Waste gas washing device
By designing the exhaust gas washing device of the spray component and the water circulation component, the problems of high water consumption and sewage blockage are solved, and the effects of water saving and environmentally friendly emissions are achieved.
Patent Information
- Application Number
- CN202422815455.0
- Authority / Receiving Office
- CN · China
- Patent Type
- Utility models(China)
- Current Assignee / Owner
- Filing Date
- 2024-11-19
- Publication Date
- 2025-09-19
- Estimated Expiration
- 2034-11-19
AI Technical Summary
Existing waste gas scrubbing equipment consumes a lot of water and is difficult to meet environmental emission requirements. In addition, the centralized discharge of sewage can easily cause pipe blockage.
An exhaust gas washing device is designed, which includes a spray component and a water circulation component. The spray component sprays into the washing channel, and the water collecting component collects and circulates the clean spray water. The sprayed water falls into the corresponding water collecting component and is discharged through an independent sewage pipe to avoid blockage caused by simultaneous drainage.
It achieves water-saving effects, extends water usage time, avoids pipe blockage caused by sewage discharge, and meets environmental protection emission requirements.
Smart Images

Figure CN223351309U_ABST
Abstract
Description
Technical Field
[0001] The utility model relates to the technical field of waste gas treatment equipment, in particular to a waste gas washing device. Background Art
[0002] The main sources of waste gas in the tobacco industry are silk exhaust, silk dust removal and roll bag dust removal. The characteristic of tobacco industry waste gas is that it contains dust particles. The main components include aromatic hydrocarbons such as benzaldehyde, phenylethanol, ethyl cinnamate, 2-heptenone and methyl benzoate, as well as trimethylamine, ammonia, benzopyrene, nitric oxide and other chemicals that pose a direct harm to the human body. After collecting this part of the waste gas, it is input into the washing device for treatment and then discharged from the fan. The odorous waste gas from silk exhaust is characterized by high temperature, high dust and high concentration. The odorous waste gas from silk dust removal and roll bag dust removal is characterized by normal temperature, low concentration and low dust content. According to the characteristics of the waste gas and working conditions, waste gas washing equipment is used to remove dust and water-soluble components in the waste gas to ensure that the treated waste gas meets the emission standards and achieves maximum economic and energy saving.
[0003] The existing waste gas washing equipment consumes a lot of water during the circulating spraying process, which makes it difficult to meet environmental emission requirements. In addition, the water supply and drainage cannot be controlled separately, and the treated sewage is discharged in a centralized manner, which can easily cause pipe blockage during the process.
[0004] In order to solve the above problems, the utility model proposes an exhaust gas scrubbing device which has low water consumption and can avoid sewage discharge from clogging pipelines. Utility Model Content
[0005] In order to solve the problems existing in the above-mentioned existing waste gas washing equipment, the utility model provides a waste gas washing device.
[0006] According to one purpose of the present invention, the present invention provides an exhaust gas scrubbing device, comprising:
[0007] a main body, the main body being provided with an inlet and an outlet, and a washing channel extending sequentially between the inlet and the outlet, the washing channel being provided with a plurality of spray assemblies sequentially arranged at intervals along the length thereof, with the output ends of the spray assemblies facing the interior of the washing channel;
[0008] A water circulation component, wherein the water circulation component and the spray component correspond one to one, the water circulation component comprises a water collecting part and a circulating cleaning part, the water collecting part, the circulating cleaning part and the spray component are circulated and connected, and each of the water collecting parts is respectively connected to a sewage pipe that can be opened and closed.
[0009] Preferably, a slope is provided on both sides of the inner bottom surface of the water collecting member in the width direction of the washing channel, and the height of the slope gradually decreases as it approaches the middle position of the inner bottom surface of the water collecting member;
[0010] The middle position of the bottom of the water collecting component extends downward to form an impurity groove, and the impurity groove is connected to the sewage pipe.
[0011] Preferably, each of the sewage pipes connected to the water collecting components is provided with a manual drainage component and an electric drainage component.
[0012] Preferably, the exhaust gas washing device further includes: a cleaning component, which includes an independent cleaning water tank, a cleaning water pump and a high-pressure nozzle. The independent cleaning water tank is arranged on the outside of the water collecting component, and the independent cleaning water tank is connected to the high-pressure nozzle through the cleaning water pump. The high-pressure nozzle is provided in each of the water collecting components, and the high-pressure nozzle is configured to be suitable for 360° rotation.
[0013] Preferably, the spray assembly includes spray heads, which are divided into two groups, namely a first group and a second group, each group containing at least two spray heads, the first group is distributed on at least one side in the length direction of the washing channel, the second group is distributed on the top of the washing channel, and the second group and the first group are staggered in the length direction of the washing channel.
[0014] Preferably, the spray assembly also includes: a spray pipe, the spray pipe includes a top pipe and several side pipes, the side pipes are arranged along the height direction of the washing channel, the side pipes are arranged in sequence along the width direction of the washing channel, the side pipes are arranged on one side in the length direction of the washing channel, a first group of nozzles are connected to the side pipe, the top pipe is arranged at the top of the washing channel, the top pipe is arranged along the width direction of the washing channel, a second group of nozzles are connected to the top pipe, and the nozzles are distributed in sequence in the length direction of the spray pipe.
[0015] Preferably, the side pipe is communicated with the top pipe, and a manual valve is provided between the side pipe and the top pipe.
[0016] Preferably, the circulating cleaning element comprises:
[0017] A circulating water pump and an automatic cleaning system are connected in sequence between the water collecting component and the spray assembly, and the automatic cleaning system is connected to the sewage pipe.
[0018] Preferably, the number of the spray assemblies is two, and the spray assemblies are divided into a first-level spray assembly and a second-level spray assembly. The first-level spray assembly and the second-level spray assembly are sequentially arranged between the inlet and the outlet. The side pipes of the first-level spray assembly are arranged vertically. The side pipes of the first-level spray assembly are divided into two groups, each group has a plurality of side pipes, and the two groups of side pipes are staggered in the length direction and width direction of the washing channel.
[0019] There are two water circulation components, namely a primary circulation component and a secondary circulation component. The primary circulation component is connected to the primary spray component, and the secondary circulation component is connected to the secondary spray component. The circulating water pump inlet end of the primary circulation component is connected to the water collecting part of the primary circulation component, and the circulating water pump outlet of the primary circulation component is connected to the automatic cleaning system of the primary circulation component.
[0020] Preferably, each of the water collecting components is connected to a water supply pipeline with a water supply pump;
[0021] A liquid level gauge is provided in the water collecting component, and the liquid level gauge controls the connection of the water supply pump, the drainage water pump and the circulating water pump respectively.
[0022] Compared with the prior art, the beneficial effects of the present invention are:
[0023] The exhaust gas scrubbing device produces exhaust gas that enters the scrubbing channel through the inlet and is then discharged through the outlet. The spray assembly sprays toward the scrubbing channel to remove water-soluble components in the exhaust gas in the scrubbing channel, ensuring that the treated exhaust gas meets emission standards. The water collecting component collects and receives the water generated by each spray assembly, and the circulating cleaning component filters and cleans the water in the water collecting component before inputting it into the spray assembly for spraying, thereby extending the use time of the water in the water collecting component and achieving the technical effect of water saving.
[0024] There are multiple water collecting components and spray components in one-to-one correspondence. The water sprayed by the spray component falls into the corresponding water collecting component. When it is necessary to discharge the sewage in the water collecting component, some sewage pipes can be selectively opened to achieve the purpose of interval drainage and independent drainage of each water collecting component, avoiding drainage of each water collecting component at the same time, causing blockage of the total sewage pipe.
[0025] The present invention is further described below with reference to the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS
[0026] Figure 1 This is a schematic diagram of an exhaust gas scrubbing device according to the present invention from one perspective;
[0027] Figure 2This is a schematic diagram of the exhaust gas scrubbing device according to the present invention from another perspective;
[0028] Figure 3 This is a schematic diagram of one perspective of a spraying first-stage component of an exhaust gas scrubbing device according to the present invention;
[0029] Figure 4 This is a schematic diagram of a spraying first-stage component of an exhaust gas scrubbing device according to the present invention from another perspective;
[0030] Figure 5 This is a schematic diagram of a spray assembly of an exhaust gas scrubbing device according to the present invention;
[0031] Figure 6 This is a schematic diagram of a water collecting component of an exhaust gas scrubbing device according to the present invention;
[0032] Figure 7 This is a schematic diagram of the slope of an exhaust gas washing device described in the present invention. DETAILED DESCRIPTION
[0033] The following description is intended to fully illustrate the present invention so that those skilled in the art can implement the present invention. The preferred embodiments described below are provided for illustrative purposes only, and those skilled in the art will readily appreciate other obvious variations. The basic principles of the present invention as defined in the following description may be applied to other embodiments, variations, improvements, equivalents, and other technical solutions that do not depart from the spirit and scope of the present invention.
[0034] See also Figure 1-7 The utility model provides a technical solution: an exhaust gas cleaning device, comprising:
[0035] A main body 100 is provided with an inlet 101 and an outlet 102, and a washing channel 103 extending sequentially between the inlet 101 and the outlet 102;
[0036] A plurality of spray assemblies 200 are provided, and the spray assemblies 200 are sequentially spaced apart along the length of the washing channel 103 , with the output ends of the spray assemblies 200 facing the interior of the washing channel 103 ;
[0037] A water circulation assembly 300, which corresponds to the spray assembly 200 on a one-to-one basis. The water circulation assembly 300 includes a water collecting member 301 and a circulating cleaning member 302. The water collecting member 301, the circulating cleaning member 302, and the spray assembly 200 are in circular communication.
[0038] The sewage pipe 400 is connected to each of the water collecting components 301 and is connected to a sewage pipe 400 that can be opened and closed.
[0039] Production waste gas enters the washing channel 103 through the inlet 101 and is then discharged through the outlet 102. The spray assembly 200 sprays into the washing channel 103 to remove water-soluble components from the waste gas in the washing channel 103, ensuring that the treated waste gas meets emission standards. The water collecting component 301 collects and receives the water generated by each spray assembly 200. The circulating cleaning component 302 filters and cleans the water in the water collecting component 301 before inputting it into the spray assembly 200 for spraying, thereby extending the use time of the water in the water collecting component 301 and achieving the technical effect of water saving.
[0040] There are multiple water collecting components 301 and spray components 200 in one-to-one correspondence. The water sprayed by the spray component 200 falls into the corresponding water collecting component 301. When it is necessary to discharge the sewage in the water collecting component 301, some sewage pipes 400 can be selectively opened to achieve the purpose of interval drainage and independent drainage of each water collecting component 301, avoiding the water collecting components 301 from draining at the same time, causing the total sewage pipe 400 to be blocked.
[0041] Preferably, the exhaust gas scrubbing device is made of corrosion-resistant high-quality 304 stainless steel.
[0042] Furthermore, the height of the inner bottom surface of the water collecting member 301 gradually decreases as it approaches the middle position. Specifically, the inner bottom surface of the water collecting member 301 is divided into two slopes 3011 on either side of the width of the washing channel 103. The two slopes 3011 are inclined downward near the middle position of the width of the washing channel 103. Preferably, the inclination angle of the slopes 3011 is 3°, that is, the angle between the slopes 3011 and the horizontal plane is 3°. Furthermore, the middle position of the bottom of the water collecting member 301 extends downward to form an impurity trough 3012. The impurity trough 3012 is connected to the sewage pipe 400, and the sewage pipe 400 is provided with a drainage pump. When in use, the height of the inner bottom surface of the water collecting component 301 on both sides in the width direction of the washing channel 103 is higher than the middle position. The impurities deposited in the water collecting component 301 can slide along the slope surface 3011 into the impurity groove 3012. By connecting the sewage pipe 400 to the impurity groove 3012, the sewage containing impurities in the water collecting component 301 can be discharged smoothly through the sewage pipe 400.
[0043] Furthermore, each of the sewage pipes 400 connected to the water collecting component 301 is equipped with a manual drainage component and an electric drainage component, and is also equipped with a maintenance manual valve. When the electric valve on the electric drainage component fails, sewage can be drained and maintained through the manual valve 2023 on the manual drainage component.
[0044] Furthermore, the exhaust gas scrubbing device further includes: a cleaning component 500, wherein the cleaning component 500 includes:
[0045] An independent cleaning water tank 501, a cleaning water pump 502 and a high-pressure nozzle 503 are provided. The independent cleaning water tank 501 is arranged on the outside of the water collecting part 301. The independent cleaning water tank 501 is connected to the high-pressure nozzle 503 through the cleaning water pump 502. At least one high-pressure nozzle 503 is provided in each of the water collecting parts 301. Specifically, the cleaning water pump 502 and the high-pressure nozzle 503 are connected through a cleaning branch. Preferably, the high-pressure nozzle 503 is configured to be suitable for 360° rotation. After the device has been running for a period of time, impurities remain inside the water collecting part 301 and the water quality is relatively dirty. An additional independent cleaning water tank 501 is added and does not participate in the circulating spraying. The water quality inside the independent cleaning water tank 501 is clean. The cleaning water pump 502 is started, and the high-pressure nozzle 503 on the cleaning branch of the water pump outlet 102 performs 360° high-speed flushing on the inside of each water collecting part 301. This process is fully automated, saving manual cleaning operations. Preferably, the high-pressure nozzle 503 uses a 23240-3 nozzle, and the water pressure will drive the nozzle 201360 degrees to rotate.
[0046] Furthermore, the spray assembly 200 includes a nozzle 201, which is divided into two groups, namely a first group and a second group, each group containing at least two nozzles 201, the first group is distributed on at least one side in the length direction of the washing channel 103, and the second group is distributed at the top of the washing channel 103, the second group and the first group are staggered in the length direction of the washing channel 103 to cover the gap between the top equipment and prevent exhaust gas from escaping, and the water collecting component 301 is located at the bottom of the washing channel 103.
[0047] Preferably, the nozzle 201 adopts an HHSJ type nozzle with a spray angle of 120. The model of the nozzle 201 can be adjusted according to the equipment.
[0048] Specifically, the spray assembly 200 further includes:
[0049] The spray pipe 202 includes a plurality of side pipes 2022 and a top pipe 2021. The side pipes 2022 are arranged along the height direction of the washing channel 103, and the side pipes 2022 are arranged in sequence and at intervals along the width direction of the washing channel 103. The side pipes 2022 are arranged on one side in the length direction of the washing channel 103. The side pipes 2022 are connected to a first group of nozzles 201. The top pipe 2021 is arranged at the top of the washing channel 103. The top pipe 2021 is arranged along the width direction of the washing channel 103. The top pipe 2021 is connected to a second group of nozzles 201. The nozzles 201 are distributed in sequence and at intervals in the length direction of the spray pipe 202.
[0050] Furthermore, there are two spray components 200, and the spray components 200 are divided into a first-level spray component 200a and a second-level spray component 200b. The first-level spray component 200a and the second-level spray component 200b are arranged in sequence between the inlet 101 and the outlet 102. The side pipes 2022 of the first-level spray component 200a are arranged vertically. The side pipes 2022 of the first-level spray component 200a are divided into two groups, and the number of the side pipes 2022 in each group is multiple. The two groups of side pipes 2022 are staggered in the length and width directions of the washing channel 103, and the side pipes 2022 of the second-level spray component 200b correspond to one group of side pipes 2022 of the first-level spray component 200a. According to the above definition, the first-level spray component 200a adopts a staggered arrangement of double-layer vertical side pipes 2022, and the nozzles 201 on the front and rear layers of side pipes 2022 are also staggered. The double-layer side pipes 2022 cooperate with the nozzles 201 to form a water curtain wall, and the top pipe 2021 cooperates with the nozzles 201 to form a top spray water curtain, so that the water curtain covers the radial section of the washing channel 103 in all directions without dead angles, ensuring that the exhaust gas is fully in contact with the water curtain when passing through the radial section of the washing channel 103, thereby achieving filtering and washing of the exhaust gas.
[0051] Furthermore, the side pipe 2022 is connected to the top pipe 2021, and the exhaust gas scrubbing device also includes a manual valve 2023 connected between the side pipe 2022 and the top pipe 2021. Specifically, the top of the side pipe 2022 is connected to the top pipe 2021 via a branch pipe, and the manual valve 2023 is connected to the branch pipe. During use, the side spray and top spray effects can be adjusted by adjusting the manual valve 2023.
[0052] Furthermore, the nozzle 201 adopts a corrosion-resistant, stainless steel spiral filling non-clogging nozzle. The nozzle 201 is in the form of a spiral nozzle, characterized by a solid conical spray nozzle with a spray angle of 60° to 170°. This compact nozzle can achieve the maximum flow rate of liquid in a pipe of a given size, and the unobstructed channel design minimizes blockage.
[0053] Regarding the specific structure of the circulating cleaning member 302, the circulating cleaning member 302 includes:
[0054] The circulating water pump 3021 and the automatic cleaning system 3022 are connected in sequence between the water collecting component 301 and the spray assembly 200 , and the automatic cleaning system 3022 is connected to the sewage pipe 400 .
[0055] In one embodiment of the present invention, there are two water circulation components 300, namely a primary circulation component 300a and a secondary circulation component 300b, the primary circulation component 300a is connected to the spray primary component 200a, and the secondary circulation component 300b is connected to the spray secondary component 200b, wherein the inlet end of the circulating water pump 3021 of the primary circulation component 300a is connected to the water collecting part 301 of the primary circulation component 300a, and the outlet 102 of the circulating water pump 3021 of the primary circulation component 300a is connected to the automatic cleaning system 3022 of the primary circulation component 300a, that is, the circulating water pump 3021 of the primary circulation component 300a and the automatic cleaning system 3022 of the primary circulation component 300a are sequentially connected between the water collecting part 301 of the primary circulation component 300a and the spray primary component 200a. During use, an automatic cleaning system 3022 is provided at the outlet 102 of the circulating water pump 3021 of the primary circulation component 300a. The circulating water passing through the automatic cleaning system 3022 is then pumped into the top spraying primary component 200a. The automatic cleaning system 3022 can filter and clean the sewage in the water collecting component 301 of the primary circulation component 300a before spraying, thereby extending the use time of the circulating water inside the water collecting component 301, reducing water consumption, and saving operating costs.
[0056] The water collecting part 301 of the first-level circulation component 300a, the water collecting part 301 of the second-level circulation component 300b and the independent cleaning water tank 501 are arranged in sequence in the length direction of the washing channel 103. The water collecting part 301 of the first-level circulation component 300a and the water collecting part 301 of the second-level circulation component 300b are sealed by a partition. The installation position of the partition is determined according to the water pump flow, and then the size of the water collecting part 301 of each level of circulation components is designed to ensure that the water circulation time of the water collecting part 301 of each level of circulation components is more than 60s.
[0057] Furthermore, the exhaust gas scrubbing device further comprises:
[0058] Water supply pipeline, each of the water collecting components 301 is connected to a water supply pipeline with a water supply pump;
[0059] A liquid level gauge is installed in the water collecting unit 301. It controls the water replenishment pump, the drainage pump, and the circulating water pump 3021. During use, the liquid level feedback signal from the liquid level gauge in each water collecting unit 301 is used to independently control the automatic replenishment, drainage, and spraying functions of each water collecting unit 301. This allows for automatic adjustment based on the project's exhaust gas operating conditions, selective activation, real-time monitoring of various system operating parameters, and automatic fault diagnosis.
[0060] In summary, the exhaust gas washing device utilizes the combination of the spray component 200 and the water circulation component 300 to achieve exhaust gas discharge that meets the standards after passing through the washing channel 103, thus complying with environmental emission requirements.
[0061] The embodiments described above are only used to illustrate the technical ideas and features of the present invention. Their purpose is to enable those skilled in the art to understand the content of the present invention and implement it accordingly. The scope of patent application of the present invention cannot be limited by these embodiments alone. That is, any equivalent changes or modifications made according to the spirit disclosed by the present invention still fall within the patent scope of the present invention.
Claims
1. An exhaust gas scrubbing device, characterized in that: include: A main body (100) is provided with an inlet (101) and an outlet (102), and a washing channel (103) sequentially extending between the inlet (101) and the outlet (102), wherein the washing channel (103) is sequentially and spaced apart along a length direction thereof, and an output end of the spraying component (200) faces the interior of the washing channel (103); A water circulation component (300) is provided, wherein the water circulation component (300) corresponds to the spray component (200) on a one-to-one basis. The water circulation component (300) comprises a water collecting part (301) and a circulating cleaning part (302). The water collecting part (301), the circulating cleaning part (302) and the spray component (200) are in circulation communication with each other, and each water collecting part (301) is connected to a sewage pipe (400) that can be opened and closed.
2. The exhaust gas scrubbing device according to claim 1, characterized in that: The inner bottom surface of the water collecting member (301) is provided with a slope surface (3011) on both sides in the width direction of the washing channel (103), and the height of the slope surface (3011) gradually decreases as it approaches the middle position of the inner bottom surface of the water collecting member (301); The middle position of the bottom of the water collecting member (301) extends downward to form an impurity groove (3012), and the impurity groove (3012) is connected to the sewage pipe (400).
3. The exhaust gas scrubbing device according to claim 1, characterized in that: The sewage pipe (400) connected to each of the water collecting components (301) is equipped with a manual drainage component and an electric drainage component.
4. The exhaust gas scrubbing device according to claim 1, characterized in that: Also includes: A cleaning assembly (500) includes an independent cleaning water tank (501), a cleaning water pump (502) and a high-pressure nozzle (503). The independent cleaning water tank (501) is arranged outside the water collecting member (301). The independent cleaning water tank (501) is connected to the high-pressure nozzle (503) through the cleaning water pump (502). Each of the water collecting members (301) is provided with the high-pressure nozzle (503), and the high-pressure nozzle (503) is configured to rotate 360 degrees.
5. The exhaust gas scrubbing device according to claim 1, characterized in that: The spray assembly (200) comprises a spray head (201), and the spray heads (201) are divided into two groups, namely a first group and a second group, each group comprising at least two spray heads (201), the first group being distributed on at least one side in the length direction of the washing channel (103), the second group being distributed on the top of the washing channel (103), and the second group and the first group being staggered in the length direction of the washing channel (103).
6. The exhaust gas scrubbing device according to claim 5, characterized in that: The spray assembly (200) further comprises: a spray pipe (202), the spray pipe (202) comprising a top pipe (2021) and a plurality of side pipes (2022), the side pipes (2022) being arranged along the height direction of the washing channel (103), the side pipes (2022) being arranged at intervals in sequence along the width direction of the washing channel (103), the side pipes (2022) being arranged on one side in the length direction of the washing channel (103), the side pipes (2022) being connected to a first group of spray heads (201), the top pipe (2021) being arranged at the top of the washing channel (103), the top pipe (2021) being arranged along the width direction of the washing channel (103), the top pipe (2021) being connected to a second group of spray heads (201), the spray heads (201) being distributed at intervals in sequence in the length direction of the spray pipe (202).
7. The exhaust gas scrubbing device according to claim 6, characterized in that: The side pipe (2022) is connected to the top pipe (2021), and a manual valve (2023) is provided between the side pipe (2022) and the top pipe (2021).
8. The exhaust gas scrubbing device according to claim 6, characterized in that: The circulating cleaning member (302) comprises: A circulating water pump (3021) and an automatic cleaning system (3022) are connected in sequence between the water collecting component (301) and the spray assembly (200), and the automatic cleaning system (3022) is connected to the sewage pipe (400).
9. The exhaust gas scrubbing device according to claim 8, characterized in that: There are two spray assemblies (200), and the spray assemblies (200) are divided into a first-level spray assembly (200a) and a second-level spray assembly (200b). The first-level spray assembly (200a) and the second-level spray assembly (200b) are sequentially arranged between the inlet (101) and the outlet (102). The side pipes (2022) of the first-level spray assembly (200a) are arranged vertically. The side pipes (2022) of the first-level spray assembly (200a) are divided into two groups, and the number of the side pipes (2022) in each group is multiple. The two groups of side pipes (2022) are staggered in the length direction and the width direction of the washing channel (103). There are two water circulation components (300), namely a primary circulation component (300a) and a secondary circulation component (300b). The primary circulation component (300a) is connected to the primary spray component (200a), and the secondary circulation component (300b) is connected to the secondary spray component (200b). The inlet end of the circulation water pump (3021) of the primary circulation component (300a) is connected to the water collecting part (301) of the primary circulation component (300a), and the outlet (102) of the circulation water pump (3021) of the primary circulation component (300a) is connected to the automatic cleaning system (3022) of the primary circulation component (300a).
10. The exhaust gas scrubbing device according to claim 1, characterized in that: Each of the water collecting components (301) is connected to a water supply pipeline with a water supply pump; A liquid level gauge is provided in the water collecting member (301), and the liquid level gauge controls the connection of the water supply pump, the drainage water pump and the circulating water pump (3021) respectively.