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REVIEW (TWS/2005)Steady, Uniform Pipe
Flo
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!eneral E"#ation$,
%ontin#ed
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Fri%tion Fa%tor !eor&ia Te%' ydra#li%$ a*,TWS/2002
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+oody ia&ram (from +#n$on et al-2002)
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Pipe Flo Pro*lem$
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+inor o$$e$2V
hL
=K2g'ere . minor lo$$ %oef%ient
Fitting KS'arp1ed&ed entran%e 0-50
Eit into a re$er3oir 4-0
*r#pt epan$ion (414/2)2
Relar 60oel*o(7an&ed/t'readed)
0-8/4-5
!lo*e 3al3e, f#lly open 40
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!ate 3al3e (f#lly/'alf open) 0-45/2-4
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Pipe$ inSerie$ and
Parallel
Serie
$ 42
8
Q1 =
Q2
= Q3
hL = hL1 +hL2
+ hL3
4
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Parallel9 2
Q = Q1 +Q2
+ Q3
hL1 =
hL2
= hL3
8
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T'ree Re$er3oir
Pro*lem!i3en: pipe propertie$ ; re$er3oir
ele3ation$
A
HGL
1pJ/
B
Let hJ = zJ + pJ/
2zA
J
C zJB
3zC
Energy Equations (A-J B-J or J-B J-C!
zA = hJ + ("1L1/#1!($1%/%gA1
%!
zB = hJ + ("%L%/#%!($%%/%gA%
%!
z
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hJ = zC + ("3L3/#3!($%/%gA3
3!
Find: 94, 92,
98
Continuity at J (positi&e in negati&e out!
$1 + $% + $3 = '
3
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Sol#tion
$$#me f#lly1ro#&' t#r*#lent fri%tionfa%tor$ $$#me initial
'< =>Sol3e ener&y e"#ation$ for 9
4
, 92
, 98et F 94?92?98 (po$iti3e in,
ne&ati3e o#t)If F @ 0, rai$e ! ('1
