3f:null 40:["$","title",null,{"children":"Making an unmotored pressure washer | Eric Yancey Dauenhauer | Observable"}] 46:T473,md` ## Um... what?? _Come with me on a journey!!!_ Imagine a world where you could _pressure wash_ your driveway _without annoying your neighbors_. Together! We can build that world!! ## The problem Many conventional gas-powered pressure washers can maintain between 2,000 to 3,000 PSI (pounds per square inch) of pressure.* _**But they are soooo annoying**_ How do we create a pressure washer that is _**just** as powerful_ but _**none** as annoying???_ What if we creating the same amount of pressure with _**only gravity**_???? 🤯 ## Reframing the question If we have a hose of infinite length hanging directly above us, how high up does the water need to be to create enough **hydrostatic pressure** to equal that of a conventional pressure washer. It turns out calculating hydrostatic pressure is [easy as pie](https://www.engineeringtoolbox.com/hydrostatic-pressure-water-d_1632.html) so we're gonna be juuuuuust fine today. *We painstakingly calculated this data from a quick glance at [PressureWashr](https://pressurewashr.com/the-best-pressure-washers/), which you know is so lgit cuz thy droppd th "e" in thir nam. `47:T703,md` ## Conclusion Wow it has been a fun, funky, spunky, spectacu-licious journey through water, hoses, and other cool shit. It turns out all we need to make an unmotored pressure washer is a mere ${Math.round(targetHeight)}_m_ long hose (${round2(targetHeightInMiles)} miles!), hoisted vertically above us, filled with water! That is approximately **1/5th cruising altitude** (30,000 ft) 😱. But it looks like this is within the legal altitude [permitted for hot air balloons](https://www.ecfr.gov/cgi-bin/text-idx?SID=46bcc89801048c2cf486c490e8a0e58d&mc=true&node=pt14.2.91#se14.2.91_1215) (though probably [not](https://skydrifters.com/faq/) [very](https://vegashotairballoonrides.com/how-high-can-hot-air-balloons-go/) [typical](http://www.hotairballoon.org/vermont/faq.html)): Hot air balloon pressure washer, here we come! ### How much water is that??? Well, assuming you're a rocking cool person, you know that most residential pressure washers use M22 connectors, which have a standard [14mm inner diameter](https://www.pwma.org/docs/PW203Final102012.pdf) for gas pressure washers, or potentially 15mm for electric. That's a little over half an inch! It turns out most garden hoses range from 1/2 inch to 3/4 inch inner diameter, so for the maths we can say our hose is 15mm in diameter. Bada-bing, bada-boom: ${round2(waterVolumeInLitersToFillHose)} liters of water to fill our hose. In "human readable" numbers, that is approximately equivalent to flushing your toilet ${Math.ceil(toiletFlushesOfWater)} times, or taking about 3 showers 😲 Of course, the water would deplete as you use it, so you might want to have a few extra liters on hand to refill. Don't forget to invest in decent walkie-talkies!! # TLDR 2: the water volume portion of this journey was less exciting `48:[] 44:{"id":"22bdf041bdfe5fad","slug":"making-an-unmotored-pressure-washer","title":"Making an unmotored pressure washer","thumbnail":"fd4d1c6beb514579006e2c642bf03626903bf5b00b540392d2bda983f4fbf5fa","access_level":"public","create_time":"$D2019-08-09T03:20:30.962Z","update_time":"$D2019-08-09T15:22:37.308Z","view_time":null,"first_public_time":"$D2019-08-09T15:19:34.358Z","has_unpublished_edits":null,"fork":false,"stars":2,"starred":false,"owner":{"type":"team","id":"0859e816ebbc8abe","login":"ericyd","name":"Eric Yancey Dauenhauer","avatar_url":"https://avatars-next.observableusercontent.com/78be3a44c98f42079131223ddec6a977e2d03c38d723ca5b06c06fd164b0c2a1","tier":"starter_2024","bio":"Just a human with a passion for all things JavaScript, web accessibility, and well-tested software.","following":false},"version":290,"publish_version":290,"role":null,"authored":false,"authors":[{"type":"individual","id":"79ba5b95753ac93a","login":"ericyd","name":"Eric Yancey Dauenhauer","avatar_url":"https://avatars-next.observableusercontent.com/78be3a44c98f42079131223ddec6a977e2d03c38d723ca5b06c06fd164b0c2a1","tier":null,"bio":"Just a human with a passion for all things JavaScript, web accessibility, and well-tested software.","following":false}],"members":[{"type":"individual","id":"79ba5b95753ac93a","login":"ericyd","name":"Eric Yancey Dauenhauer","avatar_url":"https://avatars-next.observableusercontent.com/78be3a44c98f42079131223ddec6a977e2d03c38d723ca5b06c06fd164b0c2a1","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"lapsed":null,"subscribed":null,"forks":0,"collection":null,"type":"notebook","body":{"titling":"auto","title":"Making an unmotored pressure washer","cells":[{"id":0,"value":"md`# Making an unmotored pressure washer\n\nAn exercise in calculating water pressure in a column\n\n# TLDR: We're making a hot air balloon pressure washer 🎈. No sweat.\n\n![](https://clipartix.com/wp-content/uploads/2016/05/Window-cleaning-clip-art-clipart-image.jpg)\n# + \n![](https://png.pngtree.com/element_origin_min_pic/17/01/01/e136d6d701437d911188ac606872c8b0.jpg)\n\n---\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":225,"value":"$46","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":8,"value":"targetPressureInDumbassUnits = 2500 // Pounds per Square Inch (PSI)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":14,"value":"newtonsPerPound = 4.44822","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":18,"value":"squareInchesPerSquareMeter = 1550","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":10,"value":"targetPressureInSIUnits = (targetPressureInDumbassUnits * newtonsPerPound * squareInchesPerSquareMeter) // Pascal (Pa) - aka N/m^2","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":22,"value":"md`\nDimensional analysis sucks. Get over it\n\n${tex.block` PSI = \\frac{lb}{in^2} `}\n\n${tex.block` Pa = \\frac{N}{m^2} `}\n\n${tex.block`\n\n\\frac{ \\cancel{lb} }{ \\cancel{in^2} } *\n \\frac{N}{ \\cancel{lb} } *\n \\frac{ \\cancel{in^2} }{m^2} =\n \\frac{N}{m^2}\n`}\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":37,"value":"md`\n## What have we learned so far?\n\nPascals are **hella tiny** compared to PSI. Beef it up, you SI chumps!!\n\n## How far are we in this journey?\n\nActually pretty far so stop whining you brat. It turns out this is a _much_ easier problem than my famous [cup optimization problem](https://observablehq.com/@ericyd/cup-optimization).\n\nAll we have to do is write a simple formula to calculate hydrostatic pressure and then figure out the height of the water column at our target pressure (${round2(targetPressureInSIUnits)} Pa, or ${round2(targetPressureInSIUnits / Math.pow(10, 6))} MPa).\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":64,"value":"md`acceleration due to the force of gravity is the standard 9.81 m/s²`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":53,"value":"g = 9.81 // acceleration due to gravity (m/s^2)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":60,"value":"md`\nDensity of water is 1000 kg/m³\n\nAnd yes, \"rho\" is how you spell the greek symbol that denotes pressure`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":55,"value":"rho = 1000 // density of water (kg/m^3) ","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":82,"value":"md`\nOk let's chart pressure against height of the water column\n\n${tex.block`\np = \\rho g h\n`}\n\nwhere \n\n* _p_ is pressure\n* \"rho\" (${rho} kg/m³) is the funky looking _p_ to the right of the \"=\" sign\n* _g_ (${g} m/s²) is _g_\n* and _h_ is the height of the water column\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":93,"value":"pressure = (h) => rho * g * h","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":89,"value":"{ \n const heights = range(1, 2000, 0.1)\n \n const pressureData = heights.map(h => {\n return {\n height: h,\n pressure: pressure(h),\n targetHeight: targetHeight,\n targetPressure: targetPressureInSIUnits,\n \"Height of water column (m)\": targetHeight\n }\n })\n \n const data = {\n values: pressureData,\n xAxisTitle: 'Height',\n yAxisTitle: 'Pressure',\n showTooltip: true\n }\n return drawMyChartNOW(data)\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":136,"value":"md`height of the water column in meters:`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":107,"value":"targetHeight = targetPressureInSIUnits / (rho * g)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":197,"value":"milesPerMeter = 0.000621371","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":198,"value":"targetHeightInMiles = targetHeight * milesPerMeter","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":142,"value":"$47","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":209,"value":"hoseDiameterInMillimeters = 15","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":143,"value":"hoseRadiusInMillimeters = hoseDiameterInMillimeters / 2","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":151,"value":"hoseRadiusInMeters = hoseRadiusInMillimeters / 1000","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":170,"value":"litersPerCubicMeter = 1000","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":146,"value":"waterVolumeInLitersToFillHose = volumeCylinder(hoseRadiusInMeters, targetHeight) * litersPerCubicMeter","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":163,"value":"gallonsPerLiter = 0.264172","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":165,"value":"gallonsPerAverageFlush = 1.6","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":244,"value":"toiletFlushesOfWater = waterVolumeInLitersToFillHose * gallonsPerLiter / gallonsPerAverageFlush","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":74,"value":"md` ## Dependencies \n\nStill weirds me out that Observable requires dependencies to be declared this way 🤔`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":79,"value":"vegalite = require(\"@observablehq/vega-lite\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":76,"value":"/*\nReference\nhttps://vega.github.io/vega-lite/examples/layer_scatter_errorband_1D_stdev_global_mean.html\nhttps://vega.github.io/vega-lite/examples/parallel_coordinate.html\n*/\nfunction drawMyChartNOW(data) {\n const showTooltip = data.showTooltip\n return vegalite({\n width: 600,\n height: 400,\n data: data, // this works because data.values is defined\n \n layer: [\n // curve\n {\n mark: 'line',\n encoding: {\n x: {field: \"height\", type: \"quantitative\", title: data.xAxisTitle},\n y: {field: \"pressure\", type: \"quantitative\", title: data.yAxisTitle}\n }\n },\n // target pressure annotation\n {\n mark: { type: 'circle', size: 100 },\n encoding: {\n x: {field: 'targetHeight', type: 'quantitative', title: data.xAxisTitle},\n y: {field: 'targetPressure', type: 'quantitative', title: data.yAxisTitle},\n tooltip: [\n { field: 'Height of water column (m)' }\n ]\n }\n },\n ]\n \n })\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":90,"value":"// Thank you Underscore!!! https://underscorejs.org/docs/underscore.html\nfunction range(start, stop, step) {\n if (stop == null) {\n stop = start || 0;\n start = 0;\n }\n if (!step) {\n step = stop < start ? -1 : 1;\n }\n\n var length = Math.max(Math.ceil((stop - start) / step), 0);\n var range = Array(length);\n\n for (var idx = 0; idx < length; idx++, start += step) {\n range[idx] = start;\n }\n\n return range;\n};","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":232,"value":"roundN = n => x => Math.round(x * Math.pow(10,n)) / Math.pow(10,n)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":168,"value":"round2 = roundN(2)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":236,"value":"volumeCylinder = (r, h) => Math.PI * Math.pow(r, 2) * h","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W48","stdlib":"1"}} 45:"$44:body"