Sandwich structures with tapered tubes as core:A quasi-static investigation

In this article,the experimental and finite element analysis is utilized to investigate the quasi-static compression features of sandwich constructions built with tapered tubes.3D printing technology was utilized to create the hollow centers of the tapering tubes,with and without corrugations.The results demonstrate that the energy absorption(EA)and specific energy absorption(SEA)of the single corrugated tapered tube sandwich are 51.6% and 19.8% higher,respectively,than those of the conical tube sandwich.Furthermore,the results demonstrate that energy absorbers can benefit from corrugation in order to increase their efficiency.Additionally,the tapered corrugated tubes'resistance to oblique impacts was studied.Compared to a straight tube,the tapered tube is more resistant to oblique loads and has a lower initial peak crushing force(PCF),according to numerical simulations.After conducting a parametric study,it was discovered that the energy absorption performance of the sandwich construction is significantly affected by the amplitude,number of corrugations,and wall thickness.EA and SEA of DTS with corrugation number of 8 increased by 17.4%and 29.6%,respectively,while PCF decreased by 9.2% compared to DTS with corrugation number of 10.

Nasogastric tube syndrome:A Meta-summary of case reports

BACKGROUND Since its description in 1790 by Hunter,the nasogastric tube(NGT)is commonly used in any healthcare setting for alleviating gastrointestinal symptoms or enteral feeding.However,the risks associated with its placement are often underes-timated.Upper airway obstruction with a NGT is an uncommon but potentially life-threatening complication.NGT syndrome is characterized by the presence of an NGT,throat pain and vocal cord(VC)paralysis,usually bilateral.It is poten-tially life–threatening,and early diagnosis is the key to the prevention of fatal upper airway obstruction.However,fewer cases may have been reported than might have occurred,primarily due to the clinicians'unawareness.The lack of specific signs and symptoms and the inability to prove temporal relation with NGT insertion has made diagnosing the syndrome quite challenging.AIM To review and collate the data from the published case reports and case series to understand the possible risk factors,early warning signs and symptoms for timely detection to prevent the manifestation of the complete syndrome with life-threatening airway obstruction.METHODS We conducted a systematic search for this meta-summary from the database of PubMed,EMBASE,Reference Citation Analysis(https://www.referencecitation-analysis.com/)and Google scholar,from all the past studies till August 2023.The search terms included major MESH terms"Nasogastric tube","Intubation,Gastrointestinal","Vocal Cord Paralysis",and“Syndrome”.All the case reports and case series were evaluated,and the data were extracted for patient demographics,clinical symptomatology,diagnostic and therapeutic interventions,clinical course and outcomes.A datasheet for evaluation was further prepared.RESULTS Twenty-seven cases,from five case series and 13 case reports,of NGT syndrome were retrieved from our search.There was male predominance(17,62.96%),and age at presentation ranged from 28 to 86 years.Ten patients had diabetes mellitus(37.04%),and nine were hypertensive(33.33%).Only three(11.11%)patients were reported to be immunocompromised.The median time for developing symptoms after NGT insertion was 14.5 d(interquartile range 6.25-33.75 d).The most commonly reported reason for NGT insertion was acute stroke(10,37.01%)and the most commonly reported symptoms were stridor or wheezing 17(62.96%).In 77.78%of cases,bilateral VC were affected.The only treatment instituted in most patients(77.78%)was removing the NG tube.Most patients(62.96%)required tracheostomy for airway protection.But 8 of the 23 survivors recovered within five weeks and could be decannulated.Three patients were reported to have died.CONCLUSION NGT syndrome is an uncommon clinical complication of a very common clinical procedure.However,an under-reporting is possible because of misdiagnosis or lack of awareness among clinicians.Patients in early stages and with mild symptoms may be missed.Further,high variability in the presentation timing after NGT insertion makes diagnosis challenging.Early diagnosis and prompt removal of NGT may suffice in most patients,but a significant proportion of patients presenting with respiratory compromise may require tracheostomy for airway protection.

Crashworthiness Design and Multi-Objective Optimization of Bionic Thin-Walled Hybrid Tube Structures

Thin-walled structures are widely used in cars due to their lightweight construction and energy-absorbing properties.However,issues such as high initial stress and lowenergy-absorbing efficiency arise.This study proposes a novel energy-absorbing structure inwhich a straight tube is combinedwith a conical tube and a bamboo-inspired bulkhead structure is introduced.This configuration allows the conical tube to flip outward first and then fold together with the straight tube.This deformation mode absorbs more energy and less peak force than the conical tube sinking and flipping inward.Through finite element numerical simulation,the specific energy absorption capacity of the structure is increased by 26%compared to that of a regular circular cross-section tube.Finally,the impact resistance of the bionic straight tapered tube structure is further improved through multi-objective optimization,promoting the engineering application and lightweight design of hybrid cross-section tubes.

A novel efficient energy absorber with free inversion of a metal foam-filled circular tube

In this paper, a novel efficient energy absorber with free inversion of a metal foam-filled circular tube(MFFCT) is designed, and the axial compressive behavior of the MFFCT under free inversion is studied analytically and numerically. The theoretical analysis reveals that the energy is mainly dissipated through the radial bending of the metal circular tube, the circumferential expansion of the metal circular tube, and the metal filled-foam compression. The principle of energy conservation is used to derive the theoretical formula for the minimum compressive force of the MFFCT over free inversion under axial loading. Furthermore, the free inversion deformation characteristics of the MFFCT are analyzed numerically. The theoretical steady values are found to be in good agreement with the results of the finite element(FE) analysis. The effects of the average diameter of the metal tube, the wall thickness of the metal tube, and the filled-foam strength on the free inversion deformation of the MFFCT are considered. It is observed that in the steady deformation stage, the load-carrying and energy-absorbing capacities of the MFFCT increase with the increase in the average diameter of the metal tube, the wall thickness of the metal tube, or the filled-foam strength. The specific energy absorption(SEA) of free inversion of the MFFCT is significantly higher than that of the metal tube alone.

Heat Transfer Enhancement of the Absorber Tube in a Parabolic Trough Solar Collector through the Insertion of Novel Cylindrical Turbulators

This study includes an experimental and numerical analysis of the performances of a parabolic trough collector(PTC)with and without cylindrical turbulators.The PTC is designed with dimensions of 2.00 m in length and 1.00 m in width.The related reflector is made of lined sheets of aluminum,and the tubes are made of stainless steel used for the absorption of heat.They have an outer diameter of 0.051 m and a wall thickness of 0.002 m.Water,used as a heat transfer fluid(HTF),flows through the absorber tube at a mass flow rate of 0.7 kg/s.The dimensions of cylindrical turbulators are 0.04 m in length and 0.047 m in diameter.Simulations are performed using the ANSYS Fluent 2020 R2 software.The PTC performance is evaluated by comparing the experimental and numerical outcomes,namely,the outlet temperature,useful heat,and thermal efficiency for a modified tube(MT)(tube with novel cylindrical turbulators)and a plain tube(PT)(tube without novel cylindrical turbulators).According to the results,the experimental outlet temperatures recorded 63.2°C and 50.5°C for the MT and PT,respectively.The heat gain reaches 1137.5 Win the MT and 685.8 Win the PT.Compared to the PT collector,the PTC exhibited a(1.64 times)higher efficiency.

Study on the low mechanical anisotropy of extruded Mg-Zn-Mn-Ce-Ca alloy tube in the compression process

In this study,the extruded Mg-Zn-Mn-Ce-Ca alloy tube with a low compression anisotropy along the ED,45ED and TD was prepared.The effect of the second phases,initial texture and deformation behavior on this low mechanical anisotropy was investigated.The results revealed that the alloy tube contains the high content(Mg1-xZnx)11Ce phase and the low content of Mg12Ce phase.These second phases are respectively incoherent and coherent with the Mg matrix,and their influence can be ignored.Additionally,the alloy tube exhibited a weak basal fiber texture,where the c-axis was aligned along the 0°∼30°tilt from TD to ED.Such a texture made the initial deformation(at 1.0%∼1.6%strain)of the three samples controlled by comparable basalslip.As deformation progressed(1.6∼9.0%strain),larger amounts of ETWs nucleated and gradually approached saturation in the three samples,re-orienting the c-axis to a 0°∼±30°deviation with respect to the loading directions.Meanwhile,the prismatic and pyramidal<c+a>slips replaced the dominant deformation progressively until fracture.Eventually,the similar deformation mechanisms determined by the weak initial texture in the three samples contribute to the comparable strain hardening rates,resulting in the low compressive anisotropy of the alloy tube.

Modified intratympanic steroid therapy for sudden sensorineural hearing loss via tympanic tube and gelfoam as a salvage treatment

Background: Sudden sensorineural hearing loss(SSNHL) is a prevalent emergency in ear, nose, and throat practice. Previous studies have demonstrated that intratympanic steroid therapy(IST) can serve as a salvage treatment for SSNHL after the failure of systemic steroid therapy(SST).Objective: This study aimed to analyze the efficacy of modified IST involving the insertion of a tympanic tube and gelfoam as a salvage treatment for patients with SSNHL, and to explore its associated factors.Methods: Totally, 74 patients who were aged 22–81 years with SSNHL were enrolled and allocated to either the control group(n = 25) or the treatment group(n = 49) based on their treatment modalities. All patients received SST lasting for at least 7 days. Subsequently, patients in the treatment group, after SST failure, underwent IST twice a week for 2–6 weeks, while the control group did not. Efficacy was assessed by the improvement in pure tone average at the affected frequency at the beginning and end of IST.Results: Hearing improvement in all patients after IST in the treatment group was 9.71 ± 14.84 dB, with significant improvement at affected frequencies(250-8000 Hz) compared with the control group(P < 0.05). The findings indicated the duration from the onset of SSNHL to the beginning of IST as an independent factor for pure tone average improvement after treatment(P = 0.002), whereas age, duration of SST, and time of IST were not(P > 0.05).Conclusion: The modified IST was demonstrated to be a safe and effective method as a salvage treatment for SSNHL. This study explored the efficacy of a modified IST approach, incorporating the utilization of tympanic tubes and gelfoam as key components. The findings underscore the advantages of gelfoam as a strategic drug carrier placed in the round window niche. By minimizing drug loss, extending action time, and increasing perilymph concentration, gelfoam enhances the therapeutic impact of IST, contributing to improved hearing outcomes in patients with SSNHL.

Analysis and Optimization of the Electrohydraulic Forming Process of Sinusoidal Corrugation Tubes

Aluminum alloy thin-walled structures are widely used in the automotive industry due to their advantages related to light weight and crashworthiness.They can be produced at room temperature by the electrohydraulic forming process.In the present study,the influence of the related parameters on the forming quality of a 6063 aluminum alloy sinusoidal corrugation tube has been assessed.In particular,the orthogonal experimental design(OED)and central composite design(CCD)methods have been used.Through the range analysis and variance analysis of the experimental data,the influence degree of wire diameter(WD)and discharge energy(DE)on the forming quality was determined.Multiple regression analysis was performed using the response surface methodology.A prediction model for the attaching-die state coefficient was established accordingly.The following optimal arrangement of parameters was obtained(WD=0.759 mm,DE=2.926 kJ).The attaching-die state coefficient reached the peak value of 0.001.Better optimized wire diameter and discharge energy for a better attaching-die state could be screened by CCD compared with OED.The response surface method in CCD was more suitable for the design and optimization of the considered process parameters.

High-grade serous carcinoma of the fallopian tube in a young woman with chromosomal 4q abnormality:A case report

BACKGROUND Few studies have reported an association between an increased risk of acquiring cancers and survival in patients with 4q deletion syndrome.This study presents a rare association between chromosome 4q abnormalities and fallopian tube highgrade serous carcinoma(HGSC)in a young woman.CASE SUMMARY A 35-year-old woman presented with acute dull abdominal pain and a known chromosomal abnormality involving 4q13.3 duplication and 4q23q24 deletion.Upon arrival at the emergency room,her abdomen appeared ovoid and distended with palpable shifting dullness.Ascites were identified through abdominal ultrasound,and computed tomography revealed an omentum cake and an enlarged bilateral adnexa.Blood tests showed elevated CA-125 levels.Paracentesis was conducted,and immunohistochemistry indicated that the cancer cells favored an ovarian origin,making us suspect ovarian cancer.The patient underwent debulking surgery,which led to a diagnosis of stage IIIC HGSC of the fallopian tube.Subsequently,the patient received adjuvant chemotherapy with carboplatin and paclitaxel,resulting in stable current condition.CONCLUSION This study demonstrates a rare correlation between a chromosome 4q abnormality and HGSC.UBE2D3 may affect crucial cancer-related pathways,including P53,BRCA,cyclin D,and tyrosine kinase receptors,thereby possibly contributing to cancer development.In addition,ADH1 and DDIT4 may be potential influencers of both carcinogenic and therapeutic responses.

Numerical simulation of the influence factors of NO_(x) emission on a W-type radiant tube

The radiant tube burner was modeled and analyzed by the numerical simulation method to investigate the influence factors and rules of NO_(x) emissions in a W-type radiant tube.These factors,which include air preheating temperature,excess air coefficient,and fuel gas composition,were modified to study their effects on NO_(x) emissions under varying working conditions.Simulation results were compared with the theoretical calculation value based on chemical reaction equilibrium theory and the onsite experimental value to verify the simulation accuracy.The results show that NO_(x) emissions rise with increasing air preheating temperatures.NO_(x) production increases to an extreme value and then decreases during the oxygen-poor to oxygen-enriched process with the rise of the excess air coefficient.Enhancing the proportion of coke oven gas in the fuel gas raises the combustion temperature as well as the NO_(x) discharge.Both the thermal efficiency and NO_(x) emissions should be balanced.Therefore,the recommended values based on the simulation results are as follows:the air preheating temperature should not exceed 400℃,the excess air coefficient should be between 1.1 and 1.2,and the volume fraction of the coke oven gas should not exceed 30%.

Primary ovarian cancer combined with primary fallopian tube cancer:A case report

BACKGROUND Low grade serous carcinoma of the ovary(LGSOC)is a rare type of epithelial ovarian cancer with a low incidence rate.The origin of ovarian cancer has always been a hot topic in gynecological oncology research,and some scholars believe that the origin of ovarian malignant tumors is the fallopian tubes.Primary fallopian tube cancer is the lowest incidence of malignant tumors in the female reproductive system.There are only a few reports in the literature,but the mortality rate is very high.But in clinical practice,fallopian tube cancer is very common,but in most cases,it is classified as ovarian cancer.CASE SUMMARY We report a 54 years old postmenopausal woman who was hospitalized with a lower abdominal mass and underwent surgical treatment.The final pathological confirmation was low-grade serous carcinoma of the right ovary and low-grade serous carcinoma of the left fallopian tube.No special treatment was performed after the surgery,and the patient was instructed to undergo regular follow-up without any signs of disease progression.CONCLUSION The prognosis of LGSOC is relatively good,over 80%of patients still experience disease recurrence.

Creep rupture properties and microstructure stability of the GH984G alloy tube

GH984G alloy is a significant candidate material for 650-700℃ ultra-supercritical coal-fired generating units.In this paper,creep rupture properties and microstructure stability of the GH984G alloy tube were studied,and the findings indicated excellent creep rupture properties at 700℃.Furthermore,the extrapolated strength for 100000 h was found to be 153.8 MPa,which satisfies the requirements for the long-term performance of high-temperature materials in power stations.Aging at 700℃ with the extension of time,the grain boundary carbides and the particle size of the γ′phase on the matrix gradually coarsen,but its spherical morphology remains uniformly distributed.However,no harmful phase precipitates were found even after aging at 700℃ for up to 19144 h.Excellent microstructure stability guarantees the 700℃ creep rupture properties of the GH984G alloy tube.

Clinical application of reserved gastric tube in neuroendoscopic endonasal surgery for pituitary tumor

BACKGROUND The neuroendoscopic approach has the advantages of a clear operative field,convenient tumor removal,and less damage,and is the development direction of modern neurosurgery.At present,transnasal surgery for sphenoidal pituitary tumor is widely used.But it has been found in clinical practice that some patients with this type of surgery may experience post-operative nausea and vomiting and other discomforts.AIM To explore the effect of reserved gastric tube application in the neuroendoscopic endonasal resection of pituitary tumors.METHODS A total of 60 patients who underwent pituitary adenoma resection via the endoscopic endonasal approach were selected and randomly divided into the experimental and control groups,with 30 in each group.Experimental group:After anesthesia,a gastric tube was placed through the mouth under direct vision using a visual laryngoscope,and the fluid accumulated in the oropharynx was suctioned intermittently with low negative pressure throughout the whole process after nasal disinfection,during the operation,and when the patient recovered from anesthesia.Control group:Given the routine intraoperative care,no gastric tube was left.The number of cases of nausea/vomiting/aspiration within 24 h post-operation was counted and compared between the two groups;the scores of pharyngalgia after waking up,6 h post-operation,and 24 h postoperation.The frequency of postoperative cerebrospinal fluid leakage and intracranial infection were compared.The hospitalization days of the two groups were statistically compared.RESULTS The times of postoperative nausea and vomiting in the experimental group were lower than that in the control group,and the difference in the incidence of nausea was statistically significant(P<0.05).After the patient woke up,the scores of sore throat 6 h after the operation and 24 h after operation were lower than those in the control group,and the difference was statistically significant(P<0.05).The number of cases of postoperative cerebrospinal fluid leakage and intracranial infection was higher than that of the control group,but there was no statistically significant difference from the control group(P>0.05).The hospitalization days of the experimental group was lower than that of the control group,and the difference was statistically significant(P<0.05).CONCLUSION Reserving a gastric tube in the endoscopic endonasal resection of pituitary tumors,combined with intraoperative and postoperative gastrointestinal decompression,can effectively reduce the incidence of nausea,reduce the number of vomiting and aspiration in patients,and reduce the complications of sore throat The incidence rate shortened the hospitalization days of the patients.

Impact Containment Barriers with Geotextile Tubes

Recently, tragic tailings dam collapses in Brazil have caused deaths and major destruction and the need to develop technologies capable of preventing damage to people and the environment. Brazilian tailings dams are in a situation of uncertainty due to new legislation that even requires decommissioning, an activity that involves many problems and where the risk of failure is the main one. An impact containment structure downstream of these dams can be effective and geotextile tubes, in a new approach, have emerged as an option with advantages in terms of execution, costs and safety. The technology is versatile and can bring many benefits such as the reuse of tailings or filling with low-energy or reused materials. In this research, geotextile tubes were tested as free containment barriers, experiencing impacts in reduced models. The safety factor for the stability of the structure was constructed using an equation which is the ratio between the self-weight of the barrier structure and its coefficient of static friction and the impact pressure, where the data showed an adequate correlation which suggests the viability of mitigating risks.

Comparison of decompression tubes with metallic stents for the management of right-sided malignant colonic obstruction

BACKGROUND Emergency surgical resection is a standard treatment for right-sided malignant colonic obstruction; however, the procedure is associated with high rates of mortality and morbidity. Although a bridge to surgery can be created to obviate the need for emergency surgery, its effects on long-term outcomes and the most practical management strategies for right-sided malignant colonic obstruction remain unclear.AIM To determine the appropriate management approach for right-sided malignant colonic obstruction.METHODS Forty patients with right-sided malignant colonic obstruction who underwent curative resection from January 2007 to April 2017 were included in the study.We compared the perioperative and long-term outcomes of patients who received bridges to surgery established using decompression tubes and those created using self-expandable metallic stents(SEMS). The primary outcome was the overall survival duration(OS) and the secondary endpoints were the diseasefree survival(DFS) duration and the preoperative and postoperative morbidity rates. Analysis was performed on an intention-to-treat basis.RESULTS There were 21 patients in the decompression tube group and 19 in the SEMS group. There were no significant differences in the perioperative morbidity rates of the two groups. The OS rate was significantly higher in the decompression tube group than in the SEMS group(5-year OS rate; decompression tube 79.5%,SEMS 32%, P = 0.043). Multivariate analysis revealed that the bridge to surgery using a decompression tube was significantly associated with the OS(hazard ratio, 17.41; P = 0.004). The 3-year DFS rate was significantly higher in thedecompression tube group than in the SEMS group(68.9% vs 45.9%; log-rank test,P = 0.032). A propensity score–adjusted analysis also demonstrated that the prognosis was significantly better in the decompression tube group than in the SEMS group.CONCLUSION The bridge to surgery using trans-nasal and trans-anal decompression tubes for right-sided malignant colonic obstruction is safe and may improve long-term outcomes.

Fin formation model during pre-roll ploughing of copper 3D outside fin tube

The mechanism of pre roll ploughing for 3D fins on the outside surface of copper tube was studied systematically, and especially the process and conditions of 3D fin formation were analyzed. The right mathematical model was also established. Based on the volume of fin ploughed out is equal to the volume of the metal extruded up by the extruding face of the tool, the relations between fin height, pre roll ploughing feed and pre roll ploughing depth have been achieved. With the increase of pre roll ploughing depth which must be equal to groove depth, the fin height gradually becomes larger. There are different critical feeds with the various depths of pre roll ploughing. The pre roll ploughing feed is the critical one, the height of fin is largest. And when the feed is above the critical one, the fin height will reduce with the increase of feed. The theoretical analysis basically accords with experimental results.

VISUAL OBSERBATION OF HCFC141b GAS HYDRATE FORMATION/DECOMPOSITION PROCESS OUTSIDE OF A TUBE

In order to design a kind of heat exchanger suitable to the indirect-touched gas hydrate cool storage vessel, a visual observation of HCFC141b gas hydrate formation/decomposition process was presented through a self-designed small-scale visualization apparatus of gas hydrate cool storage. Based on the shooted photos and recorded temperatures, the formation/decomposition process of HCFC141b are described, some characteristics are concluded, and some suggestions of designing heat exchanger are indicated according to the specific characteristics of HCFC141b gas hydrate formation/decomposition process.

Numerical analysis of heat transfer enhancement on steam condensation in the presence of air outside the tube

In loss-of-coolant accidents,a passive containment heat removal system protects the integrity of the containment by condensing steam.As a large amount of air exists in the containment,the steam condensation heat transfer can be significantly reduced.Based on previous research,traditional methods for enhancing pure steam condensation may not be applicable to steam–air condensation.In the present study,new methods of enhancing condensation heat transfer were adopted and several potentially enhanced heat transfer tubes,including corrugated tubes,spiral fin tubes,and ring fin tubes were designed.STAR-CCM+was used to determine the effect of enhanced heat transfer tubes on the steam condensation heat transfer.According to the calculations,the gas pressure ranged from 0.2 to 1.6 MPa,and air mass fraction ranged from 0.1 to 0.9.The effective perturbation of the high-concentration air layer was identified as the key factor for enhancing steam–air condensation heat transfer.Further,the designed corrugated tube performed well at atmospheric pressure,with a maximum enhancement of 27.4%,and performed poorly at high pressures.In the design of spiral fin tubes,special attention should be paid to the locations that may accumulate high-concentration air.Nonetheless,the ring-fin tubes generally displayed good performance under all conditions of interest,with a maximum enhancement of 24.2%.

A study on characteristics of shock train inside a shock tube

Shock tubes are devices which are used in the investigation of high speed and high temperature flow of compressible gas. lnside a shock tube, the interaction between the reflected shock wave and boundary layer leads to a complex flow phenomenon. Initially a normal shock wave is formed in the shock tube which migrates toward the closed end of the tube and that in turn leads to the reflection of shock. Due to the boundary layer interaction with the reflected shock, the bifurcation of shock wave takes place. The bifurcated shock wave then approaches the contact surface and shock train is generated. Till date only a few studies have been conducted to investigate this shock train phenomenon inside the shock tube. For the present study a computational fluid dynamics （CFD） analysis has been performed on a two dimensional axi-symmetric model of a shock tube using unsteady, compressible Navier-Stokes equations. In order to investigate the detailed characteristics of shock train, parametric studies have been performed by varying different parameters such as the shock tube length, diameter, pressure ratio used inside the shock tube.

Optimization of FX-70 refrigerant evaporative heat transfer and fluid flow characteristics inside the corrugated tubes using multi-objective genetic algorithm

In this study,the heat transfer optimization(evaporation)and the specification of the FX-70 zeotropic refrigerant flow inside a corrugated pipe have been investigated.Despite the low HTC(HTC),this type of refrigerant is highly applicable in low or medium temperature engineering systems during the evaporation process.To eliminate this defect,high turbulence and proper mixing are required.Therefore,using heat transfer(HT)augmentation methods will be necessary and effective.In order to find the most favorable operating conditions that lead to the optimum combination of pressure drop(PD)and HTC,empirical data,neural networks,and genetic algorithms(GA)for multi-objective(MO)(NSGA II)are used.To investigate the mentioned cases,the geometric parameters of corrugated pipes,vapor quality,and mass velocity of refrigerant were studied.The results showed that with vapor quality higher than 0.8 and corrugation depth and pitch of 1.5 and 7 mm,respectively,we would achieve the desired optimum design.