26 gal/min
Vel°dty = (7.48 gal/tfX(^4
X^3 in/12 in/ft)')(60 s/min)= L2 *" (0' (^37) "^
Using Fig. 11 with a velocity of 1.2 ft/s (0.37 m/s) and a solids content of 5 percent, the
multiplication factor (k) is 12. Therefore, the dynamic head loss for this system when
pumping 5 percent solids is:
Dynamic Head Loss 5 o/0 = (Dynamic Head Losswater)(&)
Dynamic Head Loss 5 o/0 = (4.12')(12) = 49.44 feet (15.1 m)
Use 50 feet of head loss (15.2 m)
The total head loss is the sum of the static head and the dynamic head Ioss 5 o/0. Therefore,
the total head loss (Total Dynamic Head or TDH) for the system is
10'+ 50'= 60 feet (18.3m)
This translates to a discharge pressure on the pump of
TDH = (60')/(2.31 ft/psi) = 26 IMn^2 (179.1 kPa)
Therefore, the design condition for the rotary lobe pump is 26 gal/min (1.64 L/s) at 26
lb/in
2
(179. IkPa).
- Choose the correct pump for the application
At this point, a rotary lobe pump manufacturers catalog is required in order to choose the
correct pump curve for this application. This is accomplished by choosing a pump per-
formance curve that meets the above design condition. An example of a manufacturers
curve that satisfies the design condition is shown in Fig. 12.
Plotting a horizontal line from 26 gal/min (1.64 L/s) on the left to the 26 lb/in
2
(179.1
kPa) pressure line and reading down gives a pump speed of approximately 175 rpm. This
means that for this pump to deliver 26 gal/min (1.64 L/s) against a pressure of 26 lb/in^2
(179.1 kPa), it must operate at 175 rpm.
The motor horsepower required for the rotary lobe pump is calculated using the fol-
lowing empirical formula (taken from the catalog of Alfa Laval Pumps, Inc. of Kenosha,
WI):
W r (NKSf) (?)(#/)!
HP= ^- [(0.043X^)(P)+ ^- + f^]Hp = Motor horsepower
Af= Pump speed (rpm)
q = Pump displacement, gal/100 revolutions (L/100 revs)
P = Differential pressure or TDH, psi, (kPa)
Sf= Factor related to pump size which is calculated using: Sf= (#)(0.757) + 3
Nf= Factor related to the viscosity of the pumped liquid which is calculated using
Nf= 2.2 ^/Viscosity (cp)The pump speed was found in Fig. 12 to be 175 rpm; the pump displacement is taken
from the pump curve and is 25 gal/100 revs (94.6 L/100 revs); the differential pressure or