Question

1. You are designing a pumping station and have been asked to size and select a pump from 2 models. The system step is as follows: the discharge line is a 21-inch diameter PVC pipe with an assumed constant friction factor of f 0.014. The length of the piping is 2300 ft with an elevation gain of 40 ft and an exit loss (K-1.0).. The pump station is located near sea level and the temperature of the flow stream is 50 degrees F. The 2-ft diameter PVC suction pipe is expected to be approximately 40 ft long (-0.014) and will contain 3 elbows (minor loss, K 0.9/elbow) and a square edge entrance (K 0.5). The electric motor's efficiency is 83%. Find: A From the attached 2 pump performance curves, select a suitable pump and impeller. (State any assumptions and state the crieria used for selecting a given pump and impeller). Draw your system curve on each pump curve. B) Determine the flow rate in the system with the pump you selected. C) What is the total head that the pump adds to the system (water horsepower) ? D) What is the efficiency of the pump? E) At the efficiency you found in part D, what is the minimum horsepower requirement of the motor (ie: what is the brake horsepower) What is the line power required (in kW) for the motor? If the cost of electricity is $0.07/kWh (kilowatt hour), what is the cost of operation for each pump for one-year if it operates on average 10 hours a day? F) G) H) Water is often sold in units of volume. What is the pump's power cost for pumping 10,000 gallons? I) Relative to the water surface, were can the pump be placed (think NPSH)? A centrifugal pump is installed to deliver water from a reservoir with a water surface elevation of 20 ft to another reservoir with a water elevation of 110 ft. The pipe is cast iron (assume f 0.022). Neglect minor losses. The diameter of the pipe is 10 inches and the length is 2000 ft. Given the following data from the pump curve 2. 1500 2500 190 170 110 Find: A) an equation for the pump curve B) an equation for the system curve C) the operating point of the system

Answer 1

ANS:::

as for given data

1) Let the system flow rate be Q gpm

Dia of suction pipe= 2 ft

Pump suction pipe area

$\small A_1=\frac{\pi}{4}D_1^2=\frac{\pi}{4}(2^2)=3.142\: ft^2$

Velocity at pump suction

0.00222800.000704Q ft/s หุ่ A1

Dia of pump discharge D₂= 21 in=1.75 ft

Pump discharge pipe area

Аз-TD5 ( 1.752-2.405 ft2

Velocity at pump discharge

00220.000926Q jtls -= 0.000926Q ft/s V2

Pipe length of suction pipe

L₁= 50 ft

Total minor loss K value for suction pipe

K₁= 3x0.9+0.5=2.75

Hence frinction drop in suction pipe is

L1 0.000704202 ) = 2.368 × 10-8 Q2ft hf,-(fDİ +K)( 1)-[]0. 014(40 +2.75](0.00070422

Pipe length of discharge pipe

L₂=2300 ft

Minor K of discharge pipe

K₂= 1

Hence friction loss in discharge pipe is

2300009262.587 し2 ю, , ,1, 1.75 -2.587 x 10- Q2ft x10-o ft

Hence total friction loss is

h f-h f1 + h f2-2.824 x 10-1 Q2 ft

The static head gain is z=40 ft

Hence pump total head is(static head +friction head, velocity head is negligible)

H = h f + 2.824 x 10-1 Q2 + 40 ft

We create a table for Q vs H(system resistance) for flow between 0 to 9000 gpm and plot the same on pump Q-H curve

The table is given below:

Q, gpm H,ft C) 섹) 40.28 200041.13 42.54 44.52 5000 47.06 50.17 53.84 58.07 900062.87 생(XX) AKK) 汝XX) 123456789

The superimposed plot is given below(in blue color):

(-) HYDRAULIC END EFRENCY饲AND ㈠POMER LMS (FT) 160 150 140 10 120 10 100 90 70 60 50- 40 30 20 10- 20 200 hp (820 motor 177 hp (820 moto 134 hp (820 moto 60 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 USGPH

From the above plot we see that the intersection of system resistance curve and pump curve for impeller diameter 490 mm gives the maximum pump efficiency (82%) . Hence we select 490 mm impeller diameter.

b) From the intersection of system resistance curve with pump head flow curve, we see that system flow is

Q=6250 gpm

c) From the intersection of pump head capacity curve with system resistance curve, the operatig head of the pump is

H=53 ft

We assume that water is being pumped(density=1.94 slug/ft³ at 50⁰F)

The fluid power(water horse power) is

WHP-0. 002228 QH ρg/550-0. 002228 (6250) ( 1.94) (32. 174)/550-83, 76 hp

d) From the intersection of system resistance curve with pump Q-H curve, the pump efficiency is 82%.

e) The motor break horse power is

BHPWHP 83.76 WHP 83.76 102.14 hp

f) The line power(motor power) is given by

BHP102.14 MHP_ 120.17 hp 89.64kW η motor

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