Machinery's Handbook, 31st Edition
ENERGY LOSSES FOR SUBSONIC FLOW 2785 where head loss h l is measured in units of length; v i is velocity entering the enlargement; v o is velocity leaving the enlargement; K is the loss coefficient for sudden enlargement; A i and A o are the areas before and after the enlargement. The equation for K is only valid if velocity at the inlet is less than 4 ft/sec (1.2 m/s). For faster flow rates, a graph of experi - mentally determined K values must be used. Gradual Enlargement: Gradual enlargement causes less energy loss than sudden en- largement because it causes less turbulence. Diffusers are gradual enlargement devices. Velocity decreases while pressure increases. Gradual enlargements generally have a conical section that joins two different pipe diameters. The divergence angle is the in- cluded angle in the cone. The following two equations give approximations of head loss in a gradual enlargement. K L is the Gibson loss coefficient (see Fig. 3). K D is the resistance coefficient (see Fig. 4). Both depend on the ratio of areas and the angle of divergence. The formulas to calculate this loss ignore the effects of friction inside the conical section. If the enlargement is very gradual, the effects of friction can become significant. Therefore, an included angle of 6° or more is recommended in the conical section to mitigate the ef- fects of friction. For area ratios up to 6:1 with angles of divergence of 40° or more, head loss may be less with a sudden expansion than with a gradual one. These two effects are clearest on the graph of K L (Fig. 3). h l K D v i 2 = h l K L 2 v =
v i o 2 – ( ) 2 g -----------
2 g ---
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3
A o A i 4 2.25 9
K L
0 0°
20° 40° 60° 80° 100° 120° 140° 160° 180°
Fig. 3. Head Loss Coefficient K L , Conical Diffuser Sudden Contraction: Sudden contraction causes energy loss due to turbulence. This head loss can be calculated by using the following equation and Fig. 5. Because loss varies with the square of velocity, small changes in flow can greatly affect energy loss. h l K C v o 2 = where v o is the velocity at the outlet and K C is the loss coefficient. D i / D o is the ratio of the inlet diameter to the outlet diameter. 2 g ---
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