user's manual for corhyd: an internal diffuser hydraulics model - IfH

Fig. 22: Graphical output: Energy and Hydraulic grade line of the whole system and the diffuser
Graphical output for T-Diffuser: In progress
6 Design and optimization
The governing equation for the individual port discharge is equation (20). Equation (18) in
(20) devided by q i and squared gives:
i
⎛ ⎞
⎜∑
q
k ⎟
2
=
( ) ( )
⎝ k 1 ⎠
p
d,i
− p
a,i
+ 2g z
d,i
− z
jet,i
+
2
ρ
e
A
d,i
1 =
(24)
2
2
2 2 n p,i
n
⎛ ⎞ ⎛ λ ⎞
r ,i
q α
⎛ ⎞ ⎛ λ ⎞
i i
∑⎜
q α
p,i, jL
i i
p,i, j
r,i, j r,i, j
+ ⎟ ⎜ζ
+ ⎟ + ∑⎜
q
L
i
⎟ ⎜ζ
+ ⎟
2
( )
p,i, j
r,i, j
C A
j=
1 ⎝ A
p,i, j ⎠ ⎝ D
p,i, j ⎠ j=
1 ⎝ A
r,i, j ⎠ ⎝ D
r,i, j ⎠
c,i
p,i
where the losses along the diffuser are included in the internal pressure p d,i from equation
(18).
The first two terms in the numerator denote the difference of the piezometric head (hydraulic
2
head) ( p
d,i
− p
a,i
) + 2g( z
d,i
− z
jet, i
) = ∆ i between the diffuser and the ambient. The third term
ρ
e
in the numerator is related to the diffuser velocities v d,i . The terms in the denominator are
related to the jet velocity v j , i = α i q i /(C c A p,i ) and the port and riser losses. For outfalls with
uniform geometries or for uniform diffuser sections with uniform port/riser groups it follows
A i = A = const., α i = α = const., D i = D = const., L i = L = const.. Assuming a uniform flow
distribution among the orifices gives v r,i = v r and v p,i = v p = const.. Therefore all losses but the
riser inlet loss and the port exit loss are constant (λ i = λ = const., ζ p,i = ζ p ). Under these
assumptions only few parameters change along the diffuser causing the variation of individual
flows. The other parameters can be joint in constants C i :
1 =
∆ i + v d,i ²
C 1 /C c,i 2 + C 2 ζ dr,i
(25)
For diffuser without risers it is:
Institut für Hydromechanik, Universität Karlsruhe 46
2