Definition and Basic Principles

A constant pressure system is an advanced configuration for water pumping that maintains steady output pressure despite variations in demand or flow rate. It is widely used in residential, commercial, and industrial water supply applications, such as well systems, boosters, and building pressurization. Unlike traditional fixed-speed pumps that use large pressure tanks and experience drops during high usage, constant pressure systems employ variable frequency drives (VFDs) to adjust the pump motor's speed dynamically, ensuring consistent delivery at a preset pressure.[1]

The system operates by monitoring real-time pressure through a sensor or transducer connected to the VFD controller. The VFD then modulates the electrical frequency and voltage supplied to the pump motor to match the required flow: increasing speed for high demand (e.g., multiple outlets open) and reducing it for low demand to save energy. Key components include a submersible or surface pump, the VFD unit, a pressure sensor, and sometimes a small buffer tank. This setup avoids the cycling of conventional pumps, providing smoother operation and reducing wear. Systems typically handle capacities from 5–25 gallons per minute at 1–2 horsepower for residential use to larger 30-horsepower units for commercial applications.[1][2]

The principle relies on precise control of motor speed to maintain constant pressure, often set between 40–60 psi, independent of inlet conditions or elevation changes. Configurations can include direct boosting from mains supply, zoned setups for multi-story buildings, or series boosters with intermediate tanks to compensate for head losses. This technology enhances efficiency by operating the pump only as needed, potentially reducing energy use by 30–50% compared to standard systems.[1]

Comparison to Other Water Pumping Systems

Constant pressure systems using VFDs provide more reliable and efficient performance than traditional setups. Conventional fixed-speed pumps with pressure switches and large tanks (e.g., 20–80 gallons) maintain pressure through on/off cycling, leading to fluctuations of 10–20 psi during use and short-cycling that accelerates wear. In contrast, VFD systems deliver steady pressure without tanks or switches, minimizing starts/stops and extending pump life.[1]

Air-charged pressure tanks in older systems lose effectiveness over time as air diffuses into the water, requiring frequent recharging, while constant pressure systems eliminate this issue through electronic control. Booster pumps without VFDs often overshoot or undershoot pressure in variable demand scenarios, whereas VFD-based systems adjust instantaneously for consistent output, ideal for high-rise buildings or variable-flow applications. Energy savings in VFD systems can reach 50% in low-demand periods by running at partial speeds, compared to the full-speed operation of non-variable pumps.[2]

Pressure profiles differ markedly: traditional systems show sawtooth patterns from cycling, while constant pressure systems maintain a flat line at the setpoint, ensuring reliable flow even during peaks like simultaneous appliance use. Although initial costs for VFDs are higher, long-term benefits in durability and efficiency make them preferable for modern installations, particularly in remote wells or urban networks.[1]

Core Mechanism

The core mechanism of a constant pressure system (CPS) in water supply applications relies on variable frequency drive (VFD) technology to maintain steady output pressure by dynamically adjusting the pump motor's speed in response to real-time demand fluctuations. Unlike traditional fixed-speed pumps that use large pressure tanks and experience pressure drops during high usage, CPS integrates a VFD controller with a pressure transducer to monitor and regulate system pressure, ensuring consistent delivery without significant decay. This design, widely adopted since the early 2000s, leverages electronic controls to optimize pump operation across varying flow rates.[1]

Operation involves the VFD receiving input from a pressure sensor installed near the pump outlet or point of use. When demand increases (e.g., multiple fixtures open), the sensor detects a pressure drop, prompting the VFD to increase the electrical frequency and voltage supplied to the pump motor, ramping up its speed to boost flow and restore the preset pressure level, typically 40–60 psi for residential systems. Conversely, during low demand, the VFD reduces motor speed to match the required output, minimizing energy use and preventing over-pressurization. The system often includes a small buffer tank (1–5 gallons) for minor flow stabilization, though the VFD's precise control largely eliminates the need for larger tanks. Once pressurized, the setup provides reliable water delivery; for example, in well systems, the pump draws from the source and delivers through plumbing without user intervention beyond initial setup.[1][2]

Pressure maintenance is achieved through closed-loop feedback via one-way check valves and the VFD's algorithmic control, which prevents backflow and sustains output until demand ceases. The pressure transducer, typically a 4–20 mA device, ensures unidirectional monitoring, while soft-start features in the VFD reduce mechanical stress during speed changes. This electronic regulation mimics a constant-pressure source, avoiding the rapid drops in conventional systems by maintaining motor efficiency across the pump curve.[1]

In terms of fluid dynamics, CPS applies principles of pump affinity laws, where flow rate (Q), head (H), and power (P) scale with motor speed (N): Q ∝ N, H ∝ N², P ∝ N³. By varying N via the VFD, the system holds pressure (related to H) constant while adjusting Q to demand, yielding efficient operation independent of volume changes. This provides consistent distribution, with systems supporting flows from 5–25 gallons per minute (gpm) in residential units to higher capacities in commercial setups.[2]

Safety features include overpressure protection in the VFD, which shuts down the pump if exceeding safe limits (e.g., 65 psi), and enclosures rated NEMA 4 for weatherproofing in outdoor installations. Check valves minimize leak risks, and some models incorporate dry-run protection sensors to prevent motor damage from low water levels.[1]

Key Technological Features

Constant pressure systems utilize robust pumps, such as submersible multistage centrifugal models constructed from stainless steel or cast iron for corrosion resistance and durability in water contact. These pumps, often vertical or horizontal configurations, handle pressures up to 100 psi and integrate with VFDs for variable speed operation, with designs featuring wear-resistant impellers and balanced seals to ensure longevity under continuous modulation. Over time, pump materials have evolved to include composite options for lighter weight and higher efficiency, supporting pressures around 50–60 psig in standard applications without air chambers.[1][2]

VFD controllers and pressure sensors in CPS prioritize precise control, with transducers using piezoelectric or strain-gauge mechanisms for accurate readings (accuracy ±1% full scale) and flow rates supporting 5–100 gpm outputs. These sensors connect directly to the VFD input and maintain feedback loops for minimal lag, often incorporating digital interfaces for setpoint adjustment. Configurable outlets allow adaptation to system needs, such as zoned boosting for multi-story buildings, achieved through modular piping that preserves pressure without loss.[1]

Integration of electric motors in CPS designs optimizes performance with three-phase induction types (1/2–30 horsepower), where VFDs enable soft starts to reduce inrush current by up to 80%. These motors are modular, with accessible windings for maintenance, ensuring controlled operation without over-pressurization via built-in relays that divert excess flow if needed, targeting 40–60 psig.[2]

Key innovations include smart connectivity features, such as Modbus RTU protocols and mobile apps for remote monitoring of pressure, flow, and diagnostics, combined with ergonomic enclosures for easy installation that minimize setup time. These elements enhance scalability, from compact residential units (e.g., 1 hp for single homes) to larger commercial boosters, while protective housings ensure reliability across environments.[1]

Origins and Invention

Constant pressure systems for water supply evolved from advancements in pump technology and control mechanisms during the late 20th century, addressing the limitations of traditional fixed-speed pumps that caused pressure fluctuations with varying demand. Early efforts focused on mechanical solutions to maintain steady pressure without electronic controls. In 1993, the Cycle Stop Valve (CSV) was developed as a pioneering mechanical device to provide constant pressure by modulating flow and reducing pump cycling in well systems.[4] This invention, born from practical needs in pump and drilling businesses, used a diaphragm valve to simulate variable speed operation, allowing smaller pressure tanks and more consistent delivery.[5]

The integration of electronic variable frequency drives (VFDs) marked a significant leap, enabling precise speed control of pump motors to match demand. VFD technology itself originated in the 1960s for industrial applications, but its adaptation for residential and commercial water systems gained traction in the 1990s. The first domestic VFD-based constant pressure systems emerged around 1999, competing with mechanical alternatives like the CSV by offering energy-efficient, sensor-driven pressure regulation.[6]

Evolution in Commercial Products

Commercial adoption accelerated in the early 2000s with specialized products from major manufacturers. Franklin Electric introduced its SubDrive series around 2003, providing VFD controllers for submersible pumps that maintained constant pressure through real-time speed adjustment, compatible with a range of motor sizes.[7] Grundfos, a leader in pump innovation since 1945, developed variable speed constant pressure solutions like the SQE series, incorporating built-in VFDs for self-regulating operation in well and booster applications.[8]

Subsequent developments included enhanced features such as digital monitoring and integration with smart home systems. By the 2010s, constant pressure systems became standard in new installations, with refinements like improved energy efficiency and reduced mechanical wear driving widespread use in residential wells, commercial boosters, and municipal networks. As of 2023, these systems continue to evolve with IoT connectivity for remote management.[1]

Residential and Commercial Applications

Constant pressure systems are widely used in residential settings, particularly for well water supplies, where they ensure steady water pressure for household use regardless of demand fluctuations. In homes with submersible pumps, these systems maintain consistent flow for showers, faucets, and appliances, eliminating pressure drops during simultaneous use.[9] They are also common in booster applications for municipal water supplies with low incoming pressure, providing reliable delivery to upper floors in multi-story buildings or remote properties.[10]

In commercial environments, such as office buildings, hotels, and retail spaces, constant pressure systems support zone-divided setups to handle varying loads across different areas. For instance, they boost pressure for irrigation systems in large properties or fire suppression networks, where stable output is critical for compliance and safety. Industrial applications include manufacturing facilities and agricultural operations, where these systems manage high-volume water needs for cooling, cleaning, or livestock watering while adapting to operational demands. Configurations may involve series-connected boosters with intermediate tanks to compensate for elevation losses in tall structures or expansive sites.[10] Overall, these systems enhance water distribution reliability in urban networks and rural installations.[11]

Performance Advantages and Limitations

Constant pressure systems offer significant performance benefits over traditional fixed-speed pumps, primarily through variable speed operation via VFD controllers. They deliver unwavering pressure—typically set at 50–70 psi for residential use—reducing energy consumption by 30–50% by matching pump speed to real-time demand, which minimizes short cycling and overheating.[9] This efficiency extends equipment life by providing soft starts and stops, lowering mechanical wear on motors and impellers, and can support flows from 5–100 gallons per minute depending on horsepower ratings (up to 30 hp for commercial units).[10]

Additional advantages include improved user comfort with no pressure variations during peak usage and integration with smart monitoring via apps for diagnostics. In performance tests, these systems maintain output without large storage tanks, using small buffers for minor surges, which saves space and installation costs.[11]

However, limitations exist, such as higher upfront costs (often 20–50% more than conventional systems) due to VFD components, and the need for professional installation to ensure sensor accuracy and electrical compatibility. They may also require more frequent electronic maintenance in harsh environments, though overall durability is enhanced compared to pressure tank setups.[12]

Commercial Adoption and Market

Constant pressure water systems, utilizing variable frequency drives (VFDs) for steady pressure, have seen widespread adoption in residential, commercial, and industrial applications since the 1990s. Key manufacturers include Grundfos, Franklin Electric, and DAB Pumps, which offer integrated solutions like the Grundfos Hydro MPC booster sets and Franklin's SubDrive controllers. These systems address varying demand in well water, building pressurization, and urban supply networks.[2][1]

The global market for domestic and commercial booster pumps, including constant pressure variants, was valued at approximately USD 1.2 billion in 2023 and is projected to grow at a compound annual growth rate (CAGR) of 5.8% through 2032, driven by urbanization, water scarcity, and energy efficiency regulations. In North America and Europe, adoption is high due to stringent building codes, while emerging markets in Asia-Pacific show rapid growth from infrastructure development.[13][14]

Regulations and Patents

Constant pressure systems must comply with local building regulations and water quality standards to ensure safe and reliable operation. In the United States, the Uniform Plumbing Code (UPC) and International Plumbing Code (IPC) mandate minimum water pressure of 15–80 psi in buildings, often requiring booster systems for multi-story structures or low-supply areas. Similar requirements exist in the European Union's Pressure Equipment Directive (PED 2014/68/EU), which governs pump safety and efficiency. Non-compliance can lead to fines or installation bans.[15][16]

Patents for VFD-based constant pressure controllers date back to the late 20th century, with innovations focusing on self-calibrating systems and energy optimization. Notable examples include U.S. Patent No. 7,751,159 (2009) for a pump controller method by Emerson Electric, and U.S. Patent No. 5,941,690 (1999) for variable speed inverter control in booster pumps. These protections have enabled companies like Grundfos to refine technologies, though the core VFD application is now standard and largely unencumbered by active patents as of 2023. No major infringement disputes specific to constant pressure water systems have been widely reported, unlike in other pump sectors.[17][18]

Definition and Basic Principles

A constant pressure system is an advanced configuration for water pumping that maintains steady output pressure despite variations in demand or flow rate. It is widely used in residential, commercial, and industrial water supply applications, such as well systems, boosters, and building pressurization. Unlike traditional fixed-speed pumps that use large pressure tanks and experience drops during high usage, constant pressure systems employ variable frequency drives (VFDs) to adjust the pump motor's speed dynamically, ensuring consistent delivery at a preset pressure.[1]

The system operates by monitoring real-time pressure through a sensor or transducer connected to the VFD controller. The VFD then modulates the electrical frequency and voltage supplied to the pump motor to match the required flow: increasing speed for high demand (e.g., multiple outlets open) and reducing it for low demand to save energy. Key components include a submersible or surface pump, the VFD unit, a pressure sensor, and sometimes a small buffer tank. This setup avoids the cycling of conventional pumps, providing smoother operation and reducing wear. Systems typically handle capacities from 5–25 gallons per minute at 1–2 horsepower for residential use to larger 30-horsepower units for commercial applications.[1][2]

The principle relies on precise control of motor speed to maintain constant pressure, often set between 40–60 psi, independent of inlet conditions or elevation changes. Configurations can include direct boosting from mains supply, zoned setups for multi-story buildings, or series boosters with intermediate tanks to compensate for head losses. This technology enhances efficiency by operating the pump only as needed, potentially reducing energy use by 30–50% compared to standard systems.[1]

Comparison to Other Water Pumping Systems

Constant pressure systems using VFDs provide more reliable and efficient performance than traditional setups. Conventional fixed-speed pumps with pressure switches and large tanks (e.g., 20–80 gallons) maintain pressure through on/off cycling, leading to fluctuations of 10–20 psi during use and short-cycling that accelerates wear. In contrast, VFD systems deliver steady pressure without tanks or switches, minimizing starts/stops and extending pump life.[1]

Air-charged pressure tanks in older systems lose effectiveness over time as air diffuses into the water, requiring frequent recharging, while constant pressure systems eliminate this issue through electronic control. Booster pumps without VFDs often overshoot or undershoot pressure in variable demand scenarios, whereas VFD-based systems adjust instantaneously for consistent output, ideal for high-rise buildings or variable-flow applications. Energy savings in VFD systems can reach 50% in low-demand periods by running at partial speeds, compared to the full-speed operation of non-variable pumps.[2]

Pressure profiles differ markedly: traditional systems show sawtooth patterns from cycling, while constant pressure systems maintain a flat line at the setpoint, ensuring reliable flow even during peaks like simultaneous appliance use. Although initial costs for VFDs are higher, long-term benefits in durability and efficiency make them preferable for modern installations, particularly in remote wells or urban networks.[1]

Core Mechanism

The core mechanism of a constant pressure system (CPS) in water supply applications relies on variable frequency drive (VFD) technology to maintain steady output pressure by dynamically adjusting the pump motor's speed in response to real-time demand fluctuations. Unlike traditional fixed-speed pumps that use large pressure tanks and experience pressure drops during high usage, CPS integrates a VFD controller with a pressure transducer to monitor and regulate system pressure, ensuring consistent delivery without significant decay. This design, widely adopted since the early 2000s, leverages electronic controls to optimize pump operation across varying flow rates.[1]

Operation involves the VFD receiving input from a pressure sensor installed near the pump outlet or point of use. When demand increases (e.g., multiple fixtures open), the sensor detects a pressure drop, prompting the VFD to increase the electrical frequency and voltage supplied to the pump motor, ramping up its speed to boost flow and restore the preset pressure level, typically 40–60 psi for residential systems. Conversely, during low demand, the VFD reduces motor speed to match the required output, minimizing energy use and preventing over-pressurization. The system often includes a small buffer tank (1–5 gallons) for minor flow stabilization, though the VFD's precise control largely eliminates the need for larger tanks. Once pressurized, the setup provides reliable water delivery; for example, in well systems, the pump draws from the source and delivers through plumbing without user intervention beyond initial setup.[1][2]

Pressure maintenance is achieved through closed-loop feedback via one-way check valves and the VFD's algorithmic control, which prevents backflow and sustains output until demand ceases. The pressure transducer, typically a 4–20 mA device, ensures unidirectional monitoring, while soft-start features in the VFD reduce mechanical stress during speed changes. This electronic regulation mimics a constant-pressure source, avoiding the rapid drops in conventional systems by maintaining motor efficiency across the pump curve.[1]

In terms of fluid dynamics, CPS applies principles of pump affinity laws, where flow rate (Q), head (H), and power (P) scale with motor speed (N): Q ∝ N, H ∝ N², P ∝ N³. By varying N via the VFD, the system holds pressure (related to H) constant while adjusting Q to demand, yielding efficient operation independent of volume changes. This provides consistent distribution, with systems supporting flows from 5–25 gallons per minute (gpm) in residential units to higher capacities in commercial setups.[2]

Safety features include overpressure protection in the VFD, which shuts down the pump if exceeding safe limits (e.g., 65 psi), and enclosures rated NEMA 4 for weatherproofing in outdoor installations. Check valves minimize leak risks, and some models incorporate dry-run protection sensors to prevent motor damage from low water levels.[1]

Key Technological Features

Constant pressure systems utilize robust pumps, such as submersible multistage centrifugal models constructed from stainless steel or cast iron for corrosion resistance and durability in water contact. These pumps, often vertical or horizontal configurations, handle pressures up to 100 psi and integrate with VFDs for variable speed operation, with designs featuring wear-resistant impellers and balanced seals to ensure longevity under continuous modulation. Over time, pump materials have evolved to include composite options for lighter weight and higher efficiency, supporting pressures around 50–60 psig in standard applications without air chambers.[1][2]

VFD controllers and pressure sensors in CPS prioritize precise control, with transducers using piezoelectric or strain-gauge mechanisms for accurate readings (accuracy ±1% full scale) and flow rates supporting 5–100 gpm outputs. These sensors connect directly to the VFD input and maintain feedback loops for minimal lag, often incorporating digital interfaces for setpoint adjustment. Configurable outlets allow adaptation to system needs, such as zoned boosting for multi-story buildings, achieved through modular piping that preserves pressure without loss.[1]

Integration of electric motors in CPS designs optimizes performance with three-phase induction types (1/2–30 horsepower), where VFDs enable soft starts to reduce inrush current by up to 80%. These motors are modular, with accessible windings for maintenance, ensuring controlled operation without over-pressurization via built-in relays that divert excess flow if needed, targeting 40–60 psig.[2]

Key innovations include smart connectivity features, such as Modbus RTU protocols and mobile apps for remote monitoring of pressure, flow, and diagnostics, combined with ergonomic enclosures for easy installation that minimize setup time. These elements enhance scalability, from compact residential units (e.g., 1 hp for single homes) to larger commercial boosters, while protective housings ensure reliability across environments.[1]

Origins and Invention

Constant pressure systems for water supply evolved from advancements in pump technology and control mechanisms during the late 20th century, addressing the limitations of traditional fixed-speed pumps that caused pressure fluctuations with varying demand. Early efforts focused on mechanical solutions to maintain steady pressure without electronic controls. In 1993, the Cycle Stop Valve (CSV) was developed as a pioneering mechanical device to provide constant pressure by modulating flow and reducing pump cycling in well systems.[4] This invention, born from practical needs in pump and drilling businesses, used a diaphragm valve to simulate variable speed operation, allowing smaller pressure tanks and more consistent delivery.[5]

The integration of electronic variable frequency drives (VFDs) marked a significant leap, enabling precise speed control of pump motors to match demand. VFD technology itself originated in the 1960s for industrial applications, but its adaptation for residential and commercial water systems gained traction in the 1990s. The first domestic VFD-based constant pressure systems emerged around 1999, competing with mechanical alternatives like the CSV by offering energy-efficient, sensor-driven pressure regulation.[6]

Evolution in Commercial Products

Commercial adoption accelerated in the early 2000s with specialized products from major manufacturers. Franklin Electric introduced its SubDrive series around 2003, providing VFD controllers for submersible pumps that maintained constant pressure through real-time speed adjustment, compatible with a range of motor sizes.[7] Grundfos, a leader in pump innovation since 1945, developed variable speed constant pressure solutions like the SQE series, incorporating built-in VFDs for self-regulating operation in well and booster applications.[8]

Subsequent developments included enhanced features such as digital monitoring and integration with smart home systems. By the 2010s, constant pressure systems became standard in new installations, with refinements like improved energy efficiency and reduced mechanical wear driving widespread use in residential wells, commercial boosters, and municipal networks. As of 2023, these systems continue to evolve with IoT connectivity for remote management.[1]

Residential and Commercial Applications

Constant pressure systems are widely used in residential settings, particularly for well water supplies, where they ensure steady water pressure for household use regardless of demand fluctuations. In homes with submersible pumps, these systems maintain consistent flow for showers, faucets, and appliances, eliminating pressure drops during simultaneous use.[9] They are also common in booster applications for municipal water supplies with low incoming pressure, providing reliable delivery to upper floors in multi-story buildings or remote properties.[10]

In commercial environments, such as office buildings, hotels, and retail spaces, constant pressure systems support zone-divided setups to handle varying loads across different areas. For instance, they boost pressure for irrigation systems in large properties or fire suppression networks, where stable output is critical for compliance and safety. Industrial applications include manufacturing facilities and agricultural operations, where these systems manage high-volume water needs for cooling, cleaning, or livestock watering while adapting to operational demands. Configurations may involve series-connected boosters with intermediate tanks to compensate for elevation losses in tall structures or expansive sites.[10] Overall, these systems enhance water distribution reliability in urban networks and rural installations.[11]

Performance Advantages and Limitations

Constant pressure systems offer significant performance benefits over traditional fixed-speed pumps, primarily through variable speed operation via VFD controllers. They deliver unwavering pressure—typically set at 50–70 psi for residential use—reducing energy consumption by 30–50% by matching pump speed to real-time demand, which minimizes short cycling and overheating.[9] This efficiency extends equipment life by providing soft starts and stops, lowering mechanical wear on motors and impellers, and can support flows from 5–100 gallons per minute depending on horsepower ratings (up to 30 hp for commercial units).[10]

Additional advantages include improved user comfort with no pressure variations during peak usage and integration with smart monitoring via apps for diagnostics. In performance tests, these systems maintain output without large storage tanks, using small buffers for minor surges, which saves space and installation costs.[11]

However, limitations exist, such as higher upfront costs (often 20–50% more than conventional systems) due to VFD components, and the need for professional installation to ensure sensor accuracy and electrical compatibility. They may also require more frequent electronic maintenance in harsh environments, though overall durability is enhanced compared to pressure tank setups.[12]

Commercial Adoption and Market

Constant pressure water systems, utilizing variable frequency drives (VFDs) for steady pressure, have seen widespread adoption in residential, commercial, and industrial applications since the 1990s. Key manufacturers include Grundfos, Franklin Electric, and DAB Pumps, which offer integrated solutions like the Grundfos Hydro MPC booster sets and Franklin's SubDrive controllers. These systems address varying demand in well water, building pressurization, and urban supply networks.[2][1]

The global market for domestic and commercial booster pumps, including constant pressure variants, was valued at approximately USD 1.2 billion in 2023 and is projected to grow at a compound annual growth rate (CAGR) of 5.8% through 2032, driven by urbanization, water scarcity, and energy efficiency regulations. In North America and Europe, adoption is high due to stringent building codes, while emerging markets in Asia-Pacific show rapid growth from infrastructure development.[13][14]

Regulations and Patents

Constant pressure systems must comply with local building regulations and water quality standards to ensure safe and reliable operation. In the United States, the Uniform Plumbing Code (UPC) and International Plumbing Code (IPC) mandate minimum water pressure of 15–80 psi in buildings, often requiring booster systems for multi-story structures or low-supply areas. Similar requirements exist in the European Union's Pressure Equipment Directive (PED 2014/68/EU), which governs pump safety and efficiency. Non-compliance can lead to fines or installation bans.[15][16]

Patents for VFD-based constant pressure controllers date back to the late 20th century, with innovations focusing on self-calibrating systems and energy optimization. Notable examples include U.S. Patent No. 7,751,159 (2009) for a pump controller method by Emerson Electric, and U.S. Patent No. 5,941,690 (1999) for variable speed inverter control in booster pumps. These protections have enabled companies like Grundfos to refine technologies, though the core VFD application is now standard and largely unencumbered by active patents as of 2023. No major infringement disputes specific to constant pressure water systems have been widely reported, unlike in other pump sectors.[17][18]