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

2
2
2
2
Vup
ρ V
V
e
⋅
ρe
⋅
down
up ρe
⋅ Vdown
ζ
e,orig
⋅ ⋅ = ζ
2
e,orig
⋅ = ζ
e
⋅
(5)
V 2
2
2
down
A similar modification is implemented for additional entered local losses: If the loss relates to
another reference velocity than the one found in the segment described by the given diameter
2 2
of the Port (D p ), the coefficient is multiplied by the ratio of the two velocities V ,
where
V p
V add
add
V p
is the needed (related) reference velocity for the given local loss coefficient and
the velocity due to the given port diameter. However, when entering the loss coefficients,
the user usually does not know the discharge through the port and, therefore, does not know
the velocity either. But the discharge through one port does not change when reaching a
different segment of this port. Therefore, instead of velocities, the modification can be done
regarding the flow devided by the areas:
2
⎛qi
⎞
2
2
V
⎜ A ⎟
add
A
add
p
ζ add = ζ add , orig ⋅ = ζ
2 add , orig ⋅
⎝ ⎠
= ζ
2 add , orig ⋅
(6)
2
V
p
⎛q
A
i
⎞
add
⎜
A
⎟
⎝ p ⎠
where ζ is the original local loss coefficient and is the related area. If there are
add , orig
several known additional local losses, each ζ
add ,i
is determined separately, modified if
necessary and then the sum of all losses is entered into the designated space. Using this
method, very complicated port-riser configurations can be calculated with the program.
A add
2.4.2 Friction losses
Continuous pressure losses due to friction along the walls or boundary layers in a pipeline are
calculated as:
p l = L ρ ⋅ 2
2
e
V
λ ⋅ ⋅ or as headloss p l /γ e = L V
λ ⋅ ⋅
(7)
D 2
D 2g
where λ is the friction coefficient, L the length of the considered pipe section, D the diameter,
V the velocity in the pipe section, and ρ e the density of the effluent. For the calculation of the
friction coefficient λ, the explicit form described by Swamee and Jain (1976) is used:
0.25
(8)
λ =
2
⎡ ⎛ k 5.74 ⎞⎤
⎢lg⎜
s
+
0.9
⎟
3.7 Re
⎥
⎣ ⎝ D ⎠⎦
It is valid for −6
k −2
10 < s
3
5
< 10 and 4 ⋅10
< Re < 10 , where ks stands for the equivalent sand
D
roughness and the Reynolds number Re = VD/ν e , where ν stands for the kinematic viscosity
of the effluent.
Values of k s for different pipe materials and surface conditions of use are listed in Table 3,
which is an excerpt of Idelchik (1986). If only Mannings n values are known a conversion to
k s can be done by using the formula:
k s = (n 5.87 (2g)^0.5 ) 6 (9)
Institut für Hydromechanik, Universität Karlsruhe 19