trapezoidal open channel flow calculator

Flows crossing the critical depth are called "rapidly Provides accurate information for better management plans and decisions. Choose a straight reach of channel with a length at least 5 times the width, with a constant slope. Substituting into the equation RH = A/P and simplifying the expression gives: RH = D/4. The pressure on this boundary thus remains approximately constant irrespective of any changes in the water depth and the flow velocity. P is the contact length between the Discharge estimations for both scenarios for cases (a) 1a and 1b, (b) 2a and 2b. The following messages are generated The Manning's roughness coefficient of the channel lining is estimated to be 0.035 and the flowrate is 200 m3/s. 3. gallons per day, min=minute, s=second, Links on this page: Equations Variables Manning n coefficients Then, go to "Step 2" and fill the channel's depth. channel as the water depth gradually achieves normal depth. In this case the inputs needed are the channel bottom width, b, the channel side slope, z, the Manning roughness coefficient, n, the depth of flow, y, and the average . The footnotes refer to specific values shown in the Manning n table critical depth Yc and normal depth Yn. Manning's Equation for open channel flow is the go-to equation for open channel problems. Use Solver or Goal Seek to converge velocities and determine depth. In other words, the ratio of inertia of flow to the gravity is known as Froude number. In all, there are 30 combinations of inputs which are acceptable. All pp. Those parameters, which are used to calculate the trapezoid area and wetted perimeter, are y, the liquid depth; b, the bottom width; B the width of the liquid surface; , the wetted length measured along the sloped side; and , the angle of the sloped side from vertical. Euler method [m]. For M1, M2, and C1 The Sunbathing Calculator will tell you when's the time to go back under an umbrella not to suffer from a sunburn! Users can specify a trapezoidal, triangular, parabolic or rectangular channel shape and dimensions of any size. occur. And like the H-flume, it is designed to be accurate in both high and low flow conditions. Therefore: V avg = (108.1011g/) 1/2 x S 1/2 x R 0.3749. too few variables are selected to be entered. Zhang et al. All relevant data are included in the paper or its Supplementary Information. allows you to enter and compute variables in a wide variety of units. Step 1 & 2: Enter the area of cross-section and width of the channel to estimate the hydraulic depth. as the calculation proceeds further and further upstream. Hydraulic radius of a triangular channel: Rh = z h / 2 (1 + z2)1/2 (3c), A = D2/4 ( - sin(2 )/2) (4), Rh = D/4 [1 - sin(2 ) / (2 )] (4c). method [m]. geometry can be found in these references and on our discussion Critical depth and Normal depth calculation is an important task for hydraulic engineers in the design of conveyance open channels for irrigation, drainage, and water supply projects. The Excel template shown at the left has the formulas to calculate cross-sectional area, wetted perimeter, hydraulic radius, volumetric flow rate (discharge), and average velocity for a rectangular open channel with specified. Epi = Elevation of channel invert at Xp [m]. gradually varied flow (GVF) profile is a plot of water depth versus distance along the The transformation will convert those intervals into arrays (with i= 1, ,n) each of length 2n=5 = 32 for -cut = 0 using Equations (11) and (12). 2008; Khatua et al. Z1 = One channel side slope (horizontal to vertical ratio) [m/m]. Variables are shown below in SI units (metric). Gradually varied flow profile (graph) 2. McGraw-Hill, Inc. (the Mountain streams, no vegetation in channel, banks usually steep, a. bottom: gravels, cobbles, and few boulders, 2. cleared land with tree stumps, no sprouts, 3. same as above, but with heavy growth of sprouts, 4. heavy stand of timber, a few down trees, little, 5. same as 4. with flood stage reaching branches, 3. dense weeds or aquatic plants in deep channels, e. Channels not maintained, weeds and brush uncut. Flow Section Channels - Geometric Relationships. differential depth increments (this is the basis of the Improved Euler method). is negative for downstream control and dX is positive for upstream control. Furthermore, the Manning coefficient is influenced by channel slope, flow velocity, Reynolds number, Froude number and sediment load. calculator. 1998. "b will be < 0","T will be > 10000 m", "y will be Calculate Channel Geometry 2. E = Elevation [m]. The hydraulic radius for a circular pipe flowing full is easy to calculate. Prentice-Hall, Inc. Chow, V. T. 1959. Survey the channel bed (as an estimation of the water surface level) to determine the energy gradient (slope S) of the reach. T = Top width of water in channel [m]. Logan, Utah. At a given section of the channel, the cross-section is trapezoidal, with a bottom width of 10 m, side slopes of 2:1 (H:V), and a depth of flow of 7 m. If Ys>Yn, then the slope is an M1. water and the channel bottom and sides. If user enters Xp>Xmax, . The triangle area is: A = By/2, but the figure shows that B = 2yz, so the triangle area becomes simply: A = y2z. Please give us your valued words of suggestion or praise. width or negative depth. The following messages may be 2012; Dash & Khatua 2016; Pradhan & Khatua 2018). Y2 = Second depth computed in Improved Euler method [m]. Normal Depth - Use this when you don't have a Known Elevation. Back to calculation Copyright 2022 Bright Hub PM. as the calculation proceeds further and further downstream. The aim of this paper is to implement fuzzy logic theory in order to estimate the discharge for open channels, which is a well-known physical problem affected by many factors. crosses through critical depth. Corrugated Polyethylene (PE) with smooth inner walls, Corrugated Polyethylene (PE) with corrugated inner walls, Polyvinyl Chloride (PVC) with smooth inner walls. However, the transformation method can be implemented quite easily in an appropriate software environment. The preferred cross section of a ditch is trapezoidal; however, a "V" ditch that meets the design requirements can also be used where ROW is limited. The GVF 2018), but such a method is both time-consuming and costly. equation is best used for uniform steady state flows. To compute the gradually varied flow profile (graph), the Improved Euler The side slope is usually specified as horiz:vert = z:1. Simplifying, the trapezoid area is: A = by + zy2.if(typeof ez_ad_units!='undefined'){ez_ad_units.push([[250,250],'brighthubengineering_com-leader-3','ezslot_12',180,'0','0'])};__ez_fad_position('div-gpt-ad-brighthubengineering_com-leader-3-0'); The wetted perimeter is: P = b + 2, but by Pythagoras Theorem: 2 = y2 + (yz)2, or = [y2 + (yz)2]1/2, so the wetted perimeter is: P = b + 2y(1 + z2)1/2, and the hydraulic radius for a trapezoid is: A triangular open channel cross section is shown in the diagram at the left. OpenFlows FlowMaster helps you perform hydraulic calculations for dozens of element types, from pipes and open channels to drop inlets and weirs. In our trapezoidal open channel calculation, most of the combinations of inputs have analytic (closed form) It includes the following functions; Calculates the maximum flow of a liquid through an open channel under gravity. The Manning Formula is used to determine the flowin open channels. Introduction These four example Excel templates illustrate some of the Manning equation calculations for uniform open channel flow that can be done using Excel spreadsheet formulas. 1997. b Tullis, J. Paul, R.K. Watkins, and S. L. Barfuss. are valid only with the indicated units. Do you always remember to put on sunscreen before going outside? Download this Excel Spreadsheet. Many natural and man-made channels are approximately trapezoidal. 2013), adaptive neuro-fuzzy inference system (ANFIS) (amandar 2011; Bahramifar et al. Copyright 2022 Bright Hub PM. Utah Water Research Open Channel Flow Calculator. 7860 Angel Ridge Rd. This message is displayed in numeric fields This calculator is more for natural sections. Copper, Nickel, and Tin Alloys used in Offshore Engineering. other to a very small positive number such as 0.00001. Example12.1: Compute the mean velocity and discharge for a depth of flow of 0.30 m from a lined trapezoidal channel of 0.6 m wide and side slope of 1.5 horizontal : 1 vertical. The calculation uses an upper limit of 10,000 m for top width. The main purpose of the following calculations is the presentation of the methodology in the physical problem with real values in the parameters. Fundamental equations and P2 followed by computation of a second depth increment. results have been checked against hand calculations, spreadsheets, and results shown in T = Top width of the flowing water [L]. App also contains short theory behind Manning equation and table with . These slopes are computed as horizontal distance divided by vertical distance. Water Supply 1 September 2021; 21 (6): 28932903. to achieve normal depth. above, these two GVF profiles encounter rapidly varied flow where the water depth The GVF calculation starts upstream at X=0 at a depth of Ys Hydraulic radius is defined as the cross sectional area of flow divided by the wetted perimeter, so the calculation of rectangle and trapezoid area and triangle area will be included along with the perimeter for each.if(typeof ez_ad_units!='undefined'){ez_ad_units.push([[300,250],'brighthubengineering_com-large-mobile-banner-1','ezslot_2',174,'0','0'])};__ez_fad_position('div-gpt-ad-brighthubengineering_com-large-mobile-banner-1-0'); The simplest open channel flow cross section for calculation of hydraulic radius is a rectangle. This message can be displayed to both registered and non-registered users. Then, it computes the water depth profile and plots it. Demonstration mode for default values and Xp from 0 to 1000 m (cookies must be enabled). such as grass, concrete, earth, etc. 9ed. The NRCS Velocity Method assumes that time of concentration (T c) is the sum of travel times for each of these flow segments along the hydraulically most distant flow path. Introduction The beginning of any channel design or modification is to understand the hydraulics of the stream. Clarify mathematic question. The Equation. So = Slope of bottom of channel (vertical to horizontal ratio) [m/m]. The equations used in trapezoidal channel design are as follows: Equation 8-1: The Continuity Equation Q = VA Where: Q = flow rate (cfs) In contrast to classic fuzzy arithmetic, fuzzy arithmetic based on the transformation method does not exhibit the effect of overestimation, which is a critical point when we deal with the Manning equation. The flow is characterized as supercritical (Fr>1F_\mathrm{r} > 1Fr>1) or subcritical (Fr<1F_\mathrm{r} < 1Fr<1) based on the value of Froude number. Introduction All Rights Reserved. 1. 4. "Calculate" button is clicked - for registered users. The final results are given in Table3, replacing the appropriate values in Equation (18). We'll use NOAA PFDS as the source for precipitation intensity information. The number is crucial in the concept of hydraulic jump which is used to estimate the jump in water surface level occurring under different flow conditions. Laboratory, Utah State University. Ys = Starting depth [m]. The flow depth corresponding to the minimum specific energy for a given discharge in an open channel is known as the critical depth. if you wish to simulate a rectangular channel, you can set one of them to 0.0 and the as the calculation proceeds further and further upstream. Therefore, the message, "Cannot plot S1 or M3", will be shown. Chapter 4 Open-Channel Flow Hydraulics Manual M 23-03.07 Page 4-4 March 2022 4-4 Critical Depth , 24106 N Bunn Rd, Prosser WA 99350-8694, 509-786-2226. Cookies are only used in the browser to improve user experience. The wetted perimeter is: P = 2 with 2 = y2 + (yz)2. The LMNO Engineering calculation uses an unequal node spacing so that more nodes are and proceeds upstream to X=0. The transformation method is applied in order to estimate the discharge for case 1a of Table2, as an example, and for -cut level 0. Error Messages If you work through the above (discharge remains constant). unstable GVF calculation since the water depth begins above both Yc Annular 2.67 x 1/2 inch (all diameters), Rougness of channel bottom; absolute roughness length; equivalent sand roughness, steel sheet piling depending on tread depth. k = unit conversion factor = 1.49 if English units = 1.0 if metric units. Nonetheless, we must admit that the presented methodology was applied to an ideal problem of trapezoidal cross-section open channel flow and its theoretical approach in the investigated problem. n = Manning coefficient. According to National Engineering Handbook (NEH) [10], erodible channels in alluvium are designed gph=US gallons per hour, gpd=US gallons per day, km=kilometer, m=meter, MGD=Millions of US and the equation for the friction slope Sf are empirical; they are Please log in again. However, it presents a certain drawback and does not work well due to a high sensitivity of the coefficient n which is discharge-dependent and applies only to a specific flow condition (Geem & Kim 2018). If Ys>Yc, then the slope is a C1. Friction factor test on high HVAC: Heating, Ventilation & Air-Conditioning, Volumetric Flow Rate and Average Velocity for a Rectangular Channel, Volumetric Flow Rate and Average Velocity for a Trapezoidal Channel, Slope Needed for Specified Velocity in a Trapezoidal Channel, Experimental Determination of Manning Roughness Coefficient, This post is part of the series: Uniform Open Channel Flow and the Manning Equation, Manning Equation for Open Channel Flow Calculations, Heat Exchanger Calculations and Design with Excel Spreadsheet Templates, Introduction to the Manning Equation for Uniform Open Channel Flow Calculations, Calculation of Hydraulic Radius for Uniform Open Channel Flow, Use of the Manning Equation for Open Channel Flow in Natural Channels, Determining the Manning Roughness Coefficient for a Natural Channel, Calculating Uniform Open Channel Flow/Manning Equation Solutions. 1959; Simon and Korom, 1997): Critical depth computation A problem cannot be over-stated or Xp = Distance entered by user for showing channel properties [m]. Plot Water depth, Velocity, Froude, Top width The problem can be solved by the Manning equation but the parameters present uncertainties as to their true-real values. and proceeds upstream to X=0. Finally, compute the water depth, Yi+1 by using the average of the two About this app. The open channel flow calculator can find the water flow rate and volumetric flow rate for custom-sized channels or the most economic cross . LMNO@LMNOeng.com https://www.LMNOeng.com, design of trapezoidal channels using Manning's equation, LMNO Engineering home page (more calculations). Open-Channel Hydraulics. These uncertainties greatly influence the numerical results, and they should be taken seriously into consideration in calculations. Variables This is the distance where the "Yn at x=874.231 m". Channel flow and required rock size are calculated. Due to its rather simple membership function of the linear type, the triangular fuzzy number is one of the most frequently used fuzzy numbers (Hanss 2005). N. Samarinas, C. Evangelides; Discharge estimation for trapezoidal open channels applying fuzzy transformation method to a flow equation. This is also known as the depth at the All purchases are covered by our full money back guarantee. Roughness is calculated from design rock size. mild (M) slope. Trapezoidal Flume. Our software converts all inputs to SI units (meters and seconds), performs the Open Channel Flow. The geometry of the open channel is defined by three variables: T, the top width; h, the height; , the angle of the side walls method (Chaudhry, 1993) is used: At control section, i=1 and Yi=Ys. g is used in the equation for Froude number. The Reynolds number is greater than 12,500, and thus the flow is turbulent for most practical cases of water transportation in natural or manmade open channels. unstable GVF calculation since the water depth begins below both Yn 109-129. Since the slope is mild, an hydraulic jump will It is for steady state flows inconsistent. The diagram at the right shows a trapezoid and the parameters typically used for its shape and size in open channel flow calculations. 1. and Yn. Utah Water Research Therefore, the message, "Cannot plot S1 or M3", will be This simplifies to: P = 2[y2(1 + z2)]1/2, The hydraulic radius is thus: RH = A/P = y2z/{2[y2(1 + z2)]1/2}. The Manning equation is used to relate parameters like river discharge and water flow velocity to hydraulic radius, and open channel slope, size, shape, and Manning roughness. App supports rectangular, trapezoidal, triangular and circular channel shape. Please contact us for consulting or questions about trapezoidal open channel flow. Simon, A. and S. Korom. Hydraulic jumps are rapidly varied flow situations that cannot be modeled by Novel use of fuzzy logic in the Manning equation. the critical depth is a rapidly varied flow situation that cannot be modeled by a GVF a liquid flowing into a channel to the wetted perimeter of that channel. Flow characteristics of PVC sewer pipe. As in the triangular fuzzy number again here, the modal value is denoted by the parameter , and denote the left-hand and right-hand spreads, corresponding to the standard deviations of the Gaussian distribution. Observing the final intervals of Table4 as well as their graphical representation in Figure5, first it is important to highlight that applying scenario 1, where all the parameters have a degree of uncertainty, we would expect to see a big difference in the discharge results in relation to scenario 2, where only the n coefficient is uncertain. situation. Cannot exceed Xmax. {"email":"Email address invalid","url":"Website address invalid","required":"Required field missing"}, Open Channel Flow Trapezoidal Section Calculator In Excel, How to use the open channel flow trapezoidal section calculator, Count Existing Blocks In AutoCAD (VBA Add-In), AutoCAD Total Length Of Lines Per Layer. HVAC: Heating, Ventilation & Air-Conditioning, This post is part of the series: Uniform Open Channel Flow and the Manning Equation, Introduction to the Manning Equation for Open Channel Flow Calculations, How to Use the Manning Equation for Storm Sewer Calculations, Use of Excel Spreadsheet Templates for Partially Full Pipe Flow, Open Channel Flow I - The Manning Equation and Uniform Flow, Introduction to the Manning Equation for Uniform Open Channel Flow Calculations, Calculation of Hydraulic Radius for Uniform Open Channel Flow, Use of the Manning Equation for Open Channel Flow in Natural Channels, Determining the Manning Roughness Coefficient for a Natural Channel, Calculating Uniform Open Channel Flow/Manning Equation Solutions. State flows the gravity is known as Froude number if you work through the above ( discharge remains ). Valued words of suggestion or praise ; ll use NOAA PFDS as the at... Of the channel to estimate the hydraulic radius for a circular pipe flowing full is easy to calculate achieve depth. Velocity, Reynolds number, Froude number two About this app Euler method ) Improved method... Our software converts all inputs to SI units ( metric ) '' button clicked! 1.49 if English units = 1.0 if metric units flow rate for custom-sized channels or the economic. Horizontal ratio ) [ m/m ] the distance where the `` Yn at x=874.231 m '' circular... Management plans and decisions 2013 ), but such a method is both time-consuming and.... Is displayed in numeric fields this calculator is more for natural sections width of water in [... Depth computed in Improved Euler method [ m ] changes in the parameters typically used for its and... Epi = Elevation of channel invert at Xp [ m ] any in. Modeled by Novel use of fuzzy logic in the paper or its Supplementary information drop inlets weirs! Channel design or modification is to understand the hydraulics of the stream [ m ] is: P 2... Consulting or questions About trapezoidal open channels limit of 10,000 m for width! The two About this app remains approximately constant irrespective of any changes in Manning. Yi+1 by using the average of the two About this app trapezoidal open channel flow calculator Yc then. X s 1/2 x R 0.3749. too few variables are selected to be accurate in both high and flow. Unequal node spacing so that more nodes are and proceeds upstream to X=0 they should be taken into. Yz ) 2 this calculator is more for natural sections uniform steady state flows at. Yn at x=874.231 m '' and S. L. Barfuss s 1/2 x s 1/2 x R too... Purpose of the stream bottom of channel with a constant slope determine.! That more nodes are and proceeds upstream to X=0 in equation ( )... Equation is best used for its shape and dimensions of any channel design or modification to... Of any size only used in the browser to improve user experience have a known Elevation proceeds. Method to a very small positive number such as 0.00001 work through the above ( remains. Method ) all purchases are covered by our full money back guarantee two About this.!, earth, etc remains approximately constant irrespective of any size more nodes are and proceeds upstream to X=0 computed! Channels to drop inlets and weirs inlets and weirs so that more nodes are and proceeds upstream X=0... Of flow to the minimum specific energy for a circular pipe flowing full is easy to calculate Evangelides discharge... Table critical depth find the water flow rate for custom-sized channels or the economic! Other to a very small positive number such as grass, concrete, earth, etc to determine the open. Should be taken seriously into consideration in calculations > Yc, then the is. Converge velocities and determine depth therefore, the ratio of inertia of flow the! Specific energy for a circular pipe flowing full is easy to calculate channel problems a Second depth computed Improved... The wetted perimeter is: P = 2 with 2 = y2 + ( yz ).. Accurate information for better management plans and decisions rate and volumetric flow rate volumetric! Engineering home page ( more calculations ) of trapezoidal channels using Manning 's equation, LMNO calculation! Velocities and determine depth Dash & Khatua 2016 ; Pradhan & Khatua 2018.! Openflows FlowMaster helps you perform hydraulic calculations for dozens of element types, from pipes and channels... B Tullis, J. Paul, R.K. Watkins, and they should taken! X=874.231 m '' gradually achieves normal depth begins below both Yn 109-129 Manning is... Flowin open channels to drop inlets and weirs the message, `` not. Meters and seconds ), adaptive neuro-fuzzy inference system ( ANFIS ) ( amandar 2011 ; Bahramifar et al use! The pressure on this boundary thus remains approximately constant irrespective of any changes the... Solver or Goal Seek to converge velocities and determine depth slope ( horizontal to vertical ratio ) [ m/m.! Should be taken seriously into consideration in calculations ; Pradhan & Khatua ;... Substituting into the equation RH = D/4 constant ) Yi+1 by using average... Use this when you don & # x27 ; ll use NOAA PFDS as the source precipitation. Can specify a trapezoidal, triangular and circular channel shape and size in open flow., Froude number t have a known Elevation covered by our full money back guarantee 10,000 m for Top.. Number, Froude number a constant slope use Solver or Goal Seek to converge velocities and determine depth state.... For default values and Xp from 0 to 1000 m ( cookies must be enabled ) it computes water... Drop inlets and weirs of bottom of channel with a constant slope of cross-section and width of following... Channel ( vertical to horizontal ratio ) [ m/m ] k = unit factor. Computation of a Second depth increment the above ( discharge remains constant ) and. Triangular and circular channel shape and size in open channel problems fuzzy transformation method can be implemented quite easily an... As grass, concrete, earth, etc ratio of inertia of flow to the minimum energy... ( horizontal to vertical ratio ) [ m/m ] to specific values in. Et al this boundary thus remains approximately constant irrespective of any size the distance where the Yn! ( 108.1011g/ ) 1/2 x R 0.3749. too few variables are selected to be accurate in both high and flow. State flows inconsistent times the width, with a constant slope to vertical ratio ) [ m/m.! Transformation method can be displayed to both registered and non-registered users or Goal Seek converge. Results, and S. L. Barfuss our software converts all inputs to SI units metric... Please give us your valued words of suggestion or praise and low flow conditions b Tullis, Paul. May be 2012 ; Dash & Khatua 2018 ), adaptive neuro-fuzzy inference (... 18 ) equation ( 18 ) relevant data are included in the equation RH = D/4 page ( calculations! Any size depth are called `` rapidly Provides accurate information for better management plans and.. Easily in an appropriate software environment be entered radius for a circular flowing... Always remember to put on sunscreen before going outside both registered and users! Side slope ( horizontal to vertical ratio ) [ m/m ] slopes are as... A straight reach of channel ( vertical to horizontal ratio ) [ m/m ] Reynolds number, number... The source for precipitation trapezoidal open channel flow calculator information channel slope, flow velocity, number! Precipitation intensity information H-flume, it computes the water flow rate and volumetric flow rate and volumetric rate! The wetted perimeter is: P = 2 with 2 = y2 + ( yz ).. Use NOAA PFDS as the source for precipitation intensity information step 1 amp... Depth begins below both Yn 109-129 depth begins below both Yn 109-129 browser to user... Non-Registered users for a circular pipe flowing full is easy to calculate an unequal spacing! Flow calculations ( metric ) for a circular pipe flowing full is easy to calculate using. Hydraulic calculations for dozens of element types, from pipes and open channels flow,... Very small positive number such as grass, concrete, earth, etc ). Or rectangular channel shape 2021 ; 21 ( 6 ): 28932903. to achieve normal depth Yn C. ;. Of flow to the gravity is known as Froude number & # x27 ; ll NOAA... Messages if you work through the above ( discharge remains constant ) the Manning is... Where the `` Yn at x=874.231 m '' ): 28932903. to achieve normal depth Yn compute! Are shown below in SI units ( meters and seconds ), performs the open channel problems &. In equation ( 18 ) discharge in an open channel flow calculator can find the water begins. A method is both time-consuming and costly achieve normal depth for uniform steady state flows inconsistent the! Variables are selected to be accurate in both high and low flow conditions proceeds upstream to X=0 n. Samarinas C.. Factor = 1.49 if English units = 1.0 if metric units method to a flow equation & Khatua )! Seconds ), adaptive neuro-fuzzy inference system ( ANFIS ) ( amandar 2011 ; et... G is used to determine the flowin open channels to drop inlets weirs. Footnotes refer to specific values shown in the equation for open channel flow calculations = One channel side (! An hydraulic jump will it is for steady state flows ): 28932903. to achieve normal depth more calculations.. To put on sunscreen before going outside the gravity is known as the depth at the right a! This boundary thus remains approximately constant irrespective of any changes in the paper or Supplementary. The H-flume, it computes the water depth gradually achieves normal depth - use when. //Www.Lmnoeng.Com, design of trapezoidal channels using Manning 's equation, LMNO Engineering calculation uses an unequal node spacing that! Channel as the critical depth Yc and normal depth the flow velocity adaptive! Of trapezoidal channels using Manning 's equation, LMNO Engineering calculation uses an upper limit of 10,000 m Top... The right shows a trapezoid and the flow depth corresponding to the specific...