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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

- - 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, Rotary2. CRANE: Flow of Fluids Through Valves, Fittings and Pipe

Acceleration due to gravity is 9.81 m/s2

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DEFINITION OF TERMS

∆P - Differential Pressure

BHP - Brake Horsepower

D - Hydraulic Diameter

f - Darcy Friction factor

g - Gravitational Acceleration

- Head losses due to friction

- Pressure head in vessel

HHP - Hydraulic Horse Power

- Vapour Pressure Head

K - Resistance Coefficients for pipe fittings

l - Straight pipe length

NPSHa - Net Positive Suction Head Available

OD - 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

hf

hp

hvp

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SUCTION SIDE

Flow Rate (Q) = 0.05560

Specific Gravity = 1

Hydraulic Diameter (D) = 0.15 m

Suction Head Calculation

Parameters

Suction Vessel Pressure (P) = 1.0135 bar (Atm)

= 8.01000E-07

= 0.00004572 m

Pipe Length (L) = 1 m (below pump suction)

= 10.331 m

Elevation Head = 1 m

Friction Head

Head Loss in Pipe length (m)

Average Velocity - V = 3.146316386

Reynolds Number, Re = 589197.8251

Darcy Friction Factor,f = 0.016237308

Head loss in pipe length (m) = 0.055 m

Head loss in fittings (m)

0 Reducers K = 5

0 Ball Valves K = 0

0 Elbows K = 0

1 Entrance K = 0.78

Total K for fittings = 5.78

Total Head loss in fittings = 0.047 m

Friction Head = 0.102 m

Total Suction Head = 11.229 m

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

m3/s

Suction vessel pressure head (hp) + Elevation head (Z) - Friction Head (hf)

Kinematic Viscosity (ν) m2/s

Specific Roughness (Є)

Suction Vessel Pressure Head (hp)

m/s2

1 90Oelbow, 1 45O deg elbow)

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DISCHARGE SIDE

Flow Rate (Q) = 0.05560

Specific Gravity = 1

Hydraulic Diameter (D) = 0.15 m

Discharge Head Calculation

Parameters

Discharge Vessel Pressure (P) = 1.0135 bar (Atm)

= 8.01E-07

= 0.00004572

Pipe Length (L) = 200 m

Discharge Vessel Pressure Head = 10.331 m

Elevation Head = 200 m

Friction Head

Head Loss in Pipe length (m)

Average Velocity - V = 3.146316

Reynolds Number = 589197.8

Darcy Friction Factor = 0.016237

Head loss in pipe length (m) = 10.923 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 m

Friction Head = 10.938 m

Total Discharge Head = 221.269 m

m3/s

Discharge vessel pressure head (hp) + Elevation head (Z) + Friction Head (hf)

Kinematic Viscosity (ν) m2/s

Specific Roughness (ε)

m/s2

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(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) = 11453.6 kW 50.30000 hp

Pump Efficiency = 75 %

Brake Horse Power = 15271.47 67.06667 hp

Rated Horse power = 17562.19 77.12667 hp

Rated Motor Nameplate HP

Net Positive Suction Head Available (NPSHa)

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)

Suction vessel pressure head (hp) + Elevation head (Z)

- Friction Head (hf)-Vapour Pressure Head(hvp)

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Appendix 1

SUMMARY OF FORMULAE USED

Pressure Head(converting from bar to m)

Liquid Velocity

Reynold's Number

when Re< 3000Darcy Friction factor

(Swamee-Jain solution to Darcy friction formular)

when Re>3000

Friction losses in straight pipe

Friction losses in fittings

Total Head (Suction/Discharge)

Differential Pressure

Hydraulic Horsepower (Watts)

Brake Horsepower

Rated Horsepower

Net Positive Suction Head Available

h(m)=P (bar )

SG×0 .0981

f=64Re

h f=flD

⋅V2

2 g

h f=fV 2

2g⋅∑ K

h p+Z−∑ hf

ΔP=0.0981×TDH×SG

HHP=Q×ΔP (ΔP in kPa )

BHP=HHPη

1 .15×BHP

NPSHa=hp+Z−∑ h f−hvp

f=0 .25

[ ln( ε3 .7D

+ 5 .74Re0.9 )]

2

V=4Q

πD2

Re=VDν

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Appendix 2