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Centrifugal pump Calculations

Formulas & Calculations

How to Calculate...

  • Head Calculation
  • Hydraulic power calculation
  • Pump Shaft Power
  • Electrical Power
  • Specific Speed
  • Centrifugal Pump Calculations Energy loss in discharge valve throttling
  • NPSHa - Net Positive Suction Head Available
  • Head ↔ Pressure
  • Volumetric flow ↔ Mass flow
  • Break Power Calculation

Formulas

Head

Head is net work done for unit weight of water.

Head of pump

H = Head ; Unit - Meter
P = Water Pressure ; Unit - kPa, psi
Γ = Specific weight of Fluid ; Unit - kN/m³
V = Water Velocity ; Unit - m/s
g = Gravitional force ; Unit = m/s² Value = 9.8m/s²
Z = Elevation to be lift

Horizontal pump - Datum is a horizontal plane from center line of shaft

Vertical pump - Datum is horizontal plane of impeller eye.

See calculations

Pump Capacity ( Volume flow rate of pump)

Capacity is the amount of water pumped per unit time.

Capacity Q = A V

A = Area of pipe
V = Volume flow rate

See calculations

Hydraulic power calculation

Hydraulic power calculation

⍴ = densityGravitional force of fluid ; Unit = kg/m³
g = Gravitional force ; Unit = m/s² Value = 9.8m/s²
H = Total Head = Hd - Hs; Unit = m
Hd = Discharge head
Hs = Suction head
Q = Discharge flow ; Unit = m³/hour

See calculations

Pump Shaft Power

Pump shaft power calculation
ηpump = Pump efficiency

Maximum shaft power 

Mmax = ɑ1 ⍴ g H Q / η0

See calculations

Electrical Power

Pump power requirements
ηmotor = Motor efficiency

See calculations

Pump Efficiency

Pump efficiency

WP = Water Power; Unit - kW
BP = Break Power [Shaft power - Power input to the pump shaft] ; Unit - kW

See calculations

Specific speed

Pump performance derivation by Pump speed, Design capacity and head.

Ns = Specific speed; Unit - RPM
N = pump speed; Unit - RPM
Q = pump design capacity
H = Head ; Unit - RPM

Pumps have similar performance and speed regardless of their sizes.

See calculations

NPSHa - Net Positive Suction Head Available


NPSHa - Net Positive Suction Head Available



BP = Barometric Pressure [meter of water]




VPw = Vapour pressure of water; Unit = m.
(H1)s = Head loss due to pipe friction in the suction line; Unit = m.
(M1)s = Minor losses in suction line; Unit = m.
VHs = Velocity head in suction line; Unit = m.
SL = suction line side lift; Unit = m.
DD = drawdown; Unit = m.
h= elevation above sea level; Unit = m.
K1, K2 = Unit constants
BP in m of water if h in meter
K1 = 10.33 and K2 = 5.55 * 10⁻⁸
BP in m of water if h in ft
K1 = 33.89 and K2 = 1.69 * 10⁻⁸


Head ↔ Pressure

Head ↔ Pressure

P = Pressure, PSI
SG – Specific gravity

Volumetric flow ↔ Mass flow


Q – Volumetric flow rate, 
M – Mass flow rate
SG - Specific gravity

Motor input current ↔ Power

P = Power, kW

Seal box pressure



System Head Calculation

Hs = SL+ DL + DD + Hi + Mi + H0 + VH

Hs = System head, m
SL =  Suction side lift, m
DL = Discharge side lift, m

DL = Eu - Ep

Eu = Elevation of the point of delivery
Ep = Elevation of pump

DD = Water source drawdown, m
Hi = Head loss due to pipe friction, m
Mi = Minor losses through fittings, m
H0 = Operating head, m
VH = Velocity head, m

VH = Q2 / KD4

Q = Flow, m3/hr
D = Discharge pipe dia, m
k = Constant [ 435.7 ]

Centrifugal Pump Calculations Energy loss in discharge valve throttling


Thanks for reading - Centrifugal pump Calculations
Naitik Patel
Industrial Guide

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