus ) for water ( pa = nm#)$
2E+011 %a
g = %$&1 'cceleration of gravity
a =1
12!4.31 m"sec ----------------------------------------------------------------
1000 x (1
+0.250
)2.1E+009 0.0093 x 2.1 E+11
3- eriod o! vi"ration :
& = 2 x L
& = 2 x 390.00
0.61 sec ------------------ -------------------------- = a 12!4.3
#- Wave propa$ation :
%ta$e 1 : &epression wave
%ta$e 2 : &epression ret'rn wave
%ta$e 3 : i$h press're wave
%ta$e # : i$h press're ret'rn wave
5- )i*e o! clos're t :
e!erin$ to the previo's para$raph :
,t sta$es 1 and 2 o! wave propa$ation a depression persist at one side o! chec valve
so that the chec valve still open at these sta$es .
)his *ean : !$1 sec
'ec(mmen)ati(n
r x ( * water
x pipe
r = +g"m3
* water
=
* pipe
= Tension elastisity modulus ( young"s modulus ) for pipe material $( pa = nm # )
m"sec 2
& : eriod o! vi"ration
t = T =
,hie) ater #/m# VD se/ence ( (#erati(n hae t( tae the time ( res#(nse t( eiminateh)ra/ic hammer in the chie) ater sstem
7/21/2019 Water Hamme
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17 Parcel , ITCC Project
WH-05
Water hammer
Design criteria :
H = 26.0 m Pump head
2!.0 m Static head
L = 320.0 m Pipeline length
D = 150 mm Pipeline diameter = 0.150 m
t = !.1 mm Pipe wall thickness = 0.00!1 m95.0 Total flow ( pump delivery capacity ) = 0.02640
Pipe material :
1- water velocity in the pipe :
S = S = 3.14 x 0.150 x 0.150 0.01!6! --------------------- -------------------------------------------4 4
V =
V =0.02640
1.49398 m " s--------- ---------------------- =S 0.01!6!
H 0 =
# = m3 " h m3 " sec
# = V x S
3.14 x D2
m2
7/21/2019 Water Hamme
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2- Wave velocity :
a =1
-----------------------------------------------------
1 $ D )
a : Wave velocity ( m sec )
1!!! Water density
2E+009 %a compression elastisity modulus ( young"s modulus ) for water ( pa = nm#)$
2E+011 %a
g = %$&1 'cceleration of gravity
a =1
1303.65 m"sec ----------------------------------------------------------------
1000 x (1
+0.150
)2.1E+009 0.001 x 2.1 E+11
3- eriod o! vi"ration :
& = 2 x L
& = 2 x 320.00
0.49 sec ------------------ -------------------------- = a 1303.6
#- Wave propa$ation :
%ta$e 1 : &epression wave
%ta$e 2 : &epression ret'rn wave
%ta$e 3 : i$h press're wave
%ta$e # : i$h press're ret'rn wave
5- )i*e o! clos're t :
e!erin$ to the previo's para$raph :
,t sta$es 1 and 2 o! wave propa$ation a depression persist at one side o! chec valve
so that the chec valve still open at these sta$es .
)his *ean : !$+% sec
'ec(mmen)ati(n
r x ( * water
x pipe
r = +g"m3
* water
=
* pipe
= Tension elastisity modulus ( young"s modulus ) for pipe material $( pa = nm # )
m"sec 2
& : eriod o! vi"ration
t = T =
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,hie) ater #/m# VD se/ence ( (#erati(n hae t( tae the time ( res#(nse t( eiminateh)ra/ic hammer in the chie) ater sstem
7/21/2019 Water Hamme
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17 Parcel , ITCC Project
WH-06
Water hammer
Design criteria :
H = 23.0 m Pump head
18.0 m Static head
L = 310.0 m Pipeline length
D = 150 mm Pipeline diameter = 0.150 m
t = !.1 mm Pipe wall thickness = 0.00!1 m96.! Total flow ( pump delivery capacity ) = 0.02685
Pipe material :
1- water velocity in the pipe :
S = S = 3.14 x 0.150 x 0.150 0.01!6! --------------------- -------------------------------------------4 4
V =
V =0.02685
1.51944 m " s--------- ---------------------- =S 0.01!6!
H 0 =
# = m3 " h m3 " sec
# = V x S
3.14 x D2
m2
7/21/2019 Water Hamme
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2- Wave velocity :
a =1
-----------------------------------------------------
1 $ D )
a : Wave velocity ( m sec )
1!!! Water density
2E+009 %a compression elastisity modulus ( young"s modulus ) for water ( pa = nm#)$
2E+011 %a
g = %$&1 'cceleration of gravity
a =1
1303.65 m"sec ----------------------------------------------------------------
1000 x (1
+0.150
)2.1E+009 0.001 x 2.1 E+11
3- eriod o! vi"ration :
& = 2 x L
& = 2 x 310.00
0.48 sec ------------------ -------------------------- = a 1303.6
#- Wave propa$ation :
%ta$e 1 : &epression wave
%ta$e 2 : &epression ret'rn wave
%ta$e 3 : i$h press're wave
%ta$e # : i$h press're ret'rn wave
5- )i*e o! clos're t :
e!erin$ to the previo's para$raph :
,t sta$es 1 and 2 o! wave propa$ation a depression persist at one side o! chec valve
so that the chec valve still open at these sta$es .
)his *ean : !$+& sec
'ec(mmen)ati(n
r x ( * water
x pipe
r = +g"m3
* water
=
* pipe
= Tension elastisity modulus ( young"s modulus ) for pipe material $( pa = nm # )
m"sec 2
& : eriod o! vi"ration
t = T =
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,hie) ater #/m# VD se/ence ( (#erati(n hae t( tae the time ( res#(nse t( eiminateh)ra/ic hammer in the chie) ater sstem
7/21/2019 Water Hamme
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17 Parcel , ITCC Project
RD-03
Water hammer
Design criteria :
H = 2!.0 m Pump head
29.0 m Static head
L = 280.0 m Pipeline length
D = 150 mm Pipeline diameter = 0.150 m
t = !.1 mm Pipe wall thickness = 0.00!1 m
103.1 Total flow ( pump delivery capacity ) = 0.02865
Pipe material :
1- water velocity in the pipe :
S = S = 3.14 x 0.150 x 0.150
0.01!6! --------------------- ------------------------------------------- =
4 4
V =
V =0.02865
1.62131 m " s--------- ---------------------- =S 0.01!6!
H 0 =
# = m3 " h m3 " sec
# = V x S
3.14 x D2
m2
7/21/2019 Water Hamme
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2- Wave velocity :
a =1
-----------------------------------------------------
1 $ D )
a : Wave velocity ( m sec )
1!!! Water density
2E+009 %a compression elastisity modulus ( young"s modulus ) for water ( pa = nm#)$
2E+011 %a
g = %$&1 'cceleration of gravity
a =
1
1303.65 m"sec ----------------------------------------------------------------
1000 x (1
+0.150
)2.1E+009 0.001 x 2.1 E+11
3- eriod o! vi"ration :
& = 2 x L
& = 2 x 280.00
0.43 sec ------------------ -------------------------- =
a 1303.6
#- Wave propa$ation :
%ta$e 1 : &epression wave
%ta$e 2 : &epression ret'rn wave
%ta$e 3 : i$h press're wave
%ta$e # : i$h press're ret'rn wave
5- )i*e o! clos're t :
e!erin$ to the previo's para$raph :
,t sta$es 1 and 2 o! wave propa$ation a depression persist at one side o! chec valve
so that the chec valve still open at these sta$es .
)his *ean : !$+, sec
'ec(mmen)ati(n
r x ( * water
pipe
r = +g"m3
* water
=
* pipe
= Tension elastisity modulus ( young"s modulus ) for pipe material $( pa = nm# )
m"sec 2
& : eriod o! vi"ration
t = T =
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,hie) ater #/m# VD se/ence ( (#erati(n hae t( tae the time ( res#(nse t( eiminateh)ra/ic hammer in the chie) ater sstem
7/21/2019 Water Hamme
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17 Parcel , ITCC Project
RD-04
Water hammer
Design criteria :
H = 22.0 m Pump head
16.0 m Static head
L = 420.0 m Pipeline length
D = 150 mm Pipeline diameter = 0.150 m
t = !.1 mm Pipe wall thickness = 0.00!1 m135.5 Total flow ( pump delivery capacity ) = 0.03!65
Pipe material :
1- water velocity in the pipe :
S = S = 3.14 x 0.150 x 0.150 0.01!6! --------------------- -------------------------------------------4 4
V =
V =0.03!65
2.13062 m " s--------- ---------------------- =S 0.01!6!
H 0 =
# = m3 " h m3 " sec
# = V x S
3.14 x D2
m2
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2- Wave velocity :
a =1
-----------------------------------------------------
1 $ D )
a : Wave velocity ( m sec )
1!!! Water density
2E+009 %a compression elastisity modulus ( young"s modulus ) for water ( pa = nm#)$
2E+011 %a
g = %$&1 'cceleration of gravity
a =1
1303.65 m"sec ----------------------------------------------------------------
1000 x (1
+0.150
)2.1E+009 0.001 x 2.1 E+11
3- eriod o! vi"ration :
& = 2 x L
& = 2 x 420.00
0.64 sec ------------------ -------------------------- = a 1303.6
#- Wave propa$ation :
%ta$e 1 : &epression wave
%ta$e 2 : &epression ret'rn wave
%ta$e 3 : i$h press're wave
%ta$e # : i$h press're ret'rn wave
5- )i*e o! clos're t :
e!erin$ to the previo's para$raph :
,t sta$es 1 and 2 o! wave propa$ation a depression persist at one side o! chec valve
so that the chec valve still open at these sta$es .
)his *ean : !$+ sec
'ec(mmen)ati(n
r x ( * water
x pipe
r = +g"m3
* water
=
* pipe
= Tension elastisity modulus ( young"s modulus ) for pipe material $( pa = nm # )
m"sec 2
& : eriod o! vi"ration
t = T =
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,hie) ater #/m# VD se/ence ( (#erati(n hae t( tae the time ( res#(nse t( eiminateh)ra/ic hammer in the chie) ater sstem
7/21/2019 Water Hamme
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17 Parcel , ITCC Project
IT-01
Water hammer
Design criteria :
H = 29.0 m Pump head
24.0 m Static head
L = 220.0 m Pipeline length
D = 150 mm Pipeline diameter = 0.150 m
t = !.1 mm Pipe wall thickness = 0.00!1 m108.! Total flow ( pump delivery capacity ) = 0.03020
Pipe material :
1- water velocity in the pipe :
S = S = 3.14 x 0.150 x 0.150 0.01!6! --------------------- -------------------------------------------4 4
V =
V =0.03020
1.!0902 m " s--------- ---------------------- =S 0.01!6!
H 0 =
# = m3 " h m3 " sec
# = V x S
3.14 x D2
m2
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2- Wave velocity :
a =1
-----------------------------------------------------
1 $ D )
a : Wave velocity ( m sec )
1!!! Water density
2E+009 %a compression elastisity modulus ( young"s modulus ) for water ( pa = nm#)$
2E+011 %a
g = %$&1 'cceleration of gravity
a =1
1303.65 m"sec ----------------------------------------------------------------
1000 x (1
+0.150
)2.1E+009 0.001 x 2.1 E+11
3- eriod o! vi"ration :
& = 2 x L
& = 2 x 220.00
0.34 sec ------------------ -------------------------- = a 1303.6
#- Wave propa$ation :
%ta$e 1 : &epression wave
%ta$e 2 : &epression ret'rn wave
%ta$e 3 : i$h press're wave
%ta$e # : i$h press're ret'rn wave
5- )i*e o! clos're t :
e!erin$ to the previo's para$raph :
,t sta$es 1 and 2 o! wave propa$ation a depression persist at one side o! chec valve
so that the chec valve still open at these sta$es .
)his *ean : !$,+ sec
'ec(mmen)ati(n
r x ( * water
x pipe
r = +g"m3
* water
=
* pipe
= Tension elastisity modulus ( young"s modulus ) for pipe material $( pa = nm # )
m"sec 2
& : eriod o! vi"ration
t = T =
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,hie) ater #/m# VD se/ence ( (#erati(n hae t( tae the time ( res#(nse t( eiminateh)ra/ic hammer in the chie) ater sstem
7/21/2019 Water Hamme
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17 Parcel , ITCC Project
IT-02
Water hammer
Design criteria :
H = 2!.0 m Pump head
24.0 m Static head
L = 350.0 m Pipeline length
D = 150 mm Pipeline diameter = 0.150 m
t = !.1 mm Pipe wall thickness = 0.00!1 m
131.0 Total flow ( pump delivery capacity ) = 0.03640
Pipe material :
1- water velocity in the pipe :
S = S = 3.14 x 0.150 x 0.150
0.01!6! --------------------- -------------------------------------------4 4
V =
V =0.03640
2.05988 m " s--------- ----------------------S 0.01!6!
H 0 =
# = m3 " h m3 " sec
# = V x S
3.14 x D2
m2
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2- Wave velocity :
a =1
-----------------------------------------------------
1
$D
)
a : Wave velocity ( m sec )
1!!! Water density
2E+009 %a compression elastisity modulus ( young"s modulus ) for water ( pa = nm#)$
2E+011 %a
g = %$&1 'cceleration of gravity
a =1
1303.65 m"sec ----------------------------------------------------------------
1000 x ( 1 + 0.150 )2.1E+009 0.001 x 2.1 E+11
3- eriod o! vi"ration :
& = 2 x L
& = 2 x 350.00
0.54 sec ------------------ -------------------------- = a 1303.6
#- Wave propa$ation :
%ta$e 1 : &epression wave
%ta$e 2 : &epression ret'rn wave
%ta$e 3 : i$h press're wave
%ta$e # : i$h press're ret'rn wave
5- )i*e o! clos're t :
e!erin$ to the previo's para$raph : ,t sta$es 1 and 2 o! wave propa$ation a depression persist at one side o! chec valve
so that the chec valve still open at these sta$es .
)his *ean : !$*+ sec
'ec(mmen)ati(n
r x ( * water
pipe
r = +g"m3
* water
=
* pipe
= Tension elastisity modulus ( young"s modulus ) for pipe material $( pa = nm # )
m"sec 2
& : eriod o! vi"ration
t = T =
,hie) ater #/m# VD se/ence ( (#erati(n hae t( tae the time ( res#(nse t( eiminateh)ra/ic hammer in the chie) ater sstem
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Water hammer
Design criteria :
H = 40.0 m Pump head
35.0 m Static head
L = 500.0 m Pipeline length
D = 250 mm Pipeline diameter = 0.250 m
t = 4.0 mm Pipe wall thickness = 0.0040 m
80.0 Total flow ( pump delivery capacity ) = 0.02222
Pipe material :
1- water velocity in the pipe :
S = S = 3.14 x 0.250 x 0.250
0.04909--------------------- -------------------------------------------
V =
V =0.02222
0.452!2 m " s--------- ---------------------- =S 0.04909
2- Wave velocity :
a =1
-----------------------------------------------------
1 $
D)
a : Wave velocity ( m sec )
1!!! Water density
2E+009 %a compression elastisity modulus ( young"s modulus ) for water ( pa = nm#)$
2E+011 %a
g = %$&1 'cceleration of gravity
a =1
1128.36 m"sec ----------------------------------------------------------------
1000 x (1
+0.250
)2.1E+009 0.00# x 2.1 E+11
H 0 =
# = m3 " h m3 " sec
# = V x S
3.14 x D2
m2
r x ( * water
x pipe
r = +g"m3
* water
=
* pipe
= Tension elastisity modulus ( young"s modulus ) for pipe material $( pa = nm # )
m"sec 2
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3- eriod o! vi"ration :
& = 2 x L
& = 2 x 500.00
0.89 sec ------------------ -------------------------- = a 1128.4
#- Wave propa$ation :
%ta$e 1 : &epression wave
%ta$e 2 : &epression ret'rn wave%ta$e 3 : i$h press're wave
%ta$e # : i$h press're ret'rn wave
5- )i*e o! clos're t :
e!erin$ to the previo's para$raph :
,t sta$es 1 and 2 o! wave propa$ation a depression persist at one side o! chec valve
so that the chec valve still open at these sta$es .
)his *ean : !$&% sec
- axi*'* press're variation :
a x V 11#&$+ - !$+*,*#$1 m------------------ ......................... =
g %$&1
& : eriod o! vi"ration
t = T =
T : eriod o! vi"ration
t : hec valve closin$ ti*e .
4't in reality ( t will "e less than ( T "eca'se o! p'*p and chec valve inertia .
6! ( t is less or e7'al to ( T then the *axi*'* press're is $iven "y the !ollowin$ !or*'la :
Dh = Dh =
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- %teady state head !riction loss :
----- x --------- D 2 g
!$!## 1"1 8riction coe!!icient o! the pipe
L = 500 m Pipeline length
D = 250 mm Pipeline diameter = 0.250 m
V = 0.453 m " sec /ean water velocity in the pipe
g = %$&1 'cceleration of gravity
!$!## -
*!!$ !$+*, -!$+*,
!$+ m------------- x -------------------- = !$#*! # - %$&1
)his press're is s'pposed to "e added to the static press're pl's the !riction head loss :
,*$!! 0 *#$! 0 !$+ = &$* m
Dhh!riction=
l x
L V 2
l =
m"sec 2
Dhfriction =
H *ax
H static
+ Dhha**er
+ Dh
!riction
H *ax