LONG TERM
4.2 Head Loss Coefficients (Input Forms 3C, 5D)
The energy lost by a fluid when work is done by the fluid against friction between two given points of flow is referred to as the head loss for the fluid between the two points. There are two types of head losses: head loss due to viscous friction, and head loss due to abrupt changes in area or turns within a tunnel. The head loss due to friction between two given points of flow is defined as follows:
h P P
(Any consistent set of units may be used with these equations.)
Expressions have been developed to determine the head loss due to friction. The most convenient expression to use is the Darcy-Weisbach equation:
h fL d
V
f = g2
2 where f = Darcy-Weisbach friction factor
L = length of tunnel between points 1 and 2 d = hydraulic diameter of the tunnel
V = velocity of the fluid
The losses that occur when sudden enlargements, contractions, or turns occur in a tunnel can be expressed in terms of the velocity head of the fluid just before the sudden change in area or the turn occurs. This loss is often referred to as the minor head loss. A minor head loss is an irreversible head loss in the total (static plus dynamic) head in the segment. The term “minor” does not imply that these losses are small, but it is a name which has been historically applied to this type of head loss. The minor head loss can also be expressed as a friction loss by calculating the equivalent length of tunnel through which the fluid would have to flow in order to lose an amount of energy equivalent to the energy lost during the rapid change in area or the turn. The minor head loss is expressed as follows:
( )
hf m =f LdVg2 =KVg22 2
where (hf)m = minor head loss
K = minor head loss coefficient V = velocity of the fluid
Various tables which supply minor head losses for certain types of system geometry provide these head losses in the form of equivalent lengths of tunnel. The above relationship must be used to convert head losses in equivalent lengths to an equivalent head loss coefficient (K) for each abrupt area change or turn.
The SES program internally calculates the head loss due to friction for each line segment in the system. Therefore, the user need only enter the minor head loss coefficients for each line and vent shaft segment in a system. The SES program requires the user to determine the minor head loss
coefficients based on changes in total pressure only (static pressure plus velocity pressure). Head loss coefficients are sometimes calculated using the change in static pressure and the user should make
4-11 flow leaves the segment. A sketch describing the forward and backward ends of a segment is given below:
+ User-Established Positive Direction Backward End
SEGMENT Segment Boundary
Forward End Segment Boundary
The minor head loss coefficients may be obtained from various sources. Table 4.3 provides loss coefficients based on total pressure loss for many types of sudden changes in area. Table 4.4 provides the loss coefficients based on total pressure loss for many different types of turns.
The user must enter the head loss coefficients for both positive and negative flow at each end of each segment in the system. The positive and negative flow directions at the forward and backward ends of a segment are shown in the diagram below:
+ User-Established Positive Direction
Backward End, Negative Flow Backward End, Positive Flow
Segment Boundary
Forward End, Positive Flow Forward End, Negative Flow
Segment Boundary
Minor Head Loss Coefficients Between Two Segments
The user must only enter the minor head loss coefficients once at each segment boundary. In other words, if the user enters the forward end positive and negative flow loss coefficients at a segment boundary, zeros must be entered for the head loss coefficients for the subsequent adjoining segment at the adjoining segment's backward end, and vice versa. It is extremely important that the user fully understand the methods for entering minor head losses outlined below. A common error often made by new users is that they enter head losses at a segment boundary twice. It cannot be emphasized strongly enough that the head losses at a segment boundary are entered only once for a given flow direction.
Example 4.2 on page 4-14 shows the four different ways minor head losses at a segment boundary may be entered.
E
Table 4.3 Loss Coefficients Based on Total Pressure Loss for Area Changes TYPE ILLUSTRATION CONDITIONS LOSS
COEFFICIENT TYPE ILLUSTRATION CONDITIONS C1
4-13
Table 4.4 Total Pressure Losses Due to Elbows (Additional Equivalent Losses in Excess Friction to Intersection of Center Lines)
TYPE ILLUSTRATION CONDITIONS
90TIMES VALUE FOR SIMILAR 90 - DEG. ELBOW
CONSIDER EQUAL TO A SIMILAR ELBOW.
BASE LOSS ON ENTERING VELOCITY.
a Values based on f values of approximately 0.02.
b Values calculated from L/D and L/W values for f =0.02.
+ User Established
Loss Coefficients Obtained As Follows From Table 4.3:
For the forward end, positive flow loss coefficient for SEGMENT X, use square edge abrupt contraction:
A2/A1 = Area SEGMENT Y/Area SEGMENT X = 0.50
C2 = K2 = 0.205 (this coefficient is referenced to the area of A2)
The loss coefficient must be referenced to area A1 (SEGMENT X)
K K A
For the forward end, negative flow loss coefficient for SEGMENT X, use abrupt expansion:
A1/A2 = Area SEGMENT Y / Area SEGMENT X = 0.50 C2 = 1.00 (obtained directly from Table 4.3)
4-15 +
Segment Boundary K=0.0
K=0.82
K=1.00 K=0.0
SEGMENT X Case I
SEGMENT Y
Segment Boundary
The minor head loss coefficients for both positive and negative flow at the boundary between SEGMENT X and SEGMENT Y have now been described. Therefore, the loss coefficients at the backward end of SEGMENT Y must be set equal to 0.0 as the loss coefficients at a segment boundary must only be described once.
Case II
Alternatively, the user may enter the minor head loss coefficients at the boundary between SEGMENT X and SEGMENT Y as follows:
Segment Boundary K=0.0
K=0.0
K=1.00 K=0.205
SEGMENT X Case II
SEGMENT Y
Segment Boundary
The loss coefficients are obtained as follows from Table 4.3:
For the backward end, positive flow loss coefficient for SEGMENT Y use square edge abrupt contraction:
A2/A1 = Area SEGMENT Y/Area SEGMENT X = 0.50 C2 = 0.205 (obtained directly from Table 4.3)
+
The minor head loss coefficient at the forward end, negative flow for SEGMENT X is the same as in