Lecture Part ‐2
Pump Curves‐Example
A general diagram of open Pumping-Loop Pumping-Loop (Revision- Module 5 Lectures- Pump Sizing). Sizing).
Z2 2
Pex Pin
(Z2- Z1) Z1 1
hlosses
Pex = exit pressure of pump;
( Pex Pin ) g
Pump unit: can be a single pump or multiple pump in combination Submersible pump: pump unit is submerged in inlet/supply tank
= pump total
Qex= Qin
minimum head (m) required = h = hp = (Z2-Z1) + hlosses+
V
2 2
Pump unit combination in series: Qin Pump-A
V 12 = eqn.
Pump-B
Qex= Q A+ QB
2g
Pump unit combination in parallel:
for system resitance curve.
Q A Pump-A
(Z2-Z1) = static delivery head (m);
QB Pump-B
hlosses = total head losses in delivery pipe and fittings (m) = (hf + + hm)
hf = = friction head losses in delivery pipes =
V = flow velocity=
Q A pipe
Q
2 D 4
;
f L V
2
2 g D
, L=total pipe length, D=pipe inner diameter,
f = Darcy-Weisbach friction factor in circular pipe (obtained
from Moody chart, pp.380, “Fluid Mechanics”, F. White, ed. 7)
V
K i , Ki =loss coeff. for each fitting-i 2 g i 2
hm = sum of minor head losses in pipe fittings fi ttings =
Revise- Example 6.16 (pp.406, “ Fluid Mechanic s” , F. White, ed. 7)
Operating or duty point
(Z2-Z1)
Pumps combined in parallel: used when delivery head is right but discharge rate is smaller than required with a single pump. Both pump A and pump B must operate at same Pex (H A=HB) Qex = Q A+B <(Q A+QB) the combined H-Q performance curve is obtained by adding Q A & QB at the same total H. If Pex,A>Pex,B, pump B can not be added in until the operating head is below the shutoff head of pump B. Shutoff head = H when Q=0. Total pump power (in parallel), Q A gH Q B gH P pump A
Operating or duty point
(Z2-Z1)
B
Pumps combined in series: used when discharge rate is right but total head is smaller than required with a single pump. Both pump A and pump B must operate at same Q (Q A=QB) Pex=Pex, A+B<(Pex, A+ Pex,B) H A+B=<(H A+ HB). The combined H-Q performance curve is obtained by adding H A & HB at the same Q. Total pump power (in series), QgH A QgH B P pump A
B
Figure: Performance and operating/duty points of two pumps operating singly and (a) in parallel or (b) in series (source: pp.803, Fig. 11.19, “Fluid Mechanics”, F. White, ed. 7). In the figures, H=hp for the system resistance curve.
Class Example (a) Fundamental equations:
Dams open to atmosphere Given ( ) Flow Rate (l/s)
Reynolds Num
Friction Factor
hf
hp
0
0
0
0
8
15
2.32 x 105
0.0178
3.56
11.56
30
4.65 x 105
0.0165
13.24
21.24
45
6.97 x 105
0.0158
28.52
36.52
Pump Curve vs System Resistance Curve 50 45 40 35 30
) m ( d25 a e H
Pump Curve - 1 Pump
20 Pump Curve - 2 pumps in Series
15
System Resistance Curve
10 5 0 0
10 20 30 40 50 60 70 80 90 100 110 120 130 140
Flow (l/s)
Pumps in Series (b) Expected duty point at 44l/s Power consumed: 17.96kW for both pumps 8.98kW per pump (c) Discharge isolation valve Non return valve Requirement for maintenance Prevention of reverse flow through th e pump during a sudden shutdown
Additional Information: Outer diameter
0.09
m
Wall thickness
0.004
m
Area
0.00528
m2
Gravity
9.81
m/s2
Density
998
kg/m3
Viscosity Efficiency
0.001
kg/(ms)
0.85
Static Head
8
m
Pipe Length
40
m
Steel Pipe, old Pipe factor
0.025
mm
Pump Curve head (one pump) m
flow m3/s 0
21
42
0.01
21
42
0.02
21
42
0.03
20.5
41
0.04
19
38
0.05
15
30
0.06
10
20
0.07 3
Flow (m /s)
head (two pumps) m
Rel. Roughness
5 Reynolds Number
Velocity
10 Friction Factor
hf
hs
htot
power
0
0.000304878
0
0.00E+00
0
0.00
8
8.00
0.00
0.005
0.000304878
0.95
7.75E+04
0.02
0.45
8
8.45
0.49
0.01
0.000304878
1.89
1.55E+05
0.019
1.69
8
9.69
1.12
0.015
0.000304878
2.84
2.32E+05
0.01775
3.56
8
11.56
2.00
0.02
0.000304878
3.79
3.10E+05
0.017
6.06
8
14.06
3.24
0.025
0.000304878
4.73
3.87E+05
0.0168
9.36
8
17.36
5.00
0.03
0.000304878
5.68
4.65E+05
0.0165
13.24
8
21.24
7.34
0.035
0.000304878
6.63
5.42E+05
0.0162
17.69
8
25.69
10.36
0.04
0.000304878
7.57
6.20E+05
0.016
22.82
8
30.82
14.20
0.045
0.000304878
8.52
6.97E+05
0.0158
28.52
8
36.52
18.93
