Sizing a magnetic drive centrifugal pump is not the same as sizing a standard mechanical seal pump. Flow rate and head are the starting point—but they are not the whole picture. For corrosive, toxic, or volatile chemicals, the real engineering challenge lies in four additional parameters: NPSH margin, torque margin, BEP (Best Efficiency Point) positioning, and material compatibility. A miscalculation in any one of these can lead to demagnetization, cavitation, bearing seizure, or—in the worst case—catastrophic chemical leakage. This guide walks you through a complete engineering-grade sizing framework for Magnetic Drive Centrifugal Pump selection, helping you configure a system that is safe, reliable, and cost-effective over its full lifecycle.
Why Magnetic Drive Pumps—And Why Sizing Is Different
What Is a Magnetic Drive Pump and How Does It Work?
A magnetic drive centrifugal pump replaces the traditional mechanical shaft seal with a magnetic coupling system. The motor drives an outer magnet assembly (the drive magnet), which transmits torque through a stationary containment shell (also called an isolation sleeve or can) to an inner magnet assembly (the driven magnet) attached to the pump impeller. Because there is no dynamic shaft seal penetrating the pressure boundary, the pumped fluid is permanently contained within the pump casing.
Magnetic Drive vs. Mechanical Seal: The Leakage Question
In a standard centrifugal pump with a mechanical seal, the rotating shaft passes through the pump casing. The mechanical seal is the only barrier preventing the pumped fluid from escaping to the atmosphere. In corrosive chemical service, mechanical seals are the number one failure point—they wear, they leak, and they require frequent replacement.
A magnetic drive pump eliminates this vulnerability entirely. There is no shaft penetration, no dynamic seal face, and no pathway for fugitive emissions. This makes magnetic drive pumps the preferred—and often mandatory—choice for:
- Toxic chemicals (hydrogen chloride, hydrogen fluoride, phosgene)
- Flammable or explosive solvents
- High-value or ultra-pure fluids
- Environmental compliance applications requiring zero emissions
Why Sizing a Mag-Drive Pump Is More Than a Centrifugal Pump Selection
A standard centrifugal pump sizing exercise focuses on hydraulics: flow, head, NPSH, and power. A magnetic drive pump adds magnetic system constraints to the equation. You must verify:
- The magnetic coupling can transmit the required torque without decoupling or demagnetizing
- The containment shell can withstand system pressure without excessive eddy current losses
- The internal bearings (which are lubricated by the pumped fluid) operate within their temperature and load limits
- The pump runs sufficiently close to its BEP to avoid excessive radial loads on the bearings
In short: hydraulic suitability is necessary but not sufficient. You must also ensure magnetic and mechanical integrity under your specific duty conditions.
Step 1: Define Your Fluid Properties—The Foundation of Safe Selection
Every magnetic drive pump sizing exercise begins with a complete fluid characterization. Skipping or underestimating any of these parameters is the most common cause of premature pump failure.
Chemical Compatibility: Matching the Pump Material to Your Fluid
The wetted materials of the pump—impeller, casing, containment shell, bearings, and gaskets—must be compatible with your fluid at your specific operating temperature and concentration.
For example, 316 stainless steel offers excellent corrosion resistance in many applications but will fail rapidly in hydrochloric acid service. Hastelloy C provides superior resistance to chlorides and strong oxidizing agents. PTFE and PFA fluoropolymers offer near-universal chemical inertness but have lower mechanical strength and higher thermal expansion.
Key questions to answer:
- What is the primary chemical and its concentration?
- Are there secondary components (trace contaminants, inhibitors, stabilizers)?
- Is the fluid oxidizing, reducing, or neutral?
- Does the fluid contain chlorides, fluorides, or other aggressive species?
Temperature Limits: Why Heat Changes Everything
Temperature affects chemical compatibility, material strength, and pump hydraulics in three critical ways:
- Corrosion rates typically double for every 10°C increase in temperature. A material that is compatible at 25°C may fail within weeks at 80°C.
- Fluoropolymer linings have maximum continuous operating temperatures: PTFE up to 200°C, PFA up to 220°C, FEP up to 150°C. Exceeding these limits causes deformation, delamination, or creep.
- Magnet strength decreases with temperature. Neodymium magnets lose significant magnetic flux above 80°C; samarium-cobalt magnets maintain strength to higher temperatures but have lower maximum energy product.
Specific Gravity and Viscosity: Don’t Underestimate the Impact
Specific gravity (relative density) directly affects the power required to achieve a given head. Concentrated sulfuric acid at 98% concentration has a specific gravity of approximately 1.84—nearly twice that of water. A pump sized for water will require approximately twice the motor power for the same flow and head when pumping concentrated acid.
Viscosity affects friction losses in the piping system and the pump’s internal hydraulic performance. High-viscosity fluids may require larger impeller clearances and reduced operating speeds.
Solids Content: When a Mag-Drive Pump Is Not the Right Choice
Magnetic drive pumps are not designed for solids-handling service. The internal clearances between the impeller and casing, and between the bearings and shaft, are typically small. Solids can:
- Accelerate bearing wear
- Abrade the containment shell
- Cause the impeller to seize or the magnetic coupling to decouple
If your fluid contains more than a trace of solids, a magnetic drive pump is generally the wrong choice. Consider a Slurry Pump or a sealless design specifically engineered for abrasive service.
Step 2: Sizing Beyond Flow & Head—NPSH, Torque Margin & BEP
NPSH Margin: Why “Just Enough” Is Never Enough
NPSH (Net Positive Suction Head) is the difference between the absolute pressure at the pump suction and the vapor pressure of the pumped fluid. If the available NPSH (NPSHa) falls below the required NPSH (NPSHr), the fluid vaporizes inside the pump, causing cavitation—the formation and collapse of vapor bubbles that can erode the impeller, damage the bearings, and destroy the pump.
For magnetic drive pumps, cavitation is particularly dangerous because:
- The internal bearings are lubricated by the pumped fluid. Cavitation disrupts this lubrication, leading to rapid bearing failure.
- The containment shell can be damaged by the high-energy bubble collapse.
- The pump’s magnetic coupling may decouple under the unstable hydraulic conditions.
Industry best practice: Maintain an NPSH margin of at least 1.5 to 2 times NPSHr, or a minimum of 3 to 5 feet (1 to 1.5 meters) of absolute margin, whichever is greater.
How to calculate NPSHa:
NPSHa = (absolute pressure at suction flange) – (vapor pressure of fluid) + (velocity head)
System losses, elevation changes, and fluid temperature all affect NPSHa. Always calculate NPSHa at the maximum expected operating temperature, because vapor pressure increases exponentially with temperature.
Torque Margin: Preventing Decoupling and Demagnetization
The magnetic coupling transmits torque from the motor to the impeller without physical contact. This coupling has a maximum torque limit—exceed it, and the magnets decouple (the inner magnet stops following the outer magnet) or demagnetize permanently.
Torque margin is the ratio between the coupling’s maximum torque capacity and the torque required by the pump at the duty point.
Industry practice: Specify a minimum torque margin of 150% to 200% (i.e., the coupling should be capable of transmitting 1.5 to 2 times the maximum expected torque).
Common torque traps to avoid:
- Oversizing the motor—A larger motor can deliver more torque, but the coupling must be capable of transmitting it. Don’t assume the coupling matches the motor.
- High specific gravity—Denser fluids require more torque.
- Viscous fluids—Higher viscosity increases friction, requiring more torque.
- Variable speed operation—Speed changes alter torque requirements; the coupling must be sized for the worst-case torque across the entire speed range.
BEP and System Curve: Where Your Pump Will Actually Run
The Best Efficiency Point (BEP) is the flow rate at which the pump operates at its maximum hydraulic efficiency. Operating a centrifugal pump away from its BEP increases radial loads on the bearings, reduces efficiency, and accelerates wear.
For magnetic drive pumps, operating too far to the left of BEP (low flow, high head) is particularly damaging because:
- Recirculation forces increase, raising bearing temperatures
- The fluid in the containment shell may overheat, degrading the magnets
- Axial thrust imbalances can overload the thrust bearings
Industry practice: Specify the pump so that the duty point falls within 80% to 120% of BEP. For variable speed operation, the entire operating envelope should remain within this range.
How to Read a Performance Curve Like an Engineer
A typical pump performance curve shows:
- Head vs. flow (the H-Q curve)—Head decreases as flow increases
- Efficiency vs. flow—Efficiency peaks at BEP
- Power vs. flow—Power increases with flow
- NPSHr vs. flow—NPSHr increases with flow
How to use the curve:
- Locate your duty flow on the horizontal axis
- Read up to the H-Q curve to confirm the pump can deliver the required head
- Read across to the efficiency curve to confirm the pump is operating near BEP
- Read the NPSHr at your duty flow and compare to your NPSHa
- Read the power required and confirm the motor is adequately sized
Critical check: Always verify the pump operates on the stable portion of the H-Q curve (positive slope region). Operation on the unstable portion can cause surging, which damages bearings and the magnetic coupling.
Step 3: Material Selection—Matching the Pump to Your Chemistry
KOLEBURG’s magnetic drive centrifugal pump can be configured with a wide range of wetted materials to match virtually any chemical service. The table below summarizes the key options and their performance characteristics.
| Component | Material Options | Key Performance Characteristic |
|---|---|---|
| Impeller & Casing | SS316 / Hastelloy C / PTFE-lined / PFA-lined | SS316 for general corrosive service; Hastelloy for severe chlorides and oxidizing acids; PTFE/PFA for universal chemical inertness |
| Containment Shell | Hastelloy C / Titanium / PEEK | Metallic shells (Hastelloy, Titanium) for high pressure; PEEK for zero eddy current losses and highest efficiency |
| Internal Bearings | Silicon Carbide (SiC) / Carbon | SiC for maximum wear resistance and high-temperature service; Carbon for lower friction and dry-run tolerance |
Metal Options: SS316, Hastelloy C, and Titanium
SS316 is the workhorse stainless steel for chemical service. It offers good corrosion resistance to many organic acids, mild inorganic acids, and caustic solutions. However, SS316 is not suitable for hydrochloric acid, hydrofluoric acid, or strong chlorides at elevated temperatures. For a complete range of stainless steel configurations, explore KOLEBURG’s Stainless Steel Pump options.
Hastelloy C (C-276 or C-22) provides exceptional resistance to pitting, crevice corrosion, and stress corrosion cracking in chloride-containing environments. It is the material of choice for hydrochloric acid, sulfuric acid, and mixed acid services at elevated temperatures.
Titanium offers outstanding resistance to seawater, chlorides, and oxidizing acids. It is lighter than Hastelloy and provides excellent corrosion resistance in many severe services.
Plastic Options: PP, PVDF, PTFE, and PFA
PP (Polypropylene) is a cost-effective option for ambient-temperature corrosive service, including dilute acids, alkalis, and wastewater. Maximum operating temperature is approximately 80°C.
PVDF (Polyvinylidene Fluoride) offers higher mechanical strength and temperature resistance than PP (up to 140°C). It is the material of choice for ultrapure water, halogens, and semiconductor chemicals.
PTFE (Polytetrafluoroethylene) and PFA (Perfluoroalkoxy) offer near-universal chemical inertness. PTFE is suitable up to 200°C and resists virtually all industrial chemicals, including boiling aqua regia and hydrofluoric acid. KOLEBURG’s PTFE Pump and Teflon Pump lines provide the highest level of chemical and thermal durability. PFA offers similar chemical resistance with higher mechanical strength and better high-temperature stability. For applications requiring high-purity or extreme chemical resistance, the Fluoroplastic Pump series delivers rugged performance with advanced polymer linings.
Containment Shell Materials: Hastelloy C, Titanium, PEEK, and Ceramic
The containment shell is a critical component—it must withstand system pressure while allowing magnetic flux to pass through with minimal loss.
Hastelloy C and Titanium are metallic shell options that offer high strength and corrosion resistance. However, metallic shells generate eddy current losses—electrical currents induced by the rotating magnetic field that generate heat and reduce efficiency. Eddy current losses can be significant at high speeds and may require cooling.
PEEK is a high-performance polymer that offers zero eddy current losses, maximizing efficiency. It has excellent chemical resistance and can operate at temperatures up to 220°C. PEEK shells are typically used in less aggressive chemical services where mechanical strength is adequate.
Ceramic shells (silicon carbide or alumina) offer extreme hardness, universal chemical inertness, and zero eddy current losses. They are the premium option for the most demanding services—highly abrasive slurries combined with corrosive chemicals.
Bearing Materials: Silicon Carbide vs. Carbon Graphite
Magnetic drive pump bearings are lubricated by the pumped fluid and operate in a boundary or mixed lubrication regime.
Silicon carbide (SiC) bearings offer exceptional hardness and wear resistance. They are the standard choice for most chemical services and handle temperatures up to 350°C. SiC is resistant to most chemicals but can be attacked by hydrofluoric acid.
Carbon graphite bearings offer lower friction and better dry-run tolerance. They are often used in services where SiC is not chemically compatible. Carbon bearings typically have a lower maximum temperature and shorter wear life than SiC.
Step 4: Configuration & Options—Customizing for Your Duty
Motor Power and Efficiency: IE3 vs. IE2
Motor efficiency directly affects operating cost. In most continuous-duty chemical pumping applications, the motor represents 60% to 80% of the total lifecycle cost. Specifying an IE3 premium efficiency motor over an IE2 standard efficiency motor typically adds 10% to 15% to the motor cost but reduces annual energy consumption by 3% to 5%—a payback period of 1 to 2 years in most regions.
Variable Frequency Drive vs. Fixed Speed
Variable frequency drives (VFDs) allow the pump speed to be adjusted to match system demand, offering significant energy savings in systems with variable flow requirements.
When to use VFD:
- Systems with variable demand (e.g., filling operations, batch processes)
- Systems where the pump is oversized for the normal duty point
- Applications requiring soft start to reduce mechanical stress
When fixed speed is preferred:
- Constant flow systems (e.g., circulation loops, continuous transfer)
- Applications where VFD harmonic distortion is a concern
- Small pumps where VFD cost is not justified
VFD considerations for magnetic drive pumps:
- The magnetic coupling torque margin must be verified across the entire speed range
- Minimum speed must be high enough to maintain adequate bearing lubrication
- Resonance frequencies must be avoided
High-Temperature Design: Thermal Growth, Eddy Current Loss, and Bearing Cooling
High-temperature service requires special attention to:
- Thermal expansion—Clearances must be increased to accommodate differential expansion between components
- Eddy current losses—Metallic containment shells generate heat; cooling may be required
- Bearing cooling—Bearing temperatures must be kept within limits; some designs incorporate cooling jackets or recirculation lines
ATEX and API 685: When You Need the Extra Layer
ATEX (Atmosphères Explosibles) certification is required for equipment used in potentially explosive atmospheres. If your pump is located in a classified area (Zone 1, Zone 2, or Division 1, Division 2), the pump must be ATEX-certified with appropriate temperature classification.
API 685 is the American Petroleum Institute standard for sealless centrifugal pumps. It applies to pumps used in petroleum, petrochemical, and natural gas industries where safety, reliability, and environmental compliance are paramount. API 685 pumps are subject to more stringent design, testing, and quality requirements than standard ANSI or ISO pumps. For a broader understanding of API standards for industrial pumps, refer to KOLEBURG’s API 610 Pump documentation.
Application Examples—Where Mag-Drive Pumps Excel
Concentrated Sulfuric Acid Transfer (93%–98% H₂SO₄)
Concentrated sulfuric acid is one of the most challenging chemicals to pump. It has high specific gravity (≈1.84 at 98%), is highly corrosive to most metals, and generates violent exothermic heat upon dilution.
Selection requirements:
- Fluoroplastic (PTFE or PFA) or Hastelloy C wetted parts
- Sealless magnetic drive design to eliminate leakage
- Motor sized for high specific gravity
- Temperature monitoring to prevent overheating
Recommended configuration: KOLEBURG Fluoroplastic Magnetic Drive Pump with PTFE-lined casing, Hastelloy containment shell, and SiC bearings. For detailed application engineering, refer to the Concentrated Sulfuric Acid Transfer Pump solution guide.
Hydrochloric Acid Circulation (up to 37% HCl)
Hydrochloric acid rapidly corrodes most metals—even 316 stainless steel fails quickly in HCl service. The acid also fumes, releasing toxic hydrogen chloride gas.
Selection requirements:
- Non-metallic wetted parts—fluoroplastic (PTFE, PFA, or FEP)
- Sealless design to prevent toxic vapor leaks
- Cavitation margin—HCl has high vapor pressure and is prone to cavitation
- Low-leaching materials to maintain product purity
Recommended configuration: KOLEBURG Fluoroplastic Magnetic Drive Pump with PTFE lining, PEEK containment shell, and SiC bearings. For comprehensive HCl handling guidance, see the Hydrochloric Acid Circulation Pump application page.
Electroplating Chemical Circulation
Electroplating solutions are chemically aggressive and often contain metal ions that must not be contaminated. Standard pumps can leach metal ions into the bath, ruining the plating quality.
Selection requirements:
- Inert materials—PVDF or fluoroplastics
- Low or zero metal ion leaching
- Sealless design to prevent chemical fumes from escaping
Recommended configuration: KOLEBURG PVDF Magnetic Drive Pump or Fluoroplastic Magnetic Drive Pump with appropriate chemical-grade materials.
High-Purity Chemical Transfer for Semiconductors and Pharmaceuticals
Semiconductor and pharmaceutical manufacturing require absolute purity—any contamination, even at parts-per-billion levels, can ruin entire batches.
Selection requirements:
- Ultra-pure materials—PTFE, PFA, or PVDF
- Zero metal ion leaching
- Non-particulating materials
- Sealless design to eliminate seal wear particles
Recommended configuration: KOLEBURG PTFE or PVDF Pump with PEEK containment shell and specially selected bearing materials.
Common Sizing Mistakes—And How to Avoid Them
Mistake 1: Sizing for Maximum Flow Instead of the Actual Duty Point
Many engineers size pumps for the maximum possible flow, then operate them at lower flow rates using a control valve or VFD. This approach is inefficient and can damage the pump.
Avoid by: Size for the normal duty point, then check the pump can handle the maximum flow without exceeding the motor power or causing cavitation.
Mistake 2: Insufficient NPSH Margin
Pumps often fail due to cavitation when the calculated NPSH margin is insufficient. This is especially common with hot fluids or volatile chemicals.
Avoid by: Always calculate NPSHa at the maximum operating temperature, and add 1.5 to 2 times NPSHr margin.
Mistake 3: Wrong Material for the Chemistry
A material that is compatible at room temperature may fail at operating temperature. Trace impurities may also affect compatibility.
Avoid by: Verify material compatibility at the actual operating temperature and concentration. Consult manufacturer’s corrosion data and, if in doubt, test coupons under actual service conditions.
Mistake 4: Underestimating Torque Margin
The magnetic coupling is sized for the duty point, but the motor can deliver more torque. If the coupling is not sized for the motor’s maximum torque, it can decouple or demagnetize.
Avoid by: Specify torque margin based on motor maximum torque, not just duty point torque.
Mistake 5: Ignoring Specific Gravity
Pumps and motors are often sized based on water, but many chemicals have significantly higher specific gravity.
Avoid by: Always confirm the motor power requirement based on the actual fluid specific gravity.
Mistake 6: Running Too Far from BEP
Operation far from BEP increases bearing loads and reduces efficiency.
Avoid by: Verify the operating range is within 80% to 120% of BEP. For VFD applications, verify this across the entire speed range.
Mistake 7: Dry Running
Magnetic drive pump bearings rely on the pumped fluid for lubrication and cooling. Even brief dry running can cause catastrophic bearing damage.
Avoid by: Install dry-run protection—flow switches, pressure switches, or temperature sensors that shut down the pump if flow is lost.
Standards and Compliance—API 685, ATEX, and Beyond
API 685: The Sealless Pump Standard
API 685 is the global standard for sealless centrifugal pumps used in petroleum, petrochemical, and natural gas industries. Key requirements include:
- Sealless design (magnetic drive or canned motor)
- Secondary containment to prevent leakage if the primary containment fails
- Temperature monitoring of the containment shell
- Vibration monitoring
- Stringent testing and documentation requirements
API 685 vs. API 610: When to Choose Which
API 610 is the standard for centrifugal pumps with mechanical seals. API 685 is the sealless pump standard.
Choose API 685 when:
- The fluid is toxic, flammable, or environmentally hazardous
- Zero emissions are required
- The fluid is difficult to seal (high temperature, high pressure, corrosive)
- The cost of seal maintenance and leakage is unacceptable
Choose API 610 when:
- The fluid is benign and easily sealed
- The application is less critical
- Cost is the primary driver
For more details on API 610 compliance and pump selection, visit the API 610 Pump standards page.
ATEX and Hazardous Area Compliance
ATEX certification is mandatory for equipment used in potentially explosive atmospheres in Europe and many other regions. The pump must be rated for the appropriate zone (Zone 1, Zone 2, or Division 1, Division 2) and have the correct temperature classification (T1 to T6).
ISO and Energy Efficiency Standards
- ISO 5199 is the international standard for centrifugal pumps for chemical and petrochemical service. It specifies design, materials, testing, and documentation requirements.
- IE efficiency classes (IE1 to IE4) define motor efficiency levels. IE3 is typically the minimum for new installations in most regions; IE4 is becoming increasingly common.
FAQ——Magnetic Drive Centrifugal Pump Sizing
Can a magnetic drive pump run dry?
No. Magnetic drive pump bearings rely on the pumped fluid for lubrication and cooling. Even brief dry running can cause catastrophic bearing damage within seconds. Install dry-run protection—flow switches, pressure switches, or temperature sensors—on any magnetic drive pump installation.
What is the typical lifespan of a magnetic drive pump?
With proper sizing, installation, and maintenance, a magnetic drive pump can operate for 10 to 20 years. However, bearing life depends on operating conditions—temperature, fluid properties, and proximity to BEP. Bearing replacement intervals typically range from 1 to 3 years in continuous chemical service.
How often does a magnetic drive pump need maintenance?
- Daily/Weekly checks: Monitor temperature, vibration, noise, and leakage (visual inspection).
- Quarterly maintenance: Check bearing wear, inspect the containment shell, verify magnet condition.
- Major overhaul (1–3 years or by operating hours): Replace bearings, inspect magnets, evaluate containment shell integrity. Follow the manufacturer’s maintenance schedule for your specific model.
How much more expensive is a magnetic drive pump compared to a standard centrifugal pump?
A magnetic drive pump typically costs 30% to 100% more than a comparable mechanical seal pump, depending on materials (Hastelloy vs. stainless steel vs. plastic), standards (API 685 vs. ANSI), and configuration. However, the total cost of ownership is often lower because magnetic drive pumps eliminate mechanical seal maintenance and replacement costs, reduce leakage-related losses, and lower environmental compliance costs.
What are the maximum flow and head of a magnetic drive pump?
Commercial magnetic drive pumps are available with flow rates from 2 m³/h to 600 m³/h and heads from 5 meters to 160 meters. Multistage magnetic drive designs can achieve higher heads. Specific capabilities vary by manufacturer and model.
Can a magnetic drive pump handle solids?
Generally, no. Magnetic drive pumps are not designed for solids handling. The internal clearances are small, and solids cause rapid wear on bearings, impellers, and the containment shell. If your fluid contains more than trace solids, consider a Slurry Pump or a different pump technology.
What is the difference between a magnetic drive pump and a canned motor pump?
Both are sealless designs, but they work differently:
- Magnetic drive pump: The motor is external. Torque is transmitted through a containment shell via magnetic coupling. The containment shell is stationary.
- Canned motor pump: The motor rotor is inside the pressure boundary, directly connected to the impeller. The stator is outside, separated by a thin metal “can” (the stator liner).
Magnetic drive pumps generally handle higher temperatures and pressures; canned motor pumps are more compact but more complex to maintain.
Ready to Size Your Magnetic Drive Centrifugal Pump?
Flow and head are just the beginning. The full engineering-grade sizing of a magnetic drive centrifugal pump requires careful evaluation of fluid properties, NPSH margin, torque margin, BEP positioning, and material compatibility. Each parameter interacts with the others, and a miscalculation in any one area can lead to premature failure, safety incidents, or costly downtime.
To get started, prepare the following information:
- Flow rate (m³/h or GPM)
- Total head (meters or feet)
- Fluid composition (chemical name, concentration, specific gravity)
- Operating temperature (minimum, normal, maximum)
- System pressure (suction and discharge)
- NPSH available at the pump suction
- Solid content (type, size, concentration)
- Environmental requirements (ATEX, API 685, emissions limits)
Next steps:
- Download the RFQ parameter template to organize your specifications
- Contact our engineering team for a complete sizing and configuration recommendation
- Request a customized material selection analysis for your specific fluid
🚀 Ready to specify a magnetic drive centrifugal pump for your chemical facility? Contact our engineering team for a complete sizing and configuration recommendation tailored to your specific fluid and duty conditions.
