# Centrifugal Pumps and Viscosity

## When a liquid flow through a pump, hydrodynamic losses depends on fluid viscosity

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When a viscous fluid is handled by a centrifugal pump

- brake horsepower requirement increases
- the head generated is reduced
- capacity is reduced
- efficiency of pump is reduced and the Best Efficiency Point -
*BEP*- is moved

The head, flow and capacity at other viscosities than used in the original documentation can be modifying with coefficients.

### Flow

q_{v }= c_{q}q (1)

where

q_{v}= flow compensated for viscosity (m^{3}/h, gpm)

c_{q}= viscosity flow coefficient

q = original flow according pump curve (m^{3}/h, gpm)

### Head

h_{v }= c_{h}h (2)

where

h_{v}= head compensated for viscosity (m, ft)

c_{h}= viscosity head coefficient

h = original head according pump curve (m, ft)

### Efficiency

μ_{v }= c_{μ}μ (3)

where

μ_{v}= effciency compensated for viscosity

c_{μ}= viscosity efficiency coefficient

μ = original efficiency according pump curve

### Power - SI units

P_{v }= q_{v}h_{v}ρ_{v}g / (3.6 10^{6}μ_{v}) (4)

where

P_{v}= power compensated for viscosity (kW)

ρ_{v}= density of viscous fluid (kg/m^{3})

g = acceleration of gravity (9.81 m/s^{2})

### Power - Imperial units

P_{v }= q_{v}h_{v}SG / (3960 μ_{v}) (5)

where

P_{v}= power compensated for viscosity (bhp)

SG = specific gravity of viscous fluid

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