Inline Pump Selection Guide for Specs, Head and Material

Selecting the right commercial or industrial pump often comes down to balancing system architecture with performance data. For projects requiring a compact footprint, straightforward piping integration, and reliable continuous duty, an Inline Pump stands out as a highly effective choice.

This guide provides a comprehensive breakdown of technical specifications, material selections, and system configurations to help engineers, procurement managers, and contractors make accurate purchasing decisions.

Key Takeaways

• Footprint & Geometry: Inline pumps feature suction and discharge ports aligned on a single centerline, allowing them to fit directly into a pipeline and minimize required floor space.
• Hydraulic Precision: Accurate sizing relies on calculating the total dynamic head (including localized friction losses from valves, bends, and heat exchangers) rather than simply matching pipe diameters.
• Material Integrity: Media characteristics determine metallurgy. Cast iron serves well for standard closed-loop water systems, while stainless steel handles purified or mildly corrosive fluids, and specialized elastomers are required for elevated temperatures or oil transport.
• Configuration Impact: Choosing between vertical or horizontal orientations and single-stage or multistage designs dictates long-term maintenance access, structural support requirements, and pressure limits.

What Is an Inline Pump?

An inline pump is a centrifugal pump engineered with its suction and discharge connections arranged along the same straight piping centerline. This specific geometric layout differentiates it from standard end-suction pumps, allowing the unit to mount directly within a continuous run of pipe.

Basic Definition of an Inline Pump

Mechanically, an inline pump integrates directly into a fluid network to facilitate circulation or pressure boosting. Because the fluid enters and exits along the same axis, the installation eliminates the need for the 90-degree piping turns typical of end-suction models.

These units are primarily deployed for handling clean water, conditioned cooling water, heating water, and low-viscosity industrial fluids. Their design minimizes structural footprints, making them standard equipment in compact mechanical rooms, modular skids, and built-environment infrastructure.

TIP: While smaller inline units can be supported directly by the piping, heavier industrial models require dedicated structural hangers or base foundations to prevent transferring pipe stress to the pump casing.

How an Inline Pump Works

The operational principles align with fundamental centrifugal design. An electric motor rotates an internal impeller, which accelerates the fluid outwards through centrifugal force. As the fluid gains kinetic energy within the volute casing, its velocity converts into static pressure before exiting through the discharge port.

Because these pumps are installed directly within fluid circuits, managing pipe alignment and physical loads is crucial. Excessive system stress can cause casing distortion, leading to premature mechanical seal failure, bearing wear, or internal rubbing.

Common Inline Pump Applications

Understanding where these units excel helps verify if an inline configuration satisfies the demands of your current installation.

Building and HVAC Applications

In commercial and institutional buildings, inline configurations serve as the primary circulation mechanism for climate control and water distribution.

• Hydronic Circulation: Managing Central Air Conditioning Chilled Water Pump networks and driving Air Conditioning Condenser Water Pump circuits.
• District Heating: Running a Heating System Hot Water Circulation Pump across a boiler primary heating network or managing secondary loops within local heat exchange stations.
• Facilities Management: Providing stable domestic hot water via a Hotel Hot Water Circulation Pump or underfloor heating networks.
• Pressure Boosting: Serving as an Office Building Variable Frequency Water Supply Pump to maintain consistent line pressure during peak demand periods.

Industrial and Process Applications

Industrial plants rely on inline pumps for localized fluid transfer, machine cooling, and water purification loops.

• Thermal Management: Running specialized Data Center Cooling Circulation Pump infrastructure, laser cutter loops, welding equipment stations, and injection molding mold cooling systems.
• Water Treatment: Managing fluid transfer through an integrated Reverse Osmosis Feed Booster Pump, running softened water supply systems, and moving purified water through process loops.
• Petrochemical & Utilities: Driving light oil transfer lines or general Pipeline Pressure Booster Pump units within refining and distribution networks.

When an Inline Pump Is Not the Best Choice

While versatile, specific operating environments require different pump architectures.

• High Solid Loading: Applications handling thick sewage, heavy drilling mud, or highly abrasive mining slurries will rapidly erode a standard inline volute.
• Deep Well Extraction: Inline units lack the deep submergence capability of dedicated downhole tools.
• Severe Self-Priming Demands: Systems with substantial suction lifts requiring regular air evacuation require specific self-priming designs.
• Extreme Volumetric Flows: Massive municipal or industrial water distribution networks generally require split-case pump geometries to distribute structural and hydraulic loads evenly.

Key Specifications for Inline Pump Selection

To prevent premature equipment failure or high energy usage, several core engineering parameters must be evaluated.

Flow Rate

Flow rate specifies the volume of liquid moved per unit of time (typically measured in $m^3/h$, L/min, or GPM). Sizing must target the system’s normal operating requirements rather than theoretical maximums.

• Under-sizing Risks: Leads to insufficient heat transfer in HVAC loops, poor pressure at high-elevation fixtures, or stagnant process fluid circulation.
• Over-sizing Risks: Forces the pump to run far to the right of its Best Efficiency Point (BEP). This causes high power draw, fluid cavitation, internal vibration, and premature bearing breakdown.
• Variable Load Management: If your application experiences wide fluctuations in fluid demand, integrating variable frequency drives (VFDs) ensures the motor speed scales dynamically with demand.

Total Head

Total Dynamic Head (TDH) represents the total equivalent height a fluid must be pumped, accounting for all friction and pressure losses in the system.

• Static Head vs. Friction Loss: Static head is the physical elevation change in an open system. Closed-loop systems have zero net static head; their TDH is derived entirely from friction losses.
• Component Resistance: Every elbow, control valve, strainer, boiler barrel, and heat exchanger adds resistance. These individual pressure drops must be added together using standard fluid piping formulas.
• The Sizing Fallacy: Never select a pump based solely on a building’s height or total run of pipe. Always size according to the calculated system curve intersect point.

Pipe Diameter and Connection Size

Because inline pumps install directly into pipelines, their nominal connection sizes must align carefully with system design parameters.

• Velocity Considerations: Matching a pump with ports that are too small accelerates fluid velocity, increasing friction losses, generating system noise, and increasing the risk of erosion.
• Suction Integrity: If a pump’s suction port is smaller than the supply line, a concentric reducer should be used to avoid creating air pockets that cause cavitation.
• Standards Compliance: Verify whether your project requires ANSI, ISO, or DIN flange drillings to avoid installation delays.

Liquid Type

Fluid chemistry directly influences internal pump geometry, seal choice, and structural metallurgy.

• Viscosity Impact: High-viscosity fluids (such as heavy oils or concentrated glycol mixtures) increase internal shear friction, requiring increased motor horsepower.
• Entrained Air: Entrained gases or foaming liquids can disrupt the hydraulic sealing of the impeller, leading to erratic discharge pressures.
• Specific Gravity: Liquids denser than clean water put a higher load on the electric motor, which requires selecting a non-overloading motor size.

Temperature

Operating temperatures alter fluid vapor pressure and dictate the structural integrity of elastomers and mechanical seals.

• Thermal Expansion: High-temperature systems induce thermal expansion within the pump shaft and casing, requiring matching metal alloys to prevent binding.
• Seal Selection: High-temperature water circulation requires specialized mechanical seals (such as silicon carbide or tungsten carbide faces paired with Viton or EPDM elastomers) to avoid rapid leaking.
• Condensation Control: In chilled water applications, localized condensation can moisture-corrode the pump-to-motor adapter. Specifying anti-condensation heaters or protective coatings preserves the assembly.

Working Pressure

Working pressure defines the maximum permissible hydrostatic pressure the pump casing can sustain without cracking or leaking.

• Static System Pressure: In high-rise buildings or deep industrial circuits, high static pressures can bear down on the pump casing even when the motor is stopped.
• Total Pressure Calculation: Casing and flange pressure ratings must exceed the sum of the maximum suction pressure plus the shut-off head generated by the pump.
• Flange Selection: Standard installations use Class 125/150 flanges, but high-pressure, heavy-duty utility loops often require Class 250/300 connections.

Motor Power and Speed

The motor must supply adequate torque across the entire operating range without exceeding its rated service factor.

• Speed Selection: Common nominal speeds are 2-pole (approx. 2900/3500 RPM) for high head and lower flow, or 4-pole (approx. 1450/1750 RPM) for quieter operation and extended seal life.
• Enclosure Standards: Specify TEFC (Totally Enclosed Fan Cooled) motors for standard industrial spaces, or explosion-proof enclosures when handling volatile fluids like light fuel oils.
• Electrical Supply: Match the facility infrastructure exactly, verifying nominal voltage ($230\text{V}/460\text{V}/575\text{V}$), frequency ($50\text{Hz}$ or $60\text{Hz}$), and phases.

Installation Space and Direction

Physical constraints within mechanical rooms often guide final product selection.

• Vertical Orientation: Minimizes floor space requirements but requires adequate overhead clearance for lifting cranes during motor or seal maintenance.
• Horizontal Orientation: Requires a larger horizontal footprint but offers lower-height access for routine maintenance.
• Stress Isolation: Ensure that neither orientation relies on the pump casing to support unanchored runs of heavy overhead piping.

Inline Pump Material Selection

Matching pump metallurgy to fluid chemistry prevents corrosion and early mechanical failures.

Cast Iron Inline Pump

A standard Cast Iron Pump is an economical and highly durable option for closed-loop hydronic networks, HVAC heating and cooling lines, and clean industrial water systems. Its structural rigidity provides strong resistance to pipe deformation, though it should not be used with soft water or fluids containing high chloride concentrations.

Stainless Steel Inline Pump

For setups where fluid purity or corrosion resistance is a priority, a Stainless Steel Pump is standard.

• 304 Stainless Steel Pump: Ideal for domestic drinking water, softened process water, and commercial laundry loops.
• 316 Stainless Steel Pump: Upgraded metallurgy that offers protection against pitting and corrosion caused by industrial chemicals, high-temperature brine, or mildly acidic process solutions.

Bronze or Brass Inline Pump

Bronze construction is primarily specified for open-loop domestic hot water systems or low-salinity marine cooling loops. It resists the oxygen-driven corrosion that degrades cast iron in fresh water systems, ensuring long-term system reliability.

Hot Water Inline Pump Materials

Systems moving fluids above $100^\circ\text{C}$ require robust components. Mechanical seals must feature high-temperature elastomers like Viton or Kalrez, and casings must use ductile iron or cast steel to safely withstand thermal stresses without fracturing.

Inline Oil Pump Materials

Transporting light fuels, lubricants, or industrial oils requires specific compatibility. This setup needs oil-resistant Nitrile or Viton seals, ductile iron or steel casings to meet plant fire safety standards, and explosion-proof motors to comply with hazardous area classifications.

Material Selection Table

Liquid / Application	Suggested Pump Type	Suggested Material	Notes
Clean Water	Inline Pump	Cast Iron / Stainless Steel	Standard transfer and pressure boosting lines
Chilled Water	Vertical Inline Pump	Cast Iron / Stainless Steel	Evaluate condensation risks near the motor
Hot Water	Hot Water Inline Pump	Cast Iron / Stainless Steel / Bronze	Confirm exact operating temperature limits
Drinking Water	Stainless Steel Inline Pump	304 / 316 Stainless Steel	Ensures system hygiene and prevents corrosion
Softened Water	Inline Pump	Stainless Steel / Cast Iron	Monitor potential low-mineral aggressive corrosion
Industrial Water	Horizontal Inline Pump	Cast Iron / Stainless Steel	Select metallurgy based on water chemical assays
Light Oil	Inline Oil Pump	Cast Iron / Stainless Steel	Check fluid viscosity and seal compatibility
Mild Corrosive Liquid	Stainless Steel Inline Pump	316 / 316L Stainless Steel	Confirm fluid pH and chloride concentrations
High Head Pressure Boosting	Vertical Inline Multistage Pump	Stainless Steel / Cast Iron	Verify maximum pressure rating of the casing

TIP: Reviewing water chemistry reports before ordering prevents early component failure caused by unexpected chloride or oxygen levels.

Types of Inline Pumps

Inline pumps are available in several structural configurations to suit specific performance requirements and spatial layouts.

Vertical Inline Pump

The vertical configuration features an electric motor mounted directly on top of the centrifugal pump casing.

• Space Saving: Its compact foot-to-flange design makes it easy to integrate into tight spaces or modular skids.
• Support: Can be suspended directly within structural piping headers or anchored to a compact floor foundation block.
• Applications: Widely used in commercial building HVAC loops, municipal water lift systems, and industrial circulation circuits.

Horizontal Inline Pump

This design features a motor positioned horizontally alongside the pump casing within the pipeline run.

• Maintenance Access: The lower physical height simplifies motor removal and seal inspection in facilities without overhead hoists.
• Stability: The horizontal footprint distributes weight across a wider base, which can reduce vibration transmission in sensitive installations.
• Applications: Used in industrial manufacturing, process liquid loops, and utility water supply systems.

Vertical Inline Multistage Pump

When a system requires high head or high discharge pressures but has limited floor space, a vertical multistage model is an effective choice.

• Multi-Impeller Architecture: Features multiple impellers stacked vertically on a single drive shaft, with each stage sequentially increasing fluid pressure.
• Efficiency: Designed for high-pressure, lower-flow applications, providing reliable performance with a compact physical footprint.
• Applications: Used as a High Rise Water Supply Pump, boiler feed water supply, and reverse osmosis filtration systems.

Horizontal Inline Multistage Pump

This configuration combines multi-impeller performance with a horizontal, linear installation layout.

• High Pressure: Delivers high discharge pressures while allowing side maintenance access.
• Rugged Construction: Well-suited for high-vibration industrial settings or heavy-duty process installations.
• Applications: Used for long-distance mine water transfer, industrial high-pressure cleaning loops, and power plant auxiliary circuits.

Hot Water Inline Pump

Engineered to handle hot water circulation loops safely and reliably.

• Thermal Isolation: Features integrated cooling jackets, heat dissipation fins, or extended seal chambers to protect the motor bearings from fluid heat.
• Robust Sealing: Equipped with heavy-duty mechanical seals that maintain structural integrity during rapid temperature changes.
• Applications: Used in municipal heating networks, commercial boiler loops, and industrial heat exchangers.

Inline Oil Pump

Specifically configured to transport light petroleum products, lubricants, and low-viscosity oils.

• Vapor Containment: Designed to prevent fugitive emissions of volatile organic compounds (VOCs).
• Safety Integration: Typically equipped with explosion-proof electric motors and non-sparking coupling guards to comply with strict plant safety codes.
• Applications: Used in refinery blending loops, fuel oil transfer skids, and bulk storage terminal loading lines.

Vertical Inline Pump vs. Horizontal Inline Pump

Choosing between a vertical or horizontal inline pump configuration depends on available space, piping layout, and maintenance preferences.

Vertical Inline Pump Overview

Vertical configurations minimize floor space requirements by placing the motor directly above the pump volute. They fit cleanly into vertical piping runs, though technicians must ensure there is sufficient overhead space to safely remove the motor during servicing.

Horizontal Inline Pump Overview

Horizontal layouts extend along the floor plane, making them easier to service in facilities with low ceilings. However, their larger footprint requires more floor space and often necessitates structural concrete pads or dedicated base supports to remain stable.

How to Choose Between Vertical and Horizontal Inline Pump

Factor	Vertical Inline Pump	Horizontal Inline Pump
Installation Space	Minimizes floor space requirements	Requires a wider horizontal footprint
Pipe Layout	Ideal for vertical or tight piping headers	Best for horizontal, ground-level lines
Maintenance Access	Requires overhead clearance for lifting hoists	Offers straightforward lateral access
Common Application	Commercial HVAC, high-rise water supply	Heavy industrial loops, process transfer
Motor Position	Vertically stacked directly above the volute	Horizontally aligned with the piping
Foundation Needs	Often suspended or secured with simple brackets	Typically requires concrete base pads

Single Stage Inline Pump vs. Multistage Inline Pump

The number of internal impellers determines the pump’s pressure capabilities and overall hydraulic performance profile.

Single Stage Inline Pump Overview

A single-stage inline pump uses a single impeller to accelerate fluid through the volute. This simple, reliable design has fewer moving parts, keeping initial costs and long-term maintenance straightforward. It is best suited for low-to-medium head applications with high volumetric flow requirements.

Multistage Inline Pump Overview

A multistage inline pump routes fluid through multiple impellers in series, with each stage adding pressure. This configuration is engineered to deliver high discharge heads while keeping a compact radial footprint, making it an efficient choice for high-pressure systems.

Which Type Should You Choose?

Factor	Single Stage Inline Pump	Multistage Inline Pump
Head Range	Low to Moderate (Typically $<60\text{ m}$)	Medium to High (Can exceed $200\text{ m}$)
Internal Mechanics	Single impeller, shorter shaft length	Multiple impellers, extended shaft
Capital Cost	Economical initial investment	Higher initial cost due to complexity
Primary Function	High-volume fluid circulation and transfer	High-head pressure boosting
Maintenance Profile	Simple, fast component replacement	Requires careful internal alignment during rebuilds

How to Select an Inline Pump Step by Step

Following a systematic selection process prevents sizing errors and helps ensure a reliable installation.

Step 1: Confirm Liquid Type

Analyze the chemical and physical characteristics of the media. Note the clear fluid temperature, pH levels, dissolved solid contents, and specific gravity to select compatible internal metallurgies and elastomeric seals.

Step 2: Confirm Flow Rate and Head

Calculate your system’s hydraulic requirements. Add together all localized piping losses, valve restrictions, and equipment resistances to determine the true Total Dynamic Head (TDH) at your required operating flow rate.

Step 3: Confirm Pipe and Installation Layout

Evaluate the physical installation space. Measure available floor space and overhead clearance, determine the nominal pipe sizes, and select either a vertical or horizontal layout based on your piping configuration.

Step 4: Select Pump Type

Match your hydraulic profile to the appropriate pump type. Use single-stage inline pumps for low-pressure circulation loops, or select multistage units when your application requires high-pressure boosting.

Step 5: Select Material and Seal

Choose materials that match your fluid chemistry. Use cast iron for standard closed-loop water systems, stainless steel for drinking water or corrosive process lines, and high-temperature mechanical seals for hot water or oil applications.

Step 6: Confirm Motor and Control

Match the motor specifications to your facility’s electrical infrastructure. Verify the available voltage, frequency, and phase, determine if a VFD is needed for variable loads, and specify explosion-proof enclosures if working in hazardous areas.

Common Mistakes When Selecting Inline Pumps

Avoiding these common selection pitfalls helps ensure stable system performance and extends equipment life.

Selecting Only by Pipe Size

Choosing a pump simply because its connections match the existing pipe diameter is a frequent mistake. It can lead to severe under-sizing or over-sizing, forcing the pump to run off its design curve and causing early component failure.

Ignoring System Resistance

Overlooking friction losses from inline components like strainers, check valves, and heat exchangers often results in an under-sized pump that cannot deliver the required flow rate.

Choosing the Wrong Pump Type

Using a standard single-stage circulation pump for high-pressure boosting—or failing to specify specialized seals for oil or hot water applications—can lead to rapid seal failure or motor overloads.

TIP: Standard clear-water mechanical seals will rapidly fail if used in high-temperature heating loops or oil transfer lines.

Ignoring Pipe Support

Inline pumps should not carry the physical weight of unanchored piping. Without proper structural pipe hangers or base supports, casing distortion can cause shaft misalignment, seal leaks, and high vibration.

Choosing the Wrong Material

Using standard cast iron for open-loop domestic water or demineralized water lines leads to rapid internal corrosion and fluid contamination. These applications require stainless steel or bronze construction.

Ignoring Temperature

Failing to account for high fluid temperatures can cause elastomeric seals to harden and fail, or result in shaft binding due to unmanaged thermal expansion.

Ignoring Noise and Vibration

Installing high-speed pumps near quiet office spaces or residential areas without using vibration isolation pads, flexible pipe connectors, or 4-pole motors can lead to distracting structural noise.

Inline Pump Specification Checklist

Use this checklist to gather all necessary technical parameters before requesting a manufacturer quote.

Hydraulic Parameters

• Required Operating Flow Rate (m³/h, GPM)
• Calculated Total Dynamic Head (m, feet)
• Minimum and Maximum Inlet Pressure
• Maximum Permissible Casing Work Pressure

Liquid Parameters

• Chemical Name or Fluid Composition
• Normal and Maximum Operating Temperatures (℃，℉)
• Fluid pH Level and Chloride Concentration
• Specific Gravity and Kinematic Viscosity

Installation Parameters

• Desired Mounting Orientation (Vertical or Horizontal)
• Nominal Pipeline Diameters and Connection Flange Standards
• Available Headroom and Floor Footprint in Mechanical Rooms
• Environment (Indoor, Outdoor, or Hazardous Area)

Electrical Parameters

• Line Voltage (230V/ 460V / 575V) and Frequency (50Hz ， 60Hz)
• Phase Configuration (Single-Phase or Three-Phase)
• Motor Enclosure Type (TEFC, ODP, or Explosion-Proof)
• Control Requirements (Fixed Speed or VFD Integration)

Choosing KOLEBURG as Your Industrial Piping Partner

Selecting a manufacturer involves evaluating engineering capabilities, quality standards, and long-term support infrastructure. For modern fluid networks, KOLEBURG designs and manufactures a diverse portfolio of heavy-duty circulation and pressure boosting solutions engineered for continuous industrial service.

Choosing KOLEBURG ensures your piping infrastructure benefits from precise hydraulic performance, durable metallurgy, and optimized energy efficiency.

• Extensive Product Portfolio: The manufacturing catalog covers essential equipment from a high-efficiency Single Stage Pump for localized loop circulation to an advanced Vertical Inline Multistage Centrifugal Pump designed for high-pressure installations.
• Engineered Material Configurations: All units are manufactured using specific alloys, offering a standard Cast Iron Pump for closed heating loops alongside a rugged Stainless Steel Pump for handling aggressive fluids, pure water, or chemical solutions.
• Application-Specific Design: Equipment lines feature dedicated configurations tailored to distinct process requirements, including a robust Single Stage Hot Water Pump for high-temperature thermal loops and specialized architectures for volatile oil transport.
• Strict Manufacturing Standards: Engineering production follows internationally recognized quality benchmarks, ensuring that each Multistage Centrifugal Pump and single-stage unit meets rigorous casing pressure tests and dynamic balancing certifications.
• Global Supply and Support: Global distribution logistics, comprehensive technical documentation, and expert engineering consultation help procurement managers and contractors streamline selection, installation, and commissioning.

Inline Pump FAQ

What is the main structural advantage of an inline pump?

Its linear configuration allows it to install directly into a straight section of pipe, which eliminates the need for complex 90-degree elbows and significantly reduces the required floor space compared to end-suction pumps.

Can a vertical inline pump be mounted horizontally?

Smaller models can sometimes be installed horizontally if explicitly supported by the piping, but larger vertical inline pumps must remain vertical. Mounting them horizontally can put uneven loads on the motor bearings, leading to early shaft and seal failure.

What causes cavitation in an inline circulation loop?

Cavitation occurs when the local suction pressure drops below the fluid’s vapor pressure, causing vapor bubbles to form and violently collapse against the impeller. This is typically caused by restricted suction piping, clogged strainers, or running the pump too far to the right of its efficiency curve.

How do I calculate the required head for a closed hydronic loop?

In a closed loop, static elevation changes cancel out. The total head is calculated by adding up the friction losses through all straight pipe sections, valves, fittings, strainers, and terminal equipment like boilers or chillers at your target flow rate.

Why do hot water inline pumps require specialized mechanical seals?

Standard mechanical seals use basic elastomers like NBR that degrade and leak at high temperatures. Hot water pumps require specialized materials like Viton, EPDM, or Kalrez, along with harder face pairings like silicon carbide, to maintain a reliable seal.

Is a concrete foundation block mandatory for all inline pumps?

Small, lightweight inline pumps can be supported directly by properly anchored pipeline hangers. However, heavy industrial units require a dedicated floor foundation or structural base to prevent transferring physical stresses into the pump casing.

What is the difference between an inline pump and an end-suction pump?

An inline pump features suction and discharge ports aligned on a single centerline for direct pipeline installation. An end-suction pump pulls fluid in through the front and discharges it up at a 90-degree angle, requiring a larger floor footprint and a dedicated base plate.

How does fluid viscosity affect pump selection?

High-viscosity fluids increase internal friction and hydraulic drag inside the pump. This alters the pump’s performance curve, reducing flow and head capacity while increasing the required motor horsepower to prevent overloading.

Can I run an inline pump continuously at zero flow?

No. Running a centrifugal pump against a closed discharge valve traps fluid inside the volute casing. The energy from the rotating impeller quickly turns into heat, boiling the liquid and causing rapid seal failure or casing damage.

What parameters must be provided to get an accurate supplier quote?

You should provide your required operating flow rate, total dynamic head, the fluid type and its temperature range, the nominal pipe connection sizes, your preferred mounting layout, and facility electrical details like voltage and phase.