CENTRIFUGAL PUMP POWER GUIDE
Quick answer: For a centrifugal pump at the same flow, head and efficiency, a denser liquid requires more hydraulic and shaft power. Specific gravity also changes the pressure represented by a given head, while the pump’s head remains a head quantity. This simplified comparison assumes viscosity and the actual operating point are otherwise comparable.
Specific gravity is easy to omit when a water performance curve is used for a chemical duty. The omission does not simply change a unit conversion. At a given centrifugal pump head, density changes the differential pressure and the hydraulic power transmitted to the liquid. A motor check based only on water can therefore understate the shaft load for a denser sulfuric acid or caustic soda solution.
The engineering task is to keep head, pressure and power distinct, then use density at the actual concentration and temperature. This article explains that relationship and provides a controlled comparison. It does not duplicate the site’s calculator or select a motor from one illustrative duty point.
Specific Gravity vs Density: What Pump Engineers Actually Need
Specific gravity is a dimensionless ratio between a liquid’s density and the density of a reference fluid, normally water at a stated reference condition. Density has units, such as kilograms per cubic metre. The hydraulic power equation uses density, so the calculation must ultimately use a consistent density value even when specific gravity is the convenient input.
For many liquid-pump calculations, engineers use SG to scale from a water density basis. That shortcut is only meaningful when the reference basis and process condition are clear. Concentration and temperature both affect sulfuric acid and sodium hydroxide density. A value copied from a product name without its concentration and temperature can introduce a material power error.
Use the process data sheet or a reliable property source for the actual solution. If the liquid is a mixture, contains solids or changes composition during a batch, document which density controls normal operation and which condition may control maximum shaft power.
Does Specific Gravity Change Centrifugal Pump Head?
A centrifugal pump is characterized by head, not by a fixed pressure rise. For the same pump geometry and speed, and for liquids with broadly comparable viscosity, the head curve is not simply multiplied by specific gravity. The pressure rise corresponding to that head does change with density, and the hydraulic power required at a given flow and head changes with density as well.
Head represents energy per unit weight of liquid and is commonly expressed in metres or feet of liquid. Differential pressure is related to density through Δp = ρgH. Therefore the same 30 m head corresponds to a larger pressure rise for a higher-density liquid than for water.
| Quantity | At the same pump geometry, speed and comparable viscosity | Role of density / SG |
|---|---|---|
| Head, H | The head curve is treated as a head quantity | Not simply multiplied by SG |
| Pressure rise, Δp | Changes for the same head | Increases in direct proportion to density |
| Hydraulic power, Phyd | Changes for the same flow and head | Increases in direct proportion to density |
| Shaft power, Pshaft | Depends on hydraulic power and pump efficiency | Higher when density rises if Q, H and efficiency are held constant |
This distinction is supported by the KSB engineering definitions of pump head and pump power output. In real chemical service, viscosity, system resistance and the selected operating point can also change, so the head-versus-SG rule is only one part of the selection.
How Specific Gravity Changes Pump Power
Hydraulic power is the useful power transferred to the liquid. In SI units, a convenient relationship is:
Phyd — hydraulic power, W
ρ — liquid density, kg/m³
g — gravitational acceleration, m/s²
Q — flow rate, m³/s
H — total head, m
Shaft power accounts for pump efficiency. Electrical input is higher again when driver efficiency and other relevant losses are included.
U.S. Customary BHP Formula
Q — flow rate in U.S. gallons per minute (GPM)
H — total dynamic head in feet (ft)
SG — specific gravity relative to water
ηpump — pump efficiency entered as a decimal
Engineering Note: Enter pump efficiency as a decimal. For example, use 0.70 for 70% efficiency.
Metric Engineering Formula
Q — flow rate, m³/h
H — total dynamic head, m
SG — specific gravity
ηpump — pump efficiency as a decimal
This formula estimates pump brake horsepower at the stated duty. Confirm the liquid properties, actual pump curve, efficiency basis and full operating range before selecting a motor.
These quantities should not be mixed. Hydraulic power describes the output to the liquid. Shaft power, often discussed as brake horsepower or BHP in U.S. customary work, is the mechanical input required by the pump. Electrical input is what the motor and supply deliver. A motor-selection decision must use the applicable shaft load, motor characteristics, operating range, startup requirement and project specification.
When Q, H and pump efficiency are held constant, density is the only changing term in this simplified comparison. Power therefore scales approximately in direct proportion to density or SG. That proportionality is useful for understanding risk, but it does not establish the final pump efficiency or motor rating for an actual chemical duty.
Use the calculator for an auditable duty check. Enter flow, head, density and efficiency with a clear source basis; then review the operating range before selecting equipment.
Worked Example: Same Duty, Three Liquid Densities
The following illustration holds flow, head and pump efficiency constant. It isolates the effect of density so the comparison is easy to audit. It does not claim that one real pump would retain 70% efficiency on all three liquids.
Density Correction Is Not Viscosity Correction
Specific gravity scales the ideal hydraulic power term at a controlled duty. Viscosity can change the pump curve, efficiency, flow, head and shaft load. Use the viscosity correction guide for ANSI pumps and the actual operating point before final motor selection.
- Flow: 100 m³/h
- Head: 30 m
- Pump efficiency: 70%
- Gravitational acceleration: 9.80665 m/s²
- Water comparison: SG 1.0000
- 50% diaphragm-grade NaOH example: SG 1.5372 from the OxyChem handbook basis
- 98.0 wt% H2SO4 example: SG 1.8437 at the Veolia table’s 60/60°F basis
| Fluid / example | SG used | Hydraulic power | Shaft power at 70% |
|---|---|---|---|
| Water baseline | 1.0000 | 8.17 kW | 11.67 kW |
| 50% NaOH example | 1.5372 | 12.56 kW | 17.95 kW |
| 98% H2SO4 example | 1.8437 | 15.07 kW | 21.52 kW |
At identical flow, head and assumed efficiency, the 50% NaOH example requires about 1.5372 times the water hydraulic and shaft power. The 98% H2SO4 example requires about 1.8437 times the water values. This is why a water-duty motor check cannot automatically be reused for a denser process liquid.
Mandatory selection boundary: This is a controlled comparison, not a pump or motor selection. Real selection must use the actual fluid density at operating conditions, verified pump efficiency and curve, viscosity effects where relevant, the full operating range, startup conditions, driver requirements and project specifications.
Sulfuric Acid Specific Gravity: Concentration and Temperature Matter
A single “sulfuric acid specific gravity” value is not technically complete. Veolia’s sulfuric acid technical information provides concentration-specific data and temperature allowances for high-concentration acid. In its 60/60°F table basis, 98.0 wt% H2SO4 has a specific gravity of 1.8437.
| Example | Specific gravity | Reference condition | Use in this article |
|---|---|---|---|
| 98.0 wt% H2SO4 | 1.8437 | Veolia Table 3, 60/60°F basis | Controlled power comparison only |
The source table also shows that neighboring high concentrations do not follow a simple linear trend, and it provides temperature allowances. That is a useful warning against treating SG as a permanent label for the chemical. Request or verify the property at the concentration and temperature used in the pump duty.
Density also affects pressure interpretation. A gauge differential converted to head must use the process-liquid density, while a head requirement converted to pressure must use the same basis. Record the conversion basis on the duty sheet so that procurement, engineering and the pump supplier are reviewing the same quantity.
Caustic Soda Specific Gravity: Why Concentration and Temperature Matter
The OxyChem Caustic Soda Handbook includes density tables and a graph of specific gravity for aqueous caustic soda solutions. The information shows that sodium hydroxide specific gravity varies with concentration and temperature. In the handbook’s dilution example, 50% diaphragm-grade NaOH uses SG 1.5372, taken from its density table basis.
| Example | Specific gravity | Source basis | Use in this article |
|---|---|---|---|
| 50% diaphragm-grade NaOH | 1.5372 | OxyChem handbook table/example basis | Controlled power comparison only |
For an actual caustic soda pump duty, use the specified solution concentration and operating temperature. A dilution system can see several concentrations and a temperature rise, so the normal density and the highest credible power condition may not be the same event. Viscosity and vapor-pressure data may also be needed for the complete pump selection.
Why a Water Test Can Understate Process-Liquid Motor Load
Water testing remains valuable. It can demonstrate a pump’s head-flow performance, efficiency and acceptance data on the stated test basis. The problem arises when the water test is treated as if it were the absorbed-power result for a denser chemical without translation.
| Review stage | Question to answer |
|---|---|
| Water test | Does the tested pump produce the required head and flow on the stated test configuration? |
| Process-liquid translation | What pressure and hydraulic power correspond to that head at the actual density? |
| Curve and efficiency review | Where will the process system operate, and what pump efficiency applies there? |
| Motor review | What is the maximum credible shaft load across normal, startup and permitted operating conditions? |
The commissioning or replacement workflow should therefore preserve the tested curve, impeller diameter, speed and efficiency basis, then apply actual liquid properties and the process system curve. If measured motor load is unexpectedly high or pressure is low, use a structured pump performance troubleshooting sequence rather than attributing the symptom to specific gravity alone.
Specific Gravity Is Not the Only Correction
Density explains the direct pressure and power scaling in the controlled example, but real chemical-pump performance can depart from the water comparison for additional reasons.
Density Correction Is Not Viscosity Correction
Specific gravity scales the ideal hydraulic power term at a controlled duty. Viscosity can change the pump curve, efficiency, flow, head and shaft load. Use the viscosity correction guide for ANSI pumps and the actual operating point before final motor selection.
- Viscosity: can reduce flow, head and efficiency relative to a water curve and can increase shaft-power risk. Use the separate guide to viscosity correction for ANSI pumps.
- Temperature: changes density, viscosity, vapor pressure, material behavior and sometimes the system condition.
- Actual pump efficiency: must come from the selected or verified curve at the operating point, with appropriate liquid corrections.
- System curve and duty point: determine where the pump operates. A calculation at design flow is incomplete if the system allows another flow.
- NPSHa and vapor pressure: must be reviewed for the process liquid and temperature. The pump calculator hub includes an NPSHa tool for preliminary checks.
- Solids or entrained gas: may affect hydraulic performance, wear and the suitability of the pump type.
Use the pump duty and replacement worksheet to keep these inputs together. The objective is a traceable duty package, not an isolated horsepower number.
Pump Duty Data to Confirm Before Motor Selection
A motor review should cover the full expected operating envelope. Provide enough information to identify both the normal absorbed power and any startup or alternate condition that may be more demanding.
Motor selection boundary: Check the full operating range, project specification, service factor, ambient temperature, altitude, starting method and VFD behavior; do not size from one illustrative duty point alone.
Density Correction Is Not Viscosity Correction
Specific gravity scales the ideal hydraulic power term at a controlled duty. Viscosity can change the pump curve, efficiency, flow, head and shaft load. Use the viscosity correction guide for ANSI pumps and the actual operating point before final motor selection.
- Fluid and concentration: include mixtures, contaminants and cleaning conditions.
- Density or SG: provide the value, source and reference temperature.
- Viscosity: give units and values at normal and startup temperatures.
- Flow and total dynamic head: state normal, minimum and maximum requirements.
- Pump efficiency: use the actual selected curve and operating point, not a generic assumption.
- Speed and impeller diameter: identify the configuration used for the curve or test.
- Operating range: include system-curve, control-valve, bypass or VFD behavior.
- Startup condition: consider cold liquid, line state, valve position and acceleration requirements.
- Existing motor data: include rating, voltage, frequency, speed, service factor, enclosure and measured load when replacing equipment.
If material selection is being reviewed at the same time, use the companion guide to select impeller material for sulfuric acid and caustic service. Additional calculation and sourcing references are available in the technical resources library.
Need the complete duty reviewed?
Send the fluid properties, operating temperatures, required flow and head, selected curve, impeller diameter, speed and existing motor data. A technical review can then separate hydraulic power, shaft load, viscosity correction and motor requirements.
Frequently Asked Questions
Does specific gravity affect centrifugal pump head?
For the same pump geometry and speed, and a fluid of broadly comparable viscosity, the head curve is not simply multiplied by SG. The pressure rise and power corresponding to that head do change with density.
Does specific gravity affect pump pressure?
Yes. For a given head, differential pressure is proportional to density through Δp = ρgH. A denser liquid produces a larger pressure rise for the same head.
Does a higher specific gravity require more pump horsepower?
At the same flow, head and pump efficiency, higher SG requires proportionally more hydraulic and shaft power. Final motor selection must also use the actual curve, viscosity, operating range, startup conditions and driver requirements.
How do I calculate centrifugal pump power from specific gravity?
Convert SG to a density on a clear reference basis, then use P_hyd = ρgQH. Divide by pump efficiency to estimate shaft power. Use consistent units and verify the actual operating point and liquid corrections.
What is the specific gravity of 98% sulfuric acid?
Veolia lists SG 1.8437 for 98.0 wt% H2SO4 at its 60/60°F table basis. Do not use this value for another sulfuric acid concentration or temperature without verified property data.
What is the specific gravity of 50% caustic soda?
The OxyChem handbook uses SG 1.5372 for 50% diaphragm-grade NaOH in its table/example basis. Caustic soda SG varies with concentration and temperature.
Can I size the motor from a water performance curve alone?
No. A water curve is useful for head-flow and test evidence, but process-liquid shaft load must use the actual density, curve efficiency, viscosity correction where relevant, full operating range and startup or driver requirements.
Does viscosity change this calculation?
Yes. Viscosity can change the pump’s actual flow, head and efficiency relative to water, so power must be recalculated with corrected performance. Use the current applicable correction method and the liquid viscosity at normal and startup temperatures.
Technical Sources
- KSB Centrifugal Pump Lexicon: Pump Power Output
- KSB Centrifugal Pump Lexicon: Head
- OxyChem: Caustic Soda Handbook
- Veolia: Sulfuric Acid Technical Information
- ANSI Pumps Pro: Pump Calculators and Engineering Tools
Editorial scope: This article explains the density, head, pressure and power relationship for chemical-process pump review. The numerical example is a controlled comparison and not a pump, motor or project specification.
