Page 161 - Chemical Process Equipment - Selection and Design

7.2. PUMP THEORY 133

EXAMPLE Some values are
7.2
Operating E’~oin8~ of Single and Double Pumps in Parallel and
Series
The head loss in a piping system is represented by Me equation Q/lOO 0.8 1.0 1.2 1.286
H, 10.88 7.00 2.28 0
H$ = 50 + 4.0(Q/lOO)’ + Hu, 4 59.92

where is the head loss in the control valve. The pump to be used (b) In parallel each pump has half the total flow and the same
has the characteristic cume of the pump of Figure 7.7(b) with an head H,:
8 in. impeller; that curve is represented closely by the equation
50 + 6.0(Q/100)’ = 68 - (0.5/2)(Q/l00) - (4.5/4)(Q/100)’,
I%, = 68 - 0.5(Q/lOO) - 4.5(Q/100)’.
:. Q = 157.2 gpm, H, = 64.83 ft.
The following will be found (see Figure 7.17):
(c) In series each pump has the same flow and one-half the
(a) The values of 1% corresponding to various flow rates Q gpm. total head loss:
(b) The flow rate and head on the pumps when two pumps are
connected in parallel and the valve is wide open (11, = 0). $(50 + 6.0(Q/100)’] = 68 - 0.5(Q/100) - 4.5(Q/lOO)’,
(c) Tihe same as (b) but with the pumps in series. :. Q = 236.1 gpm, H, = 83.44 ft.
(d) The required speed of the pump at 80gpm when no control
valve is used in the line.
Series flow allows 50% greater gpm than parallel.
(a) The operating point is found by equating H, and Hp from
which (d) H, = 50 + 4.8 = 54.8,
H, = (68 - 0.4 - 2.88)(n/1750)’,
& = 68 - 0!.5(Q/lOO) - 4.5(Q/100)’-. [50 + 6.O(Q/lOO)’]. :. n = 1750d5- = 1610 rpm.

mixed units For example, at 3500 rpm, 1000 gpm, and S = 7900, the required
NPSH is 34 ft.
Ns = (rpm)’(g~rn)~.~/(ft)~,~~ (7.12) For common fluids other than water, the required NPSH
usually is lower than for cold water; some data are shown in Figure
For double suction pumps, Q is one half the pump output. 7.16.
The net head at the suction of the pump impeller must exceed a
certain value in order to prevent formation of vapor and resulting
cavitation of the metal. This minimum head is called the net PUMPING SYSTEMS
positive suction head and is evaluated as
The relation between the flow rate and the head developed by a
centrifugal pump is a result of its mechanical design. Typical curves
WPSN = (pressure head at the source) are shown in Figure 7.7. When a pump is connected to a piping
f (static suction head)
- (friction head in the suction line) system, its head must match the head loss in the piping system at
- (vapor pressure of the liquid). (7.13) the prevailing flow rate. The plot of the flow rate against the head
loss in a line is called the system curve. The head loss is given by the
Usually each manufacturer supplies this value for his equipment. mechanical energy balance,
(Some data are in Figure 7.7.) A suction specific speed is defined as

S = (rpm)(gpm)0.5/(NPSM)0.75. (7.14) (7.16)
Standards for upper limits of specific speeds have been
established, like those shown in Figure 7.6 for four kinds of where & is the head loss of a control valve in the he.
pumps. When these values are exceeded, cavitation and resultant The operating point may be found as the intersection of plots
damage to the pump may QCCUT. Characteristic curves correspond- of the pump and system heads as functions of the flow rate. Or an
ing to widely different values of N, are shown in Figure 7.3 for equation may be fitted to the pump characteristic and then solved
several kinds of pumps handling clear water. The concept of specific simultaneously with Eq. (7.16). Figure 7.17 has such plots, and
speed is utilized in Example 7.3. Further data are in Figure 7.6. Example 7.2 employs the algebraic method.
Recommendations also are made by the Hydraulic Institute of In the normal situation, the flow rate is the specified quantity.
suction specific speeds for multistage boiler feed pumps, with With a particular pump curve, the head loss of the system may need
S=7900 for single suction and S=66601 for double suction. Thus to be adjusted with a control valve in the line to make the system
the required NPSW can be found by rearrangement of Eq. (7.14) as and pump heads the same. Alternately, the speed of the pump can
be adjusted to make the pump head equal to that of the system.
NPSH = [(rpm)(gpm)’ 5/S]4”. (7.15) From Eq. (7.9) the relation between speeds and pump heads at two