Question

Question of Save & Exit Submit It is proposed to run a pump at 880 rpm to pump water at 20°C through the system of the image shown below. The pipe is 20-cm clometer commerciel steel. For water, take p- 998 kg/m and p= 0.0010 kgs. For commercial steel, take=0.046 mm. gamin 2000 4000 3000 10000 192 hoo GB Hit Р. hp 139 12 134 100 B 10 43 m Pume 12 m References ellook & Resources Section Break Oculty Medium 6. Required information 10.00 points What flow rate in ft/min results? Round the final answer to the nearest whole number timin

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

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 = 4 m and Z2 = 11 m

Hp is pump head

Hf = Head loss due to friction  

  Hence, above equation reduces to,

0 + 4 + Hp = 0 + 11 + Hf

=> Hp= 7 + Hf...................................(1)

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

Assume fully developed turbulent flow to determine friction factor, f

f = 1 / [1.14 + 2Log(D/e)]^2

Riughness of steel pipe (e) = 0.046 mm

=> f = 1 / [1.14 + 2Log(200/0.046)]^2

=> f = 0.014

Hence, Hf = 8 (0.014)(40) $Q^2$ / ($\pi^2$ x 9.81 x )

025

=> Hf = 144.74 $Q^2$

Putting values in equation 1,

Hp = 7 + 144.74 $Q^2$

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	7	23
2000	0.126	9.30	30.50
4000	0.252	16.20	53.15
6000	0.378	27.68	90.81
8000	0.504	43.76	143.57
10000	0.63	64.44	211.41

Now plot the system curve on given pump performance curve as shown below :

250 200 150 Hp (ft) -Pump performance curve -System curve 100 50 0 0 2000 4000 6000 8000 10000 12000 Q(gpm)

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

Operating discharge = 5600 gpm or 12.43 cfs or 745.8 $ft^3$ /min