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Data management and workflowsWe adopt best-practice approaches for open and reproducible research planning, execution, reporting, and management throughout the project (see e.g.29,30,31,32). Specifically, we use community-approved standards for experimental design and data collection29, and clean and manage the data using a fully scripted and reproducible data workflow, with data and code deposited at open repositories (Fig. 2).Fig. 2The data collection and management workflow of the FunCaB project. Reproducibility throughout the research process is assured as follows: Experimental design and data collection was based on best-practice community methods and protocols, adapted for the projects’ needs. Measurements were digitalized and the raw data stored in the project Open Science Foundation (OSF) repository before the raw data were cleaned and managed through code-based data curation, with version control secured via GitHub. The clean data are stored at the OSF repository, and a time-stamped version of the code to retrieve and clean data is provided through Zenodo. This data paper describes and documents the data collection and workflow, and describes how to access and use clean data, raw data, and code.Full size imageResearch site selection and basic information, and general study setupSite selectionOur study is conducted across the twelve calcareous grassland experimental sites in the Vestland Climate Grid (VCG), in south-western Norway (Fig. 1a). The VCG sites were chosen to fit within a climate grid reflecting a fully factorial design encompassing the major bioclimatic variation in Norway. Potential sites were identified using a combination of topographic maps, geological maps (NGU) and interpolated maps of summer temperature and annual precipitation using the 1960–1990 climate normal (100 m resolution gridded data, met.no; see33 and references therein). The three temperature levels (alpine, sub-alpine, boreal) and four levels of precipitation in the climate grid (Fig. 1b) were selected to reflect a difference in mean growing season temperature of ca. 2 °C between three temperature levels (alpine = 6.5 °C, sub-alpine = 8.5 °C, boreal = 10.5 °C mean temperature of the four warmest months of the year) and a difference in mean annual precipitation of 700 mm between four precipitation levels (precipitation levels 1 – 4 representing 700 mm, 1400 mm, 2100 mm, and 2800 mm, respectively). Climate data for the site selection was based on 100-m resolution downscaled data using the 1960–1990 climate normal from met.no. The final sites were selected from approximately 200 potential sites visited and surveyed in the summer of 2008, with selection criteria set to ensure that other factors such as grazing regime and history, bedrock, vegetation type and structure, slope and exposure were kept as constant as possible among the selected sites34. Geographical distance between sites is on average 15 km and ranges from 175 km to 650 m.Study system and experimental area selection within sitesAt each site, we selected an experimental area of ca. 75 –200 m2, targeting a homogeneous and representative part of the target grassland vegetation at large at that site. The experimental areas were placed on southerly-facing slopes, avoiding depressions and concave areas in the landscape and other features such as big rocks or formations that may affect light conditions, hydrology and/or snowdrift. The target vegetation type was forb-rich semi-natural upland grassland vegetation34,35, within the plant sociological association Potentillo-Festucetum ovinae tending towards Potentillo-Poligonium vivipara in the alpine sites and Nardo-Agrostion tenuis in some lowland sites36. The most common vascular plants across sites, based on sum of covers, are the graminoids Agrostis capillaris, Festuca rubra, Avenella flexuosa, Anthoxanthum odoratum, and Nardus stricta and the forbs Leucantemum vulgare, Hypericum maculatum, Silene acaulis, Alchemilla alpina, and Lotus corniculatus. Common bryophytes are Pleurotium schreberi, Hylocomium splendens, Polythricum spp, Racomitrium lanuginosum, R. fasciculare, and Dicranum spp. All sites were moderately grazed prior to the study by sheep, cattle, goats, reindeer, deer, moose, and/or horses; and the experimental areas were fenced for the duration of the study to prevent animal and human disturbance of the experimental infrastructure. The fenced area was lightly mowed at the end of each growing season to mimic past grazing pressure and minimize fence effects. For further description of the sites, see34 and for access to and further description of site-level data, see35.Block and experimental plot setupWithin these study areas we established four blocks, with a distance between the blocks ranging from one up to (in rare cases) 50 meters. Blocks were selectively placed in homogenous grassland vegetation, avoiding rocks, depressions, and other features as described above. Each block accommodates eight 25 × 25 cm plots, with at least 25 cm between adjacent plots. If a plot contained more than 10% bare rock, shrubs, or other non-grassland features, they were rejected or moved slightly to avoid these features. The plots were permanently marked with four aluminium 10-cm long pipes in the soil in the outer corners of all the 25 × 25 cm treatment plots, ensuring the pipes to fit the corners of a standardized vegetation analysis frame (aluminium frame demarking a 25 × 25 cm inner area, with poles fixed in the corners that fit into the aluminium tubes used for plot demarcation in the field). The upslope left corner tube was marked with a colour-coded waterproof tape. Note that in 31 out of 48 cases (12 sites × 4 blocks), the blocks were located within larger experimental blocks in the VCG sites, and control plots and various block-level data are then shared with other experiments in these larger blocks. Linking keys are described in the FunCaB data dictionaries below (see Fig. 3 and data records iii-vii below). For some datasets, additional plots within blocks were needed. These are described as needed below.Fig. 3Data structure for the FunCaB functional group removal experiment and associated Vestland Climate Grid (VCG) and FUNDER project data. Within each of the three projects, boxes represent data tables. The FunCaB project data tables include biomass of functional groups removed and forb species-level biomass (datasets i, ii), soil temperature and moisture (datasets iii, iv) plant community composition and the associated taxon table (dataset v), seedling recruitment (dataset vi), ecosystem carbon fluxes (dataset vii) and reflectance (dataset viii). Names of individual data tables are given in the coloured title area, and a selection of the main variables available within tables in the internal lists. For full sets of variables for each FunCaB dataset, see Tables 3–9. The lines linking three of the boxes exemplify links using species as keys across tables, note that all bold variables are shared between several tables and can be used as keys to join them. Keys can also be used to link to/from data from other projects in the VCG (for general VCG project keys, see top right hatched outline box, for keys between the FunCaB and FUNDER projects see the bottom right hatched outline box (both including an example value for each variable on the right). The (other) datasets* boxes refer to extensive datasets on plant community composition, cover, biomass, fitness, and reproduction available from previous projects in the VCG27 and upcoming datasets in the FUNDER project.Full size imageBackground abiotic and biotic data from the Vestland Climate GridThe Vestland Climate Grid field sites were established in 2008, and from a series of research projects within the grid over the years we have collected a broad range of datasets on the climate and environment, soils, land-use and environment, vegetation, and ecosystems, along with basic descriptive data of the 12 sites, as described in34. All these datasets are available from the previous projects through the VCG OSF (Open Science Framework) repository35, and the results are presented in associated papers, see for example34,37,38,39,40,41,42,43,44,45. The overall data structure, and the most relevant datasets from the VCG for the FunCaB project is laid out in Fig. 3, and briefly described below. Code to download and link these data to the FunCaB experimental data and sites are provided in the FunCaB github repository28 (see R/download_VCG_data).A new research project, ‘FUNDER – Direct and indirect climate impacts on the biodiversity and FUNctioning of the UNDERground ecosystem’ funded by the Norwegian Research Council KLIMAFORSK programme (project number 315249, 2021 – 2025) will augment the FunCaB experiment with data on the belowground components of the plant-soil ecosystem, including roots, mesofauna, fungi and microbes. These upcoming data will all link with the FunCaB and VCG project based on the given experimental, site and organismal keys, as indicated in Fig. 3.VCG Basic site-level attributesBasic descriptive data on the 12 sites include latitude, longitude, elevation, geology, land-use, soils, and their position within the climate grid (precipitation and temperature levels). These data are described in34,40, provided in35, and can be downloaded using28 (see R/download_VCG_data). For convenience, the climate grid information is also provided in the biomass dataset (see below).VCG Site-level climate dataTemperature was measured continuously at each of the 12 VCG sites at four heights (2 m and 30 cm above ground, at ground level, and 5 cm below ground), soil moisture was measured continuously with two replicate loggers ca. 5 cm below ground, and precipitation was measured at each site during the snow-free season. For these measurements, we used Delta T GP1 loggers (Delta T devices, Cambridge, UK) equipped with two temperature probes, two SM200 moisture sensors which were later replaced as necessary with SM300 and SM150T loggers, and an ARG 100 tipping bucket (EML LTD, North Shields, UK) from 2009 onwards. UTL-3 version 3.0 temperature loggers (GEOTEST AG, Zollikofen, Switzerland) were used for measuring the 2 m and 30 cm temperatures. Soil moisture was measured as the mean of four measurements taken along each side of the turf, several times during the growing season using a Delta T HH2 version 2.3 Moisture Meter with the same probes as for the GP1 logger (SM200, SM150T). These data are described in34,40, provided in35, and can be downloaded using28 (see folder R/download_VCG_data).VCG Soil chemical and structural dataOver the years, various soil chemical variables have been measured at the block level within each of the 12 VCG sites, including soil pH (2009) and % Loss-On-Ignition (2009, 2013), and available N, as sum of N available as NH4-N and NO3-N (available N per deployment period, 2010 & 2012). Soil pH was measured after adding 50 ml distilled water to 25 g soil and mixing for two hours. Loss-on-ignition (LOI), was measured by weighing dry soil (105 °C for 24, one hour in a desiccator), and burnt soil (six hours at 550 °C, one hour in the desiccator) and calculating LOI as the (burnt soil mass/dry soil mass) × 100. NH4-N and NO3-N were measured using in-situ ion exchange resin bags (IERBs) were used to measure the amount of plant-available nutrients in the soil. These data are partially described in34,40, and the full data are provided in35.VCG Litter decomposition dataDecomposition has been assessed at each of the 12 VCG sites using local plant litter and the Tea Bag Index method (Keuskamp et al., 2013). Local litter (dead leaves detached from live plants) was collected at each site in 2013 or 2014, with the specific timing of the collections at each site tuned to ensure that litter was present, not covered by snow, and not decomposed. In practice, this necessitated litter collection after snowmelt in spring in many sites. The litter was washed, dried, and stored in dark, dry, cool conditions. In 2016, five replicate litter bags containing 1 g of graminoid litter were buried at each site, and collected at four points in time after burial (1, 2, 3 and 12 months). Harvested litter bags were cleaned (soil and roots removed), dried for 48 h at 60 °C and weighed. The Tea Bag Index method46 was used in 2014, 2015 and 2016 to measure decomposition at all sites of the climate grid. At each site, 10 replicates of each tea type were buried pair-wise, 8 cm below ground and with at least 10 cm between the tea bags. For a couple of sites, the number of replicate tea bag pairs was higher in 2015 (12 replicates at the site Gudmedalen and 16 replicates at Låvisdalen). After collection, adhering soil particles and roots were removed and the tea bags were dried (48 h at 60 °C) and weighed. These data are partially described in47, and the full data are provided in35 and can be downloaded using28 (see folder R/download_VCG_data).VCG Species-level cover, biomass, and performance dataA variety of plant species and community composition, cover, biomass, fitness, and reproductive data exists for the sites and blocks in the VCG from 2008 to 2021. These data are described in e.g34,37,38,41,43,44,45,48,49,50, and provided in35.VCG Site-level plant functional traitsIn 2016 and 2017, we measured 11 leaf functional traits that are related to potential physiological growth rates and environmental tolerance of plants, following the standardized protocols in Pérez-Harguindeguy et al.51: leaf area (LA, cm2), leaf thickness (LT, mm), leaf dry matter content (LDMC, g/g), specific leaf area (SLA, cm2/g), carbon (C, %), nitrogen (N, %), phosphorus (P, %), carbon nitrogen ratio (C:N), nitrogen phosphorus ratio (N:P), carbon13 isotope ratio (δ13C, ‰), and nitrogen15 isotope ratio (δ15N, ‰). Trait data are available at the site level for species making up at least 80% of the vegetation cover in the control plots at each of the 12 VCG sites. The plants were collected outside of the experimental plots and within a 50 m perimeter from the blocks, and we aimed to collect up to five individuals from each species in each site. To avoid repeated sampling from a single clone, we selected individuals that were visibly separated from other ramets of that species. The sampled plant individuals were labelled, put in plastic bags with moist paper towels, and stored in darkness at 4 °C until processing, which was done as soon as possible and always within 4 days. These data are described in52, provided in35, and can be downloaded using28 (see folder R/download_VCG_data).Experimental designThe functional group removal experiment was designed to examine the impact of aboveground interactions among the major plant functional groups – graminoids, forbs and bryophytes – on the performance and functioning of other components of the vegetation and ecosystem. The experiment consists of eight 25 × 25 cm plots per site and block, with a fully factorial combination of removals of three plant functional groups, with treatments randomized within each block. The general experimental design, with the different removal treatments detailed, are provided as an insert to the timeline in Fig. 1c. The functional groups are delineated and abbreviated in the various datasets as follows: G = graminoids (including grasses, sedges and rushes), F = forbs (including herbaceous forbs, pteridophytes, dwarf-shrubs, and small individuals of trees and shrubs), B = Bryophytes (including mosses, liverworts, and hornworts). Note that all species are also coded by their respective functional group into which they were classified in the FunCaB taxon table. The experimental treatments are coded by functional group removed so that FGB = bare-ground gaps with all plants removed, FB = only graminoids remaining, GB = only forbs remaining, GF = only bryophytes remaining, B = graminoids and forbs remaining, F = bryophytes and graminoids remaining, G = bryophytes and forbs remaining, and C = intact vegetation controls with no vegetation removed. In 2016, four extra control (XC) plots were marked per site for aboveground biomass harvest and ecosystem carbon flux measurements. This sampling regime gave a total of 384 plots in the core FunCaB experiment, plus the additional 48 controls in 2016.Functional group removals were done once in 2015 (at peak growing season due to late snowmelt), twice per year in 2016 and 2017 (after the spring growth and at peak growing season) and annually from 2018 to 2021 (at peak growing season) as regrowth had declined (see below) and biannual removals were no longer necessary. At each sampling, all above-ground biomass of the relevant plant functional group was removed from each plot as follows: for each plot, all the above-ground parts of the relevant functional group(s) were removed using scissors and tweezers to cut the plants at the ground layer (i.e., the soil-vegetation interface). Roots and other below-ground parts were not removed, and non-target plant functional groups and litter were left intact.Species identification, taxonomy, and floraAll vascular plant species were identified to the species level in the field, with nomenclature following Lid and Lid53. Exceptions are sterile specimens of species that are not possible to identify without reproductive parts, and where flowers are either too rare or individuals too short-lived for comparisons of the position of individuals within the plots over years to be used to ascertain identifications (For example, Alchemilla spp. excluding A. alpina, and the annual Euphrasia spp.). Species identifications were confirmed by comparing records over time as described below. All unidentified specimens are included and flagged in the dataset, as described in Data Records below. The full taxon names are provided in the taxon table on OSF (Fig. 3).Dataset collection methodsDatasets (i–ii): Biomass and functional group removalAs described above, functional group removals were done once in 2015 at peak growing season, and twice per year in 2016 and 2017 (after the spring growth; at peak growing season) and annually at peak growing season from 2018 to 2021. For each removal plot and occasion, a picture was taken of the plot pre-removal, the biomass to be removed was collected in separate pre-marked paper bags for each functional group (graminoids, forbs and bryophytes), and a picture was taken post-removal. The collected biomass was then dried at 60 °C for 48 hours and weighed to the nearest 0.01 g (Model LPG-1002, VWR). From the four extra control (XC) plots in 2016, total above-ground biomass as well as litter (defined as dead biomass detached from live plants, see28) was collected at peak growing season. From these plots, biomass was sorted into functional groups as described above, except the forb functional group, which was sorted into species. The graminoid and bryophyte functional groups, each forb species, and litter were individually dried and weighed as described above. The data is available as (i) a biomass dataset, consisting of the removed biomass per plot, date, removal treatment, and functional group for all treatment plots, and the total biomass per functional group plus litter for the extra control plots in 2016, and (ii) a species-level forb biomass dataset from the extra control plots in 2016 (Fig. 3, Table 1).Datasets (iii-iv) – Soil microclimateWe measured soil temperature 3–5 cm below the soil surface for each plot using iButton temperature sensors (DS1922L, Manufacturer reports temperature accuracy of ±0.5 °C, Maxim Integrated INC., San Jose, CA, USA). The data are reported with a resolution of 0.0625 at 140 min intervals from June 2015 to July 2016. We measured soil moisture as volumetric soil moisture; expressed as % water volume per soil volume ((m3 water /m3 soil) × 100). These measurements were done c. 3–5 times during the growing seasons from 2015–2019, usually in connection with the flux and vegetation measurements, by taking the average of four measurements, one at each side of each plot (SM300, Manufacturer reports accuracy ±2.5% vol over 0 to 50% vol and 0–60 °C, Delta-T Devices, Cambridge, UK). The data is available as (iii) temperature and (iv) volumetric soil moisture % per plot and time point (temperature) or date (moisture) (Fig. 3, Table 1).Dataset (v): Vascular plant community composition and vegetation structureWe recorded the full vascular plant species composition of all experimental plots in 2015 (pre treatment), and the control plots plus the extra control plots in 2016. In 2017, 2018, and 2019, we recorded the community composition in controls and in the functional groups that remained in the experimental plots according to the plot’s treatment. At each analysis, each plot was sub-divided into 25 5 × 5 cm subplots, using a subplot overlay. We first recorded all species of vascular plants in the central five subplots, (i.e., the central + shaped area of each plot, Fig. 1c) noting the subplot cover of each species present in each of the five subplots (1 – 25% = 1, 26 – 50% = 2, 51 – 75% = 3, >76% = 4). Additionally, we noted if the individual was fertile (records circled if buds, flowers, or fruits were present). The five subplots were recorded and numbered (1-5) by row, and from left to right, starting from the top up-slope subplot. For the entire 25 × 25 cm plot, any additional species not present in one of the central subplots were recorded and their fertility noted. We then visually estimated the percentage cover of each vascular plant species in the whole plot to the nearest 1% and measured vegetation height in mm at four points within the plot. Note that the total coverage in each plot can exceed 100% due to layering of the vegetation. The vascular plant vegetation data is available as percentage cover and fertility status (sterile or fertile) per species per subplot and plot per sampling date, and vegetation height in mm per plot per sampling date (Fig. 3, Table 1).Other variables that were measured were percentage cover of bryophytes, litter, bare ground, and rock (measured per plot and per subplot) and moss layer depth in mm (mean of 4 measurements/plot), date of analysis, recorder/scribe (if any), and free-text comments. These data are available as % cover, depth in mm, date (year.month.day) and text strings per subplot and /or plot per sampling date (Fig. 3, Table 1).Dataset (vi): Seedling recruitmentThe total number of forb seedlings that emerged in the plots was recorded in 2018 and 2019. At peak growing season in 2018 (round 1, July-August, depending on site), all dicotyledonous seedlings were marked with wooden toothpicks and their x and y coordinates in the plot (mm, recorded from the bottom left hand-corner of the plot, Fig. 1c) and tentative species identity noted. Toward the end of the growing season (round 2, August-September, depending on site), each plot was revisited, seedling survival established, and any further seedlings marked. Survival (recorded when a seedling was present in subsequent surveys; recorded as mortality if absent) and new seedling emergence were followed up in the same manner in 2019 (rounds 3 and 4, respectively). Species identification was (re)assessed at all censuses and corrected if needed as the seedlings grew and identification uncertainty decreased. New seedlings were differentiated from emergent clonal ramets by looking for cotyledons or signs of above- or below-ground ramet connections. These data are available as talleys of seedlings, each with a status (dead or alive) and species identity (or NA when not identifiable), per subplot and /or plot per sampling round (Fig. 3, Table 1).Dataset (vii): Ecosystem carbon flux data and flux calculationsCarbon flux measurementsEcosystem CO2 fluxes were measured to estimate net ecosystem exchange (NEE), ecosystem respiration (Reco) and gross primary production (GPP). The dataset covers the years 2015, 2016 and 2017, and individual plots have multiple measurements for ecosystem carbon flux per year as detailed below. At peak growing season in 2015, a median of 2 sets of paired carbon flux measurements were measured pre-removal for all plots, where a paired set consist of a light and a dark flux measurement of an individual plot. In 2016, a median of 8 sets of paired measurements were made for all control plots, and a median of 7 for the 4 extra controls (see experimental design above). In the data files, some additional measurements exist for other experiments in the VCG sites (a median of 7 paired sets of measurements for controls (TTC) and graminoid removal plots (RTC), see42 for a presentation of this experiment and35 for technical details). In 2017, a median of 5 paired sets of measurements were made for all treated plots in nine of the sites, excluding the second wettest precipitation level (sites Gudmedalen, Rambera, and Arhelleren). These measurements were made ca. 1 week after the first round of plant functional group removals in that season.At each sampling occasion, a clear chamber (25 × 25 × 40 cm) equipped with two fans for air circulation and connected to an infrared gas analyzer (Li-840; Manufacturer reports accuracy within 1.5% of the reading value; LI-COR Biosciences, Lincoln, NE, USA) was used to measure CO2 fluxes at all plots. To prevent cutting of roots and disruption of water flow in the plots by installing collars, we instead attached a windshield to the bottom of the chamber and weighed it down on the ground by a heavy chain to prevent wind-air mixing. At each sampling occasion we made paired measurements of fluxes under light and dark conditions, covering the chamber with a fitted light-excluding cover for the dark measurements.NEE was estimated from measurements of CO2 flux under ambient light and dark conditions: NEElight = GPP – Reco, NEEdark = (-) Reco. We define NEE such that negative values reflect CO2 uptake in the ecosystem, and positive values reflect CO2 release from the ecosystem to the atmosphere. For each measurement, CO2 concentration was recorded at 5 s intervals over a period of 90–120 s. NEE was calculated from the temporal change of CO2 concentration within the closed chamber according to the following formula:$$NEE=frac{delta C{O}_{2}}{delta t}times frac{PV}{Rtimes Atimes (T+273.15)}$$where (delta frac{C{O}_{2}}{delta t}) is the slope of the CO2 concentration against time (µmol mol−1 s−1), P is the atmospheric pressure (kPa), R is the gasconstante (8.314 kPa m3 K−1 mol−1), T is the air temperature inside the chamber (°C), V is the chamber volume (m3) and A is the surface area (m2).Light intensity was measured as photosynthetically active radiation (PAR, µmol m−2 s−1) using a quantum sensor (Li-190; Manufacturer reports absolute calibration accuracy of ±5%; LI-COR Biosciences, Lincoln, NE, USA) placed inside the chamber. Temperature inside the chamber was measured using an iButton temperature logger (DS1922L, Manufacturer reports temperature accuracy of ±0.5 °C, Maxim Integrated, San Jose, CA, USA). Volumetric soil moisture content (m3 water/m3 soil) × 100 was measured by calculating the average of four measurements with a soil moisture sensor (SM300, Manufacturer reports moisture accuracy of ±2.5%, Delta-T Devices, Cambridge, UK), taken at each side of a plot.Data management and calculationsData from the LiCOR data logger and iButton was downloaded in the field and stored. The information from the field data sheets (metadata of CO2 measurements and plot soil moisture) was manually entered into digital worksheets, manually proof-read and stored. Data from the data logger (PAR and CO2) and the iButton temperature logger were linked based on information from the field data sheets. All measurements were first visually evaluated for quality and only measurements that showed a consistent linear relationship between CO2 over a time for a period of at least 60 s were used for NEE calculations. A second inclusion criterion was that this relationship had R2 ≤ 0.2 or R2 ≥ 0.8 for NEE measurement in light conditions and R2 ≥ 0.8 for NEE dark measurements (Reco). Measurements of NEE in light conditions with R2 ≤ 0.2 ensures representation of measurements with equal rates for Reco and GPP. Third, paired measurements that were more than 2 h apart were excluded. These data are available as raw fluxes and as GPP and Reco per plot per measurement (Fig. 3, Table 1).Dataset (vi): ReflectanceReflectance measures of Normalized Difference Vegetation Index (NDVI) were taken for each plot during the 2019 (post functional group removal) and 2021 (pre and post removal) field seasons (July-August), using a Trimble Greenseeker Handheld Crop Sensor (Trimble Inc., Sunnydale, CA, USA). As the sensor measures an elliptical plane, two measures perpendicular to each other were taken for each subplot (25 × 25 cm plot), with the centre of each ellipse being the centre of the subplot. Care was taken to ensure that sampling quadrat frames were not within the sensor range when conducting measurements (see methods Dataset ii). Measures of NDVI were taken at 60 cm above the surface where possible. Height was measured perpendicular to the sampled ground surface. These data are available as reflectance per plot per sampling date (Fig. 3, Table 1). More

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Rotational velocityFigure 3 shows the effect of flow rate, nozzle diameter and number of nozzles on the rotational velocity of water in a circular tank. The results indicate that the rotational velocity increases with increasing flow rates and deceasing nozzle diameter. It could be seen that, the rotational velocity decreased from 10.1 to 5.0 cm s−1, when the nozzle diameter increased from 10 to 20 mm, respectively for 5 nozzles used, and it decreased from 5.1 to 4.0 cm s−1, when the nozzle diameter increased from 10 to 15 mm, respectively, for 10 nozzles used with 5 m3 h−1 flow rate. At 15 m3 h−1, the rotational velocity was decreased from 23.5 to 17.5, 12.0 to 7.5, 10.0 to 6.9, 7.6 to 4.7 and 5.9 to 4.0 cm s−1 when the nozzle diameter increased from 10 to 20 mm, respectively, for 5, 10, 15, 20 and 25 nozzles, respectively. The results also indicate that when the nozzle diameter increased from 20 to 25 mm, the rotational velocity decreased from 19.0 to 16.5, 12.0 to 10.0 and 7.1 to 5.5 cm s−1 for 3, 6 and 9 nozzles, respectively, with 15 m3 h−1 flow rate.Figure 3Effect of flow rate, nozzle diameter and number of nozzles on the rotational velocity of water in a circular tank.Full size imageAt 30 m3 h−1 flow rate, the highest value of the rotational velocity was 33.5 cm s−1 was found for 5 nozzles and 10 mm nozzle diameter. While, the lowest value of the rotational velocity was 7.3 cm s−1 was found for 25 nozzles and 25 mm nozzle diameter. At 45 m3 h−1 flow rate, the rotational velocity ranged from 11.0 to 49.9 cm s−1 for all treatments under study.At 60 m3 h−1 flow rate, the rotational velocity deceased from 61.0 to 50.1, 47.7 to 34.0, 36.3 to 23.0, 23.5 to 17.5, 21.0 to 15.0 and 17.0 to 11.5 cm s−1 when the nozzle diameter increased from 10 to 20 mm, respectively at 5, 10, 15, 20, 25 and 30 number of nozzles. The results also indicate that, when the nozzle diameter increased from 20 to 25 mm, the rotational velocity decreased from 56.0 to 47.0, 43.0 to 33.0, 27.0 to 22.0 and 19.0 to 16.5 cm s−1 at 3, 6, 9 and 12 nozzles, respectively.At 75 m3 h−1 flow rate, the rotational velocity deceased from 60.9 to 49.1, 48.4 to 38.0, 39.0 to 30, 31.8 to 23.0, 23.5 to 17.5 and 22.0 to 15.0 cm s−1 when the nozzle diameter increased from 10 to 20 mm, respectively for 5, 10, 15, 20, 25 and 30 nozzles, respectively. The results also indicate that, when the nozzle diameter increased from 20 to 25 mm, the rotational velocity decreased from 50.48 to 43.0 to 38.5, 33.0 to 27.5 and 23.5 to 22.0 cm s−1 for 3, 6, 9 and 12 nozzles, respectively.The results also indicate that the highest values of the rotational velocities were 10.1, 23.5, 33.5, 49.9, 60.9 and 61.0 cm s−1 were found for 5 nozzles and 10 mm nozzle diameter at 5, 15, 30, 45, 60 and 75 m3 h−1 flow rate, respectively. While, the lowest values of the rotational velocities were 4.0, 7.5 and 11.5 cm s−1 for 25 nozzles and 15 mm nozzle diameter at 5, 15 and 30 m3 h−1 flow rate, respectively. They were 11.5 and 15 cm s−1 were found for 30 nozzles and 15 mm nozzle diameter at 60 and 75 m3 h−1 flow rate, respectively. The velocity of water obtained seemed to be in the recommended range of safe and proper velocity for fish according to12. Due to it is effective compromise to allow heavy solids settle rapidly, yet sufficiently fast to create “good” hydraulics. Timmons and Youngs18 mentioned that the water velocity needed to maintain self-cleaning properties ranges from 3 to 40 cm s−1 varying greatly according to the physical properties of the biosolids. When fish swims at lower speed than its optimal, a large amount of energy will be used for higher spontaneous activity such as aggression. In contrast, when fish swim at higher speed than optimal, they become stressful, unstable, increase lactate production and fatigue6.Multiple regression analysis was carried out to obtain a relationship between the rotational velocity of water as dependent variable and different both of flow rate and nozzle diameter as independent variables. The best fit for this relationship with coefficient of determination of 0.95 and an error of 1.06% is in the following form:-$$ RV = 6.97 + 0.41Q – 0.19Dquad {text{R}}^{{2}} = 0.95 $$
(3)
where RV is the rotational velocity of water, cm s−1, Q is the water flow rate, m3 h−1, D is the nozzle diameter, mm.This equation could be applied in the range of 5 to 75 m3 h−1 water flow rate and from 10 to 25 mm of nozzle diameter.Impulse force of waterFigure 4 shows the effect of flow rate, diameter and number of nozzles on the impulse force of water in a circular tank. The results indicate that the impulse force of water increases with increasing flow rates and deceasing nozzle diameter and number of nozzles. It could be seen that, the impulse force of water decreased from 5.1 to 1.7 N, when the number of nozzles increased from 5 to 15, respectively at 10 nozzle diameter, and it decreased from 2.3 to 1.2 N, when the number of nozzles increased from 5 to 10, respectively, at 15 diameter nozzle with 5 m3 h−1 flow rate. At 15 m3 h−1, the impulse force of water was decreased from 84.7 to 9.4 N when the number of nozzles increased from 5 to 30, respectively 10 mm diameter nozzle. The results also indicate that when the number of nozzles increased from 5 to 25, the impulse force of water decreased from 14.8 to 1.4 N at 15 mm nozzle diameter, respectively, and it decreased from 9.5 to 1.9 and 5.3 to 1.3 N at 20 and 25 mm, respectively, when the number of nozzles increased from 3 to 9.Figure 4Effect of flow rate, nozzle diameter and number of nozzles on the impulse force of water in a circular tank.Full size imageAt 30 m3 h−1 flow rate, the impulse force of water deceased from 84.7 to 46.9, 56.9 to 14.8, 28.5 to 5.3, 14.9 to 3.0 and 11.8 to 2.2 N when the nozzle diameter increased from 10 to 15 mm, respectively at 5, 10, 15, 20 and 25 nozzles. The results also indicate that, when the nozzle diameter increased from 20 to 25 mm, the impulse force of water decreased from 21.4 to 14.9, 14.8 to 5.4, 5.3 to 2.2 and 2.3 to 1.9 N for 3, 6, 9 and 12 nozzles, respectively.At 45 m3 h−1 flow rate, the impulse force of water was ranged from 2.1 to 111.2 N for all treatments under this study. Also, at 60 m3 h−1 flow rate, the impulse force of water ranged from 5.1 to 151.3 N for all treatments under this study. At 75 m3 h−1 flow rate, the highest value of the impulse force of water 211.2 N was found for 5 numbers of nozzles and 10 mm nozzle diameter, respectively. While, the lowest value of the impulse force of water was 9.1 N was found for 12 nozzles and 25 mm nozzle diameter, respectively.The results also indicate that the highest value of the impulse force of water 211.2 N was found for 5 nozzles and 10 mm nozzle diameter at 75 m3 h−1 flow rate, respectively. While, the lowest value of the impulse force of water was 1.2 N was found for 10 nozzles and 15 mm nozzle diameter at 5 m3 h−1 flow rate, respectively.The results indicated that, the relationship between the rotational velocity and impulse force of water is linear relationship at the same treatments. When the rotational velocity increased from 10.7 to 37.6, 8.1 to 28.8, 10.2 to 36.0 and 11.0 to 31.9 cm s−1, the impulse force of water increased from 3.1 to 106.6, 1.8 to 31.1, 1.3 to 32.5 and 1.4 to 22.8 N, respectively, at the same treatments. The trend of these results agreed with those obtained by19.Multiple regression analysis was carried out to obtain a relationship between the impulse force of water as dependent variable and different both of flow rate and nozzle diameter as independent variables. The best fit for this relationship with coefficient of determination of 0.88 and an error of 2.13% is in the following form:-$$ F_{i} = 38.18 + 0.67Q – 2.35Dquad {text{R}}^{{2}} = 0.88 $$
(4)
This equation could be applied in the range of 5 to 75 m3 h−1 water flow rate and from 10 to 25 mm of nozzle diameter.Average velocity of waterFigure 5 shows the effect of flow rate, diameter and number of nozzles on the average velocity of water in a circular tank. The results indicate that the average velocity of water increases with increasing flow rates and deceasing nozzle diameter and number of nozzles. It could be seen that, the average velocity of water decreased from 3.32 to 1.59 cm s−1, when the number of nozzles increased from 5 to 15, respectively at 10 nozzle diameter, and it decreased from 1.13 to 1.07 cm s−1, when the number of nozzles increased from 5 to 10, respectively, at 15 diameter nozzle with 5 m3 h−1 flow rate. At 15 m3 h−1, the average velocity of water was decreased from 12.03 to 4.33 cm s−1 when the number of nozzles increased from 5 to 30, respectively 10 mm diameter nozzle. The results also indicate that when the number of nozzles increased from 5 to 25, the average velocity of water decreased from 6.93 to 2.89 cm s−1 at 15 mm nozzle diameter, respectively, and it decreased from 7.55 to 4.00 and 4.89 to 2.95 cm s−1 at 20 and 25 mm, respectively, when the number of nozzles increased from 3 to 9.Figure 5Effect of flow rate, nozzle diameter and number of nozzles on the average velocity of water in a circular tank.Full size imageAt 30 m3 h−1 flow rate, the highest value of the average velocity of water 18.51 cm s−1 was found for 5 nozzles and 10 mm nozzle diameter. While, the lowest value of the average velocity of water was 4.65 cm s−1 was found for 12 nozzles and 25 mm nozzle diameter. At 45 m3 h−1 flow rate, the average velocity of water ranged from 6.66 to 23.26 for all treatments under study, also, at 60 m3 h−1 flow rate, the average velocity of water ranged from 9.23 to 34.82 for all treatments under study. At 75 m3 h−1 flow rate, the average velocity of water ranged from 10.00 to 48.76 for all treatment of this study.The results also indicate that the highest value of the average velocity of water 48.76 cm s−1 was found for 5 nozzles and 10 mm nozzle diameter at 75 m3 h−1 flow rate, respectively. While, the lowest value of the average velocity of water was 1.07 cm s−1 was found for 10 nozzles and 15 mm nozzle diameter at 5 m3 h−1 flow rate, respectively. These results agreed with those obtained by18,20. Fish distribution in the circular tank is influenced by the heterogeneity of water velocity in the area between inlet flow and the center of the tank9. Fish distribution in the circular tank is mostly concentrated in the area between high and low velocity area. The high velocity area will be avoided by most fishes as it requires high swimming energy, while dead volumes (low velocity area) are unfavorable condition for fish (low DO and higher metabolites accumulation)21.Multiple regression analysis was carried out to obtain a relationship between the average velocity of water as dependent variable and different both of flow rate and nozzle diameter as independent variables. The best fit for this relationship with coefficient of determination of 0.91 and an error of 1.48% is in the following form:$$ V_{avg} = 6.53 + 0.26Q – 0.37Dquad {text{R}}^{{2}} = 0.91 $$
(5)
This equation could be applied in the range of 5 to 75 m3 h−1 water flow rate and from 10 to 25 mm of nozzle diameter. More

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