Marine Outfalls 32.4 Hydraulic Analysis and Design 727
Part C | 32.4
Table 32.4 Set of simultaneous equations for manifold flow calculations
Description
Equations
No. of
equations
Unknowns
No. of
unknowns
Inputs
Equation
Continuity: total flow
rate is equal to sum of
individual port flow
rates
Q T D
n
P
iD1
Q Pi
1
Q Pi
n
Q T
(8a)
Port exit velocity
V Pi D
QP i
4 D
2
P i
n
V Pi
n
D Pi
(8b)
Velocity in manifold
section between adjacent ports
V Ti D
i
P
1
QP i
4 D 2
T i
n
V Ti
n
D Ti
(8c)
Reynolds number
in manifold section
between adjacent ports
Re Ti D
VT i DT i
n
Re Ti
n
(8d)
Darcy friction factor
in manifold section
between adjacent ports
f Ti D
0:25
"
log
ks i
3:7D T i
C 5:74
Re 0:9
T i
!# 2
n
f Ti
n
k si
(8e)
Head loss between
manifold station i and
just downstream of
port i
P H L.Ti!Pi/ D
V
2
P i
2g
P
K LT i !P i
Á
n
P H L.Ti!Pi/
n
P
K LT i !P i
(8f)
Head loss between
outfall shaft and just
downstream of the
n-th port
P H L.0!Pn/ D
V
2
Tn
2g
f Tn
lT n
DT n
C
P
K L .0!Tn/
Á
C
P H L.Tn!Pn/
1
P H L.0!Pn /
1
l Tn
D Tn
P
K L .0!Tn/
(8g)
Head loss between
manifold station
(i C 1) and just downstream of port i
P H L.T iC1 !Pi/ D
V 2
T i
2g
f Ti
lT i
DT i
C
P
K L.T iC1 !Ti/
Á
C
P H L.Ti!Pi/
n 1
P H L.T iC1 !Pi/ n 1
l Ti
P
K L.T iC1 !Ti/
(8h)
Pressure just downstream of port i,
expressed in terms
of the ambient seawater density
p Pi D
z SL z Pi
a g
n
p Pi
n
z SL
z Pi
a
(8i)
Energy equation applied between point 0
and the most upstream
port (n/
V
2
0
2g C
p0
eg C z 0
D
V 2
Pn
2g C
pP n
eg Cz Pn C
P H L.0!Pn/
1
z 0
1
V 0
p 0 ;
e
z Pn
(8j)
Parallel flow: head
loss is the same between manifold station
i C 1 and just downstream of either port i
or port i C 1
P H L.T iC1 !Pi/ D
P H L.T iC1 !P iC1 /
n 1
-
-
-
(8k)
Total:
8n C 1
8n C 1
based on some velocity into an effective loss coefficient
based on another velocity, the following equation can
be used,
V
2
1
2g
K L1 D
V
2
2
2g
K L
0
1
) K L
0
1
D
V
2
1
V
2
2
K L1 :
(32.8)
Manifold Section Diameters
The equations in Table 32.4 are kept general so that
geometric parameters can be varied along the length
of the manifold. In some cases, it may be necessary
to progressively reduce the manifold diameter in order
to maintain velocities that prevent settlement of solids
Part C | 32.4
Table 32.4 Set of simultaneous equations for manifold flow calculations
Description
Equations
No. of
equations
Unknowns
No. of
unknowns
Inputs
Equation
Continuity: total flow
rate is equal to sum of
individual port flow
rates
Q T D
n
P
iD1
Q Pi
1
Q Pi
n
Q T
(8a)
Port exit velocity
V Pi D
QP i
4 D
2
P i
n
V Pi
n
D Pi
(8b)
Velocity in manifold
section between adjacent ports
V Ti D
i
P
1
QP i
4 D 2
T i
n
V Ti
n
D Ti
(8c)
Reynolds number
in manifold section
between adjacent ports
Re Ti D
VT i DT i
n
Re Ti
n
(8d)
Darcy friction factor
in manifold section
between adjacent ports
f Ti D
0:25
"
log
ks i
3:7D T i
C 5:74
Re 0:9
T i
!# 2
n
f Ti
n
k si
(8e)
Head loss between
manifold station i and
just downstream of
port i
P H L.Ti!Pi/ D
V
2
P i
2g
P
K LT i !P i
Á
n
P H L.Ti!Pi/
n
P
K LT i !P i
(8f)
Head loss between
outfall shaft and just
downstream of the
n-th port
P H L.0!Pn/ D
V
2
Tn
2g
f Tn
lT n
DT n
C
P
K L .0!Tn/
Á
C
P H L.Tn!Pn/
1
P H L.0!Pn /
1
l Tn
D Tn
P
K L .0!Tn/
(8g)
Head loss between
manifold station
(i C 1) and just downstream of port i
P H L.T iC1 !Pi/ D
V 2
T i
2g
f Ti
lT i
DT i
C
P
K L.T iC1 !Ti/
Á
C
P H L.Ti!Pi/
n 1
P H L.T iC1 !Pi/ n 1
l Ti
P
K L.T iC1 !Ti/
(8h)
Pressure just downstream of port i,
expressed in terms
of the ambient seawater density
p Pi D
z SL z Pi
a g
n
p Pi
n
z SL
z Pi
a
(8i)
Energy equation applied between point 0
and the most upstream
port (n/
V
2
0
2g C
p0
eg C z 0
D
V 2
Pn
2g C
pP n
eg Cz Pn C
P H L.0!Pn/
1
z 0
1
V 0
p 0 ;
e
z Pn
(8j)
Parallel flow: head
loss is the same between manifold station
i C 1 and just downstream of either port i
or port i C 1
P H L.T iC1 !Pi/ D
P H L.T iC1 !P iC1 /
n 1
-
-
-
(8k)
Total:
8n C 1
8n C 1
based on some velocity into an effective loss coefficient
based on another velocity, the following equation can
be used,
V
2
1
2g
K L1 D
V
2
2
2g
K L
0
1
) K L
0
1
D
V
2
1
V
2
2
K L1 :
(32.8)
Manifold Section Diameters
The equations in Table 32.4 are kept general so that
geometric parameters can be varied along the length
of the manifold. In some cases, it may be necessary
to progressively reduce the manifold diameter in order
to maintain velocities that prevent settlement of solids