Hi Friends,
f.Le.V2 Where, e = Surface roughness = 4.5 x 10-5 for Steel i.e. f = 0.01336.
L/D ratio for 45o standard Bend = 16 f.Le.V2 0.01336 x 70328 x (1.38)2
In earlier posts, we have already discussed about NPSHA, head loss due to friction and other useful derivations like empirical formula to estimate the specific gravity of slurry required for various process design and engineering design calculations for Alumina refinery. Now, we have to proceed further to understand the detailed methodology to arrive at motor rating calculations for centrifugal pumps.
In present post, we will discuss the detailed sample calculations for working out the motor rating of a pump discharging raw water from source river or canal to the storage pond of Alumina refinery site. Assumed basic input data and step by step procedures have been elaborated in subsequent paragraphs-
Sample Input Data:-
Elevation of source river / canal = 50 m above MSL
Elevation of Alumina Refinery site = 130 m above MSL
Distance from source plant site = 70 km = 70000 m
Design velocity of water in pipelines = 1.5 - 2.44 m/sec.
Required water supply rate = 1400 m3/hr
Material of pipes and bends = Carbon Steel.
Details of Suction line of pump:-
Length of suction pipe to pump = 20 m
No. of standard 90o elbow = 1
No. of fully open gate valves = 1
Details of pump delivery line up to Plant site:-
Length of delivery pipeline to plant = 70000 m
No. of standard 90o elbow = 5
No. of standard 45o elbow = 20
No. of standard Tee = 1
No. of fully open gate valves = 1
Design of Delivery Line:-
We know that
Discharge = Cross sectional area x velocity
\ Q = A x V
Here, Q = 0.3889 m3/sec. and V = 1.5 m/sec.
\ 0.3889 = p/4 x d2 x 1.5
\ Diameter, d= 0.5746 m
= 5746 mm.
Say, 600 mm NB.
Design of Suction Line:-
Generally suction line is taken one size bigger than delivery.
\Suction line diameter, D = 700 mm NB.
Calculations for Total Head of Raw Water Pump:-
Total head, H = Hd + Hg.
Where, H = Total head to be developed by the pump.
Hd = Delivery Head &
Hg = Gravitational or Static Head.
Suction head is negligible as considered flooded.
Discharge head is also zero, as water will be discharged at atmospheric pressure in raw water storage in plant premises.
Calculations For Static Head-
Static Head = Gravitational Head
= 130 meters – 50 meters
= 80 m.
Calculations For Frictional Head Loss in Delivery Line-
Hfd = -------- .
2.g.d
Where, f = Frictional factor
Le = Equivalent length of delivery line with fittings.
V = Velocity of water in delivery line.
Now, d = 600 mm = 0.6 m
Q = 1400 m3/hr.
Q = A. V
\0.3889 = p /4 x (0.60)2 x V
\ V = 1.38 m/sec.
Now, Reynold number,
Re = r.V.d/m
Where, r = 1000 kg/m3 for water
V = 1.38 m/sec.
m = Dynamic viscosity of water
= 1 centi poise = 1 x 10-3 kg/m3
Re = 1000 x 1.38 x0.6 / (1 x 10-3)
= 828000.
= 8.28 x 105
Since Re > 2200,
Hence the flow of water in delivery line is turbulent.
1.325
Friction factor, f = --------------------------------------
[ln{(e/3.7 d) + (5.74/Re 0.9)}]2
d = Dia. of delivery pipe = 0.60 m
Re = Reynold Number = 8.28 x 105
1.325
\ Friction factor, f = ---------------------------------------------------------
[ln{(4.5x10-5/3.7 x 0.6) + (5.74/8280000.9)}]2
1.325 1.325
f = -------------------------------------------- = ----------
[ln{2.03 x10–5 + 2.71 x 10-5}]2 99.14
Calculations for Equivalent Length-
Straight length of pipe line = 7000 m
L/D ratio for Fully opened Gate valve = 17
Size of Gate valve, D = 0.5 m
No. of Gate Valve in Delivery Line = 1
Equivalent length for Valve, LValve =17 x 0.6 x 1.
\ LValve = 10 m
Equivalent Length of Standard Tee-
L/D ratio for Standard Tee = 60
Size of Standard Tee , D = 0.6 m
No. of Standard Tee in Delivery Line =1
Equivalent length for Std. Tee, LTee = 60 x 0.6 x 1.
\ LTee = 36 m
L/D ratio for 90o standard Bend = 30
Size of 90o standard Bend D = 0.6 m
No. of 90o standard Bend in Delivery Line = 5
Equivalent length for 90o standard Bend = 30 x 0.6 x 5.
\ Lbend90 = 90 m
Size of 45o standard Bend, D = 0.6 m
No. of 45o standard Bend in Delivery Line = 20
Equivalent length for 45o standard Bend Lbend45 = 16 x 0.6 x 20.
\ Lbend45 = 192 m
\Total equivalent Length, Le = 70000 + 10 + 36 + 90 +192 m.
\ Le = 70328 m
\ Frictional Head Loss,
Hfd = -------- = ----------------------------------
2.g.d 2 x 9.81 x 0.6
= 152 m.
\ Total Head = Static Head + Frictional Head.
= 80 m + 152 m = 232 m.
Calculations for Drive Motor Rating:-
Basic Assumptions:
Efficiency of Pump = 75%
Efficiency of Motor = 97%
Water Discharge Rate = 0.3889 m3/sec.
Specific gravity of Water = 1.0
Fluid Power =r .g. Q. H
= 1.00 x 9.81 x 0.3889 x 232 kW.
= 885 kW.
Fluid Power
\Connected Motor = -----------------
hPump x hMotor
885
\Connected Motor = ---------------
0.75 x 0.97
= 1216 kW.
~ 1200 kW.
Thus motor rating of 1200 kW shall be required to be connected with the pump for the purpose.
Trust, the methodology outlined here is simple, systematic and easy to understand and the same can be adopted for working out motor rating for any pump for required duty conditions just by putting the required input parameters.
Please put your views / suggestions / remarks / comments, if any.
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Thanks and regards.
Kunwar Rajendra
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