Pumps and Pumping Stations

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• Pumps add energy to fluids and therefore are accounted for in the energy equation

• Energy required by the pump depends on:– Discharge rate– Resistance to flow (head that the pump must overcome)– Pump efficiency (ratio of power entering fluid to power supplied

to the pump)– Efficiency of the drive (usually an electric motor)

2 21 1 2 2

1 22 2pump L

v p v pz H z H

2L f minor f i

vH h h h K

Pump Jargon• (Total) Static head – difference in head between suction

and discharge sides of pump in the absence of flow; equals difference in elevation of free surfaces of the fluid source and destination

• Static suction head – head on suction side of pump in absence of flow, if pressure at that point is >0

• Static discharge head – head on discharge side of pump in absence of flow

Total static head

Static suction head

Static discharge

Pump Jargon• (Total) Static head – difference in head between suction

and discharge sides of pump in the absence of flow; equals difference in elevation of free surfaces of the fluid source and destination

• Static suction lift – negative head on suction side of pump in absence of flow, if pressure at that point is <0

• Static discharge head – head on discharge side of pump in absence of flow

Total static head Static suction

Static discharge

Pump Jargon

Total static head (both) Static suction

Static discharge

Static suction head

Static discharge

Static suction head

Static suction lif

Static discharge head

Static d t

Total static h

ischarge he d

Note: Suction and discharge head / lift measured from pump centerline

Pump Jargon• (Total) Dynamic head, dynamic suction head or lift, and dynamic

discharge head – same as corresponding static heads, but for a given pumping scenario; includes frictional and minor headlosses

Total dynamic

Dynamic suction lift

Dynamic discharge

Energy Line

Example. Determine the static head, total dynamic head (TDH), and total headloss in the system shown below.

Total static head 730 ft 630 ft 100 ft

pd =48 psig

ps =6 psig

El = 630 ft

El = 640 ft

El = 730 ft

2.31 ftTDH 48 6 psi 124.7 ft

TDH Static head 124.7 100 ft 24.7 ftLH

Example. A booster pumping station is being designed to transport water from an aqueduct to a water supply reservoir, as shown below. The maximum design flow is 25 mgd (38.68 ft3/s). Determine the required TDH, given the following:• H-W ‘C’ values are 120 on suction side and 145 on discharge side• Minor loss coefficients are

0.50 for pipe entrance0.18 for 45o bend in a 48-in pipe0.30 for 90o bend in a 36-in pipe0.16 and 0.35 for 30-in and 36-in butterfly valves, respectively

• Minor loss for an expansion is 0.25(v22 v1

Short 30 pipe w/30 butterfly valve

El = 6349 to 6357 ft

El = 6127 to 6132 ft

30 to 48 expansion

4000of 48 pipe w/two 45o bends

8500of 36 pipe w/one 90o bend and eight butterfly valves

1. Determine pipeline velocities from v = Q/A..

v30= 7.88 ft/s, v36= 5.47 ft/s, v48= 3.08 ft/s

2. Minor losses, suction side:230

2 230 48

,minor

Entrance: 0.50 0.49 ft2

Butterfly valve: 0.16 0.16 ft2

Expansion: 0.25 0.21 ft2

Two 45 bends: 2* 0.18 0.05 ft2

0.91 ft

3. Minor losses, discharge side:

,minor

8 Butterfly valves: 8* 0.35 1.30 ft2

One 90 bend: 0.30 0.14 ft2

1.90 ft

2.630.43f

, 2.63

38.74000 2.76 ft

0.43 120 48 /12f suctionh

4. Pipe friction losses:

2.630.43fh Q

, 2.63

38.78500 16.77 ft

0.43 145 36 /12f dischargeh

5. Loss of velocity head at exit:236Exit: 0.46 ft

Static head 6357 6127 ft 230 ft

6. Total static head under worst-case scenario (lowest water level in aqueduct, highest in reservoir):

, ,TDH

230 0.91 1.90 2.76 16.77 0.46 ft

252.8 ft

static L minor f L exitH h h h

7. Total dynamic head required:

Pump Power

• P = Power supplied to the pump from the shaft; also called ‘brake power’ (kW or hp)

• Q = Flow (m3/s or ft3/s)• TDH = Total dynamic head = Specific wt. of fluid (9800 N/m3 or 62.4 lb/ft3 at 20oC)• CF = conversion factor: 1000 W/kW for SI, 550 (ft-lb/s)/hp for US• Ep = pump efficiency, dimensionless; accounts only for pump,

not the drive unit (electric motor)

Useful conversion: 0.746 kW/hp

Example. Water is pumped 10 miles from a lake at elevation 100 ft to a reservoir at 230 ft. What is the monthly power cost at $0.08/kW-hr, assuming continuous pumping and given the following info:

• Diameter D = 48 in; Roughness = 0.003 ft, Efficiency Pe =80%• Flow = 25 mgd = 38.68 ft3/s• T = 60o F• Ignore minor losses

El = 100 ft

10 mi of 48 pipe,

=0.003 ft

El = 230 ft 2

1 2pump

2 Lz H

2 1TDHpump stat L fH z z H H h

TDH stat fH h

El = 100 ft

10 mi of 48 pipe,

=0.0003 ft

El = 230 ft 2

TDH stat fH h

230 100 ft 130 ftstatH

L vh f

/ 3.08 ft/sv Q A

Find f from Moody diagram

3.08 ft/s 4 ftRe 1.01x10

1.22x10 ft /s

40.003 ft7.5x10

El = 100 ft

10 mi of 48 pipe,

=0.0003 ft

El = 230 ft 2

6Re 1.01x1047.5x10

0.0185f

3.08 ft/s10*5280 ft0.0187 36.4 ft

4 ft 2 32.2 ft/sfh

TDH 130 36.4 ft 166.4 ftstat fH h

3 338.68 ft /s 166.4 ft 62.4 lb/ftTDH918 hp

CF ft-lb/s550 0.80

kW $0.08 hrDaily cost 918 hp 0.746 24 $1315 / d

hp kW-hr d

Pump Selection

• System curve – indicates TDH required as a function of Q for the given system– For a given static head, TDH depends only on HL, which is

approximately proportional to v2/2g

– Q is proportion to v, so HL is approximately proportional to Q2 (or Q1.85 if H-W eqn is used to model hf)

– System curve is therefore approximately parabolic

Example. Generate the system curve for the pumping scenario shown below. The pump is close enough to the source reservoir that suction pipe friction can be ignored, but valves, fittings, and other sources of minor losses should be considered. On the discharge side, the 1000 ft of 16-in pipe connects the pump to the receiving reservoir. The flow is fully turbulent with D-W friction factor of 0.02. Coefficients for minor losses are shown below.

K values

Suction Discharge

1 @ 0.10 1 @ 0.12

1 @ 0.12 1 @ 0.20

1 @ 0.30 1 @ 0.60

2 @ 1.00 4 @ 1.00

The sum of the K values for minor losses is 2.52 on the suction side and 5.52 on the discharge side. The total of minor headlosses is therefore 8.04 v2/2g.

An additional 1.0 v2/2g of velocity head is lost when the water enters the receiving reservoir.

The frictional headloss is: 2 2 21000 ft

0.02 152 1.33 ft 2 2f

L v v vh f

D g g g

Total headloss is therefore (8.04+1.0+15.0)v2/2g = 24.04 v2/2g. v can be written as Q/A, and A = D2/ 4 = 1.40 ft2. The static head is 34 ft. So:

TDH 34 ft 24.042

/1.40 ft s34 ft 24.04 34 ft 0.19

ft2 32.2 ft/s

stat L

sTDH 34ft 0.19

0 5 10 15 20 25

Discharge, Q (ft3/s)

Static head

System curve

Pump Selection

• Pump curve – indicates TDH provided by the pump as a function of Q; – Depends on particular pump; info usually provided by manufacturer– TDH at zero flow is called the ‘shutoff head’

• Pump efficiency– Can be plotted as fcn(Q), along with pump curve, on a single graph– Typically drops fairly rapidly on either side of an optimum; flow at

optimum efficiency known as “normal” or “rated” capacity– Ideally, pump should be chosen so that operating point corresponds

to nearly peak pump efficiency (‘BEP’, best efficiency point)

Shutoff head

Rated capacity

Rated hp

Pump Performance and Efficiency Curves

Pump Selection

Pump Efficiency• Pump curves depend on pump geometry (impeller D) and speed

Pump Selection• At any instant, a system has a single Q and a single TDH, so both

curves must pass through that point; operating point is intersection of system and pump curves

Pump System Curve• System curve may change over time, due to fluctuating reservoir levels,

gradual changes in friction coefficients, or changed valve settings.

Pump Selection: Multiple Pumps• Pumps often used in series or parallel to achieve desired pumping

scenario• In most cases, a backup pump must be provided to meet maximum

flow conditions if one of the operating (‘duty’) pumps is out of service.• Pumps in series have the same Q, so if they are identical, they each

impart the same TDH, and the total TDH is additive• Pumps in parallel must operate against the same TDH, so if they are

identical, they contribute equal Q, and the total Q is additive

Adding a second pump moves the operating point “up” the system curve, but in different ways for series and parallel operation

Example. A pump station is to be designed for an ultimate Q of 1200 gpm at a TDH of 80 ft. At present, it must deliver 750 gpm at 60 ft. Two types of pump are available, with pump curves as shown. Select appropriate pumps and describe the operating strategy. How will the system operate under an interim condition when the requirement is for 600 gpm and 80-ft TDH?

Flow rate (gpm)

Pump A onlyPump B only

System curve

, % Pump B

Pump A

200 400 120010008006000

Either type of pump can meet current needs (750 gpm at 60 ft); pump B will supply slightly more flow and head than needed, so a valve could be partially closed. Pump B has higher efficiency under these conditions, and so would be preferred.

Flow rate (gpm)

Pump A onlyPump B only

System curve

, % Pump B

Pump A

200 400 120010008006000

The pump characteristic curve for two type-B pumps in parallel can be drawn by taking the curve for one type-B pump, and doubling Q at each value of TDH. Such a scenario would meet the ultimate need (1200 gpm at 80 ft), as shown below.

Flow rate (gpm)

A onlyB only Two B’s

System curve

, % Pump B

Pump A

200 400 120010008006000

A pump characteristic curve for one type-A and one type-B pump in parallel can be drawn in the same way. This arrangement would also meet the ultimate demand. Note that the type-B pump provides no flow at TDH>113 ft, so at higher TDH, the composite curve is identical to that for just one type-A pump. (A check valve would prevent reverse flow through pump B.) Again, since type B is more efficient, two type-B pumps would be preferred over one type-A and one type-B.

Flow rate (gpm)

System curve

, % Pump B

Pump A

200 400 120010008006000

One A and one B in parallel

At the interim conditions, a single type B pump would suffice.

A third type B pump would be required as backup.T

Flow rate (gpm)

System curve

, % Pump B

Pump A

200 400 120010008006000

One A and one B in parallel

Pumps and Pumping Stations

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