Question

A 38-in pump is installed for the system below. The pipe (100-cm diameter) has a friction factor of 0.012 and a total length of 20 km. Given that Ke = 0.5 (pipe entrance) and Ke = 1.0 (pipe exit). For water at 80 degrees Fahrenheit, estimate the flow rate (in grm), the power required (in horsepower, HP), and the net positive suction head required (in ft) to avoid cavitation for the system when the pump running. Elevation = 180 m Elevation = 150 m 20 km (Pump 100 cm The measured performance curves of the pump are shown below: n= 710 r/min 400 25 NPSH 20 350 —41)-in dia. Hoe NPSH, ft 15 80% 84% %88 %98 10 300 38-in dia. %68 Total head, ft -88% 250 -35-in dia. 86% +84% 200 1500 bhp * 150 1000 bhp 1250 bhp 100 0 4 8 28 12 16 20 24 U.S. gallons per minute x 1000

Answer 1

Ans) Apply Bernoulli equation between point 1 and 2 located at water surface elevation of lower and upper reservoir respectively,

P1/$\gamma$ +
V1
/ 2g + Z1 + Hp = P2/$\gamma$ +
V22
/ 2g + Z2 + Hf + Hm

Since,both point 1 and 2 are open to atmosphere, pressure is only atmospheric,hence gauge pressure, P1 = P2 = 0

Velocity at surface is negligible so, V1 = V2 = 0

Elevation, Z1 = 150 m and Z2 = 180 m

Hp is pump head

Hf = Head loss due to friction  

Hm is minor head loss due to entry and exit

  Hence, above equation reduces to,

0 + 150 + Hp = 0 + 180 + Hf

=> Hp= 30 + Hf...................................(1)

Also, Hf = 8 f L $Q^2$ / ($\pi^2$ g $D^5$ )

=> Hf = 8(0.012)(20000) $Q^2$ / ($\pi^2$ x 9.81 x $1^5$ )

=> Hf = 19.85 $Q^2$

Also, Hm = (
entry
+
rit
) $Q^2$ / 2 g
1

Area of pipe (A) = ($\pi$/4)($1^2$) = 0.785 sq.m

=> Hm = (0.5 + 1)$Q^2$ / (2 x 9.81 x )

0.7852

=> Hm = 0.124 $Q^2$

Putting values in equation 1,

=> Hp = 30 + 19.85 $Q^2$ + 0.124 $Q^2$

=> Hp = 30 + 20 $Q^2$

The above equation is system head curve equation where Q is in m3/s and Hp is in meter

Q (gal/min)	Q (m3/s)	Hp (m)	Hp (ft)
0	0	30	98.42
8000	0.50	35	114.83
16000	1	50	164
24000	1.51	75.6	248
28000	1.76	91.95	301.6

Now plot the system curve on given pump performance curve for 38 in impeller diameter as shown below :

350 300 250 Hp (ft) 200 -Pump performance curve -System curve 150 100 0 4000 8000 12000 16000 20000 24000 Q(gpm)

Now,

We know the point of intersection of performance curve and system curve is operating point.Hence,

Operating flowrate = 21000 gpm or 46.62 cfs

Similarly, horsepower corresponding to operating point = 1250 hp

NPSH corresponding to operating point = 17 ft