LOSS OF HEAD CAUSED BY SUDDEN
ENLARGEMENT OF PIPE
Water flows through a pipe at 4 ft
3
/s (113.249 L/s). Compute the loss of head resulting
from a change in pipe size if (a) the pipe diameter increases abruptly from 6 to 10 in
(152.4 to 254.0 mm); (b) the pipe diameter increases abruptly from 6 to 8 in (152.4 to
203.2 mm) at one section and then from 8 to 10 in (203.2 to 254.0 mm) at a section farther
downstream.
Calculation Procedure:
- Evaluate the pressure-head differential required to decelerate
the liquid
Where there is an abrupt increase in pipe size, the liquid must be decelerated upon enter-
ing the larger pipe, since the fluid velocity varies inversely with area. Let subscript 1 refer
to a section immediately downstream of the enlargement, where the higher velocity pre-
vails, and let subscript 2 refer to a section farther downstream, where deceleration has
been completed. Disregard the frictional loss.
Using Eq. 11 we seep 2 /w ^p 1 Iw+ (V 1 V 2 - V%)/g. - Combine the result of step 1 with Eq. 9
The result is Borda's formula for the head loss hE caused by sudden enlargement of the
pipe cross section:
, (^i-K 2 )
2
*'° 2 g (23)As this investigation shows, only part of the drop in velocity head is accounted for by
a gain in pressure head. The remaining head hE is dissipated through the formation of
eddy currents at the entrance to the larger pipe.
- Compute the velocity in each pipe
Thus
Pipe diam, in (mm) Pipe area, ft^2 (m^2 ) Fluid velocity, ft/s (cm/s)
6(152.4) 0.196(0.0182) 20.4(621.79)
8 (203.2) 0.349 (0.0324) 11.5 (350.52)
10 (254.0) 0.545 (0.0506) 7.3 (222.50)- Find the head loss for part a
Thus, hE = (20.4 - 7.3)^2 /64.4 = 2.66 ft (81.077 cm). - Find the head loss for part b
Thus, HE = [(20.4 - 11.5)^2 + (11.5- 7.3)^2 ]/64.4 = 1.50 ft (45.72 cm). Comparison of these
results indicates that the eddy-current loss is attenuated if the increase in pipe size occurs
in steps.