Centrifugal Pumps Viscosity

Overview

Engineering reference data for Centrifugal Pumps Viscosity in pumps.

Key Formulas

Pump Power

$P = \frac{Q \cdot H \cdot \rho \cdot g}{\eta}$

Hydraulic power / efficiency.

NPSH Available

$NPSH_a = \frac{P_s}{\rho g} + \frac{v_s^2}{2g} - \frac{P_v}{\rho g}$

Net Positive Suction Head available.

Affinity Laws

$Q \propto n, \quad H \propto n^2, \quad P \propto n^3$

Flow, head, power vs speed.

Variables

Viscosity Effects on Pump Performance

When a centrifugal pump handles fluids with higher viscosity than its design conditions, several performance characteristics change:

• Brake horsepower requirement increases — more power is needed to overcome viscous friction
• Head generated is reduced — viscous losses decrease the total dynamic head
• Capacity is reduced — flow rate decreases compared to water performance
• Efficiency is reduced — energy losses increase with viscosity
• Best Efficiency Point (BEP) shifts — the operating point of maximum efficiency moves

These effects can be quantified using viscosity correction coefficients applied to the original pump curve data.

Viscosity Correction Formulas

The head, flow, and efficiency with fluids of different viscosities can be calculated using correction coefficients:

Compensated Flow:

$q_v = c_q \cdot q$

Compensated Head:

$h_v = c_h \cdot h$

Compensated Efficiency:

$\mu_v = c_\mu \cdot \mu$

Compensated Power (SI units):

$P_v = \frac{q_v \cdot h_v \cdot \rho_v \cdot g}{3.6 \times 10^6 \cdot \mu_v}$

Compensated Power (Imperial units):

$P_v = \frac{q_v \cdot h_v \cdot SG}{3960 \cdot \mu_v}$

The viscosity correction coefficients ($c_q$, $c_h$, $c_\mu$) are determined from hydraulic institute charts or empirical correlations based on the fluid viscosity and pump impeller size. These coefficients are always less than or equal to 1.0, indicating reduced performance with viscous fluids.

Impact of Viscosity on Centrifugal Pump Performance

When handling more viscous fluids, centrifugal pumps experience:

• Increase in brake horsepower requirement
• Reduction in generated head
• Reduction in capacity (flow rate)
• Reduction in efficiency
• Shift of the Best Efficiency Point (BEP)

Viscosity Correction Formulas

The following correction formulas adjust pump performance parameters for viscous fluids:

Flow Correction

$q_v = c_q \cdot q$

Where:

• $q_v$ = flow compensated for viscosity (m³/h, gpm)
• $c_q$ = viscosity flow coefficient
• $q$ = original flow according to pump curve (m³/h, gpm)

Head Correction

$h_v = c_h \cdot h$

Where:

• $h_v$ = head compensated for viscosity (m, ft)
• $c_h$ = viscosity head coefficient
• $h$ = original head according to pump curve (m, ft)

Efficiency Correction

$\mu_v = c_\mu \cdot \mu$

Where:

• $\mu_v$ = efficiency compensated for viscosity
• $c_\mu$ = viscosity efficiency coefficient
• $\mu$ = original efficiency according to pump curve

Power Correction (SI Units)

$P_v = \frac{q_v \cdot h_v \cdot \rho_v \cdot g}{3.6 \times 10^6 \cdot \mu_v}$

Where:

• $P_v$ = power compensated for viscosity (kW)
• $\rho_v$ = density of viscous fluid (kg/m³)
• $g$ = acceleration of gravity (9.81 m/s²)

Power Correction (Imperial Units)

$P_v = \frac{q_v \cdot h_v \cdot SG}{3960 \cdot \mu_v}$

Where:

• $P_v$ = power compensated for viscosity (bhp)
• $SG$ = specific gravity of viscous fluid

Key Effects of Viscosity on Pump Operation

When handling a more viscous fluid, a centrifugal pump's performance is altered in several critical ways:

• Brake horsepower requirement increases
• Generated head is reduced
• Capacity (flow rate) is reduced
• Pump efficiency is reduced
• The Best Efficiency Point (BEP) shifts

Viscosity-Compensated Power Equations

Power (SI Units)

$P_v = \frac{q_v \cdot h_v \cdot \rho_v \cdot g}{3.6 \times 10^6 \cdot \mu_v}$ Where:

• $P_v$ = Power compensated for viscosity (kW)
• $q_v$ = Flow compensated for viscosity (m³/h)
• $h_v$ = Head compensated for viscosity (m)
• $\rho_v$ = Density of viscous fluid (kg/m³)
• $g$ = Acceleration due to gravity (9.81 m/s²)
• $\mu_v$ = Efficiency compensated for viscosity (decimal)

Power (Imperial Units)

$P_v = \frac{q_v \cdot h_v \cdot SG}{3960 \cdot \mu_v}$ Where:

• $P_v$ = Power compensated for viscosity (bhp)
• $q_v$ = Flow compensated for viscosity (gpm)
• $h_v$ = Head compensated for viscosity (ft)
• $SG$ = Specific gravity of the viscous fluid

References

• Original Source