Pump Sizing Calculation Sheet

Objectives -

To calculate the System Differential Pressure To determine the Net Positive Suction Head Avaliable in the system To determine the required Brake Horsepower To select a suitable Motor Horse Power rating for the Pump

Basics -

Diesel Transfer Pumps are positive displacement pumps Specific gravity of Diesel is 0.84 - 0.89; Used value is 0.85 Acceleration due to gravity is 9.81 m/s2 Hydraulic Diameter = 0.0508 m (2 in) Suction Pipe length is 1 m. Discharge pipe length is 4.27 m Discharge Vessel Elevation head is 4 m Specific roughness of pipe material is 0.00004572 m

References 1. API 676: Positive Displacement Pumps, Rotary 2. CRANE: Flow of Fluids Through Valves, Fittings and Pipe

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DEFINITION OF TERMS

∆P - Differential Pressure BHP - Brake Horsepower D

- Hydraulic Diameter

f

- Darcy Friction factor

g

- Gravitational Acceleration

hf - Head losses due to friction hp - Pressure head in vessel HHP - Hydraulic Horse Power hvp - Vapour Pressure Head K - Resistance Coefficients for pipe fittings l - Straight pipe length NPSHa OD

- Net Positive Suction Head Available - Outside Diameter of Pipe

P - Pressure in Vessel Q

- Flow Rate

Re

- Reynold's Number

SG

- Specific Gravity

V - Velocity Z - Elevation Head

ε - Absolute Roughness ѵ - Kinematic Viscosity

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SUCTION SIDE 0.05560 m3/s

Flow Rate (Q)

=

Specific Gravity

=

1

Hydraulic Diameter (D)

=

0.15

m

Suction Head Calculation Suction vessel pressure head (hp) + Elevation head (Z) - Friction Head (hf) Parameters Suction Vessel Pressure

(P)

1.0135 bar

=

Kinematic Viscosity (ν)

=

Specific Roughness (Є)

=

Pipe Length (L)

=

(Atm)

8.01000E-07 m2/s 0.00004572 m 1 m

(below pump suction)

Suction Vessel Pressure Head (hp)

=

10.331

m

Elevation Head

=

1

m

Friction Head Head Loss in Pipe length (m) Average Velocity - V

=

3.146316386 m/s2

Reynolds Number, Re

=

589197.8251

Darcy Friction Factor,f

=

0.016237308

Head loss in pipe length (m)

=

0.055

5

m

Head loss in fittings (m) 0

Reducers

K

=

0

Ball Valves

K

=

0

Elbows

K

=

1

Entrance

K

=

0 1 90Oelbow, 1 45O deg elbow)

0 0.78

Total K for fittings

=

5.78

Total Head loss in fittings

=

0.047

Friction Head Total Suction Head

m =

0.102

m

=

11.229

m

(All formulas used in the calculations above are shown in Appendix 1)

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DISCHARGE SIDE 0.05560 m3/s

Flow Rate (Q)

=

Specific Gravity

=

1

Hydraulic Diameter (D)

=

0.15

m

Discharge Head Calculation Discharge vessel pressure head (hp) + Elevation head (Z) + Friction Head (hf) Parameters Discharge Vessel Pressure (P)

=

1.0135 bar

Kinematic Viscosity (ν)

=

8.01E-07 m2/s

Specific Roughness (ε)

=

Pipe Length (L)

=

(Atm)

0.00004572 200 m

Discharge Vessel Pressure Head

=

10.331

m

Elevation Head

=

200

m

=

10.938

m

=

221.269

m

Friction Head Head Loss in Pipe length (m) Average Velocity - V

=

3.146316 m/s2

Reynolds Number

=

589197.8

Darcy Friction Factor

=

0.016237

=

10.923

Head loss in pipe length (m)

m

Head loss in fittings (m) 3

Elbows

K

=

1.721155

1

Exit

K

=

0.016237

0

Check Valve

K

=

0

1

Ball Valve

K

=

0.048712

Total K for fittings

=

1.786104

Total Head loss in fittings

=

0.015

Friction Head Total Discharge Head

m

(All formulas used in the calculations above are shown in Appendix 1)

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PERFORMANCE REQUIREMENTS Total Dynamic Head

=

Total Discharge Head - Total Suction Head

=

210.040

m

Pressure Differential

=

20.6

bar

Hydrualic Horse Power (HHP)

=

Pump Efficiency

=

75

Brake Horse Power

=

15271.5

67.06667 hp

Rated Horse power

=

17562.2

77.12667 hp

11453.6 kW

50.30000 hp

%

Rated Motor Nameplate HP

Net Positive Suction Head Available (NPSHa) Suction vessel pressure head (hp) + Elevation head (Z) - Friction Head (hf)-Vapour Pressure Head(hvp)

Vapour pressure of liquid

=

0.6

bar

Vapour pressure head of liquid

=

6.116

m

NPSHa

=

5.11

m

(All formulas used in the calculations above are shown in Appendix 1)

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Appendix 1 SUMMARY OF FORMULAE USED Pressure Head (converting from bar to m)

h(m) 

Liquid Velocity

4Q

V 

Reynold's Number

P (bar ) SG  0 .0981

D 2

Re 

VD

f 

64 Re



Darcy Friction factor

when Re< 3000

0 . 25

f 

   5 . 74    ln  3 . 7 D  Re 0 . 9     

(Swamee-Jain solution to Darcy friction formular)

when Re>3000

Friction losses in straight pipe

hf  f

l V2  D 2g

Friction losses in fittings

hf  f

V2 K 2g

hp  Z   h f

Total Head (Suction/Discharge)

P  0.0981 TDH  SG

Differential Pressure

Hydraulic Horsepower (Watts)

HHP  Q  P

Brake Horsepower

BHP 

(P in kPa)

HHP

 1.15  BHP

Rated Horsepower

NPSHa  h p  Z   h f  hvp

Net Positive Suction Head Available

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2

Appendix 2

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