{"id":2639,"date":"2026-10-15T00:36:03","date_gmt":"2026-10-14T23:36:03","guid":{"rendered":"https:\/\/wpcalc.com\/pl\/inzynieria\/spadek-cisnienia-w-rurze\/"},"modified":"2026-10-15T00:36:03","modified_gmt":"2026-10-14T23:36:03","slug":"spadek-cisnienia-w-rurze","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/pl\/inzynieria\/spadek-cisnienia-w-rurze\/","title":{"rendered":"Spadek ci\u015bnienia w rurze"},"content":{"rendered":"<section class=\"not-prose calculator-box\" aria-labelledby=\"calculator-title\"><div class=\"flex items-baseline sm:items-center justify-between gap-2 sm:gap-3\"><div class=\"flex flex-col sm:flex-row sm:items-center gap-2\"><span class=\"icon icon-calculator text-primary-700! text-base! dark:text-primary-300!\" aria-hidden=\"true\"><\/span><h2 id=\"calculator-title\" class=\"text-lg font-display font-bold\">Straty ci\u015bnienia na tarcie (Darcy\u2013Weisbach)<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"2639\" data-favorite-title=\"Spadek ci\u015bnienia w rurze\" data-favorite-url=\"https:\/\/wpcalc.com\/pl\/inzynieria\/spadek-cisnienia-w-rurze\/\" data-favorite-excerpt=\"Oblicz spadek ci\u015bnienia i strat\u0119 wysoko\u015bci ci\u015bnienia w rurze za pomoc\u0105 r\u00f3wnania Darcy\u2019ego\u2013Weisbacha z wsp\u00f3\u0142czynnikiem tarcia wg Swamee\u2013Jaina. Wpisz d\u0142ugo\u015b\u0107 rury, \u015brednic\u0119, przep\u0142yw, w\u0142a\u015bciwo\u015bci cieczy i chropowato\u015b\u0107, aby otrzyma\u0107 \u0394p w kPa i psi, pr\u0119dko\u015b\u0107, liczb\u0119 Reynoldsa oraz wsp\u00f3\u0142czynnik tarcia.\" aria-label=\"Dodaj do ulubionych\" data-favorite-icon=\"icon icon-pipeline\">\n    <span class=\"icon icon-shape-star-empty\" aria-hidden=\"true\"><\/span>\n  <\/button>\n  <div class=\"calcdash-favorite__tip\" aria-hidden=\"true\">\n   <span class=\"favorite-tooltip\" id=\"favorite-tooltip\"><\/span>\n  <\/div>\n  <span class=\"sr-only\" role=\"status\" id=\"favorite-status\"><\/span>\n<\/div><\/div><form action=\"https:\/\/wpcalc.com\/pl\/inzynieria\/spadek-cisnienia-w-rurze\/\" method=\"POST\" class=\"calculator\" id=\"calculator-2639\" data-post=\"2639\"><fieldset class=\"fieldset-input is-2\"><legend class=\"sr-only\">Pola danych<\/legend><div class=\"field has-term\" id=\"input-1\"><label for=\"field-1\">D\u0142ugo\u015b\u0107 rury (L)<\/label><div class=\"term\">L<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><div class=\"field-group\"><input type=\"text\" name=\"dugo_rury_l\" id=\"field-1\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0\" value=\"100\"\/><div class=\"grid grid-cols-1\"><select id=\"field-2\" name=\"jednostka\" aria-label=\"Jednostka\"><option value=\"m\" selected>m<\/option><option value=\"ft\">ft<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><\/div><div class=\"field has-term\" id=\"input-2\"><label for=\"field-3\">\u015arednica wewn\u0119trzna (D)<\/label><div class=\"term\">D<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><div class=\"field-group\"><input type=\"text\" name=\"rednica_wewntrzna_d\" id=\"field-3\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0\" value=\"100\"\/><div class=\"grid grid-cols-1\"><select id=\"field-4\" name=\"jednostka\" aria-label=\"Jednostka\"><option value=\"mm\" selected>mm<\/option><option value=\"in\">in<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><\/div><div class=\"field has-term\" id=\"input-3\"><label for=\"field-5\">Przep\u0142yw (Q)<\/label><div class=\"term\">Q<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><div class=\"field-group\"><input type=\"text\" name=\"przepyw_q\" id=\"field-5\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0\" value=\"10\"\/><div class=\"grid grid-cols-1\"><select id=\"field-6\" name=\"jednostka\" aria-label=\"Jednostka\"><option value=\"ls\" selected>L\/s<\/option><option value=\"gpm\">US gpm<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><\/div><div class=\"field has-term\" id=\"input-4\"><label for=\"field-7\">G\u0119sto\u015b\u0107 p\u0142ynu (\u03c1)<\/label><div class=\"term\">\u03c1<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><div class=\"field-group\"><input type=\"text\" name=\"gsto_pynu_\" id=\"field-7\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0\" value=\"998\"\/><div class=\"grid grid-cols-1\"><select id=\"field-8\" name=\"jednostka\" aria-label=\"Jednostka\"><option value=\"kg\" selected>kg\/m\u00b3<\/option><option value=\"lb\">lb\/ft\u00b3<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><\/div><div class=\"field has-term\" id=\"input-5\"><label for=\"field-9\">Lepko\u015b\u0107 dynamiczna (\u03bc)<\/label><div class=\"term\">\u03bc<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"lepko_dynamiczna_\" id=\"field-9\" aria-describedby=\"calc-unit-9 calc-info-9\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0\" value=\"1.002\"\/><div class=\"unit\" id=\"calc-unit-9\">mPa\u00b7s<\/div><small id=\"calc-info-9\">Woda w temperaturze 20 \u00b0C \u2248 1,0 mPa\u00b7s<\/small><\/div><div class=\"field has-term\" id=\"input-6\"><label for=\"field-10\">Chropowato\u015b\u0107 rury (\u03b5)<\/label><div class=\"term\">\u03b5<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><div class=\"field-group\"><input type=\"text\" name=\"chropowato_rury_\" id=\"field-10\" aria-describedby=\"calc-info-10\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0\" value=\"0.045\"\/><div class=\"grid grid-cols-1\"><select id=\"field-11\" name=\"jednostka\" aria-label=\"Jednostka\"><option value=\"mm\" selected>mm<\/option><option value=\"in\">in<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><small id=\"calc-info-10\">Stal handlowa \u2248 0,045 mm; rury ci\u0105gnione \u2248 0,0015 mm; beton \u2248 0,3\u20133 mm<\/small><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Przelicz ponownie\" id=\"calculate-button\" data-post=\"2639\">Oblicz<\/button><button type=\"reset\">Wyczy\u015b\u0107<\/button><\/div><div class=\"field is-checkbox hidden!\" id=\"field-auto-calc\"><input type=\"checkbox\" id=\"auto-calc\"><label for=\"auto-calc\">Obliczaj automatycznie<\/label><small>Po w\u0142\u0105czeniu wynik aktualizuje si\u0119 automatycznie po zmianie dowolnej warto\u015bci.<\/small><\/div><div class=\"fieldset-result is-hidden\" aria-labelledby=\"result-title\" aria-live=\"polite\" role=\"region\"> <h3 class=\"result-title bg-gradient-to-r from-primary-50 to-gray-50 dark:from-primary-900 dark:to-gray-800\" id=\"result-title\"><span class=\"icon icon-s-pulse\" aria-hidden=\"true\"><\/span> Wyniki oblicze\u0144 strat tarcia<\/h3><div class=\"result-box\"><div class=\"field-result\" id=\"output-1\"><span class=\"field-title\"><span>Spadek ci\u015bnienia na tarcie<\/span><span class=\"result-term\">\u0394p<\/span><\/span><span class=\"field-value\" id=\"result-1\" data-unit=\"kPa\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Kopiuj wynik\" aria-label=\"Kopiuj wynik\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-2\"><span class=\"field-title\"><span>Spadek ci\u015bnienia<\/span><\/span><span class=\"field-value\" id=\"result-2\" data-unit=\"psi\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Kopiuj wynik\" aria-label=\"Kopiuj wynik\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-3\"><span class=\"field-title\"><span>Strata wysoko\u015bci ci\u015bnienia<\/span><span class=\"result-term\">h\u2097<\/span><\/span><span class=\"field-value\" id=\"result-3\" data-unit=\"m\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Kopiuj wynik\" aria-label=\"Kopiuj wynik\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-4\"><span class=\"field-title\"><span>Pr\u0119dko\u015b\u0107 przep\u0142ywu<\/span><span class=\"result-term\">v<\/span><\/span><span class=\"field-value\" id=\"result-4\" data-unit=\"m\/s\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Kopiuj wynik\" aria-label=\"Kopiuj wynik\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-5\"><span class=\"field-title\"><span>Liczba Reynoldsa<\/span><span class=\"result-term\">Re<\/span><\/span><span class=\"field-value\" id=\"result-5\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Kopiuj wynik\" aria-label=\"Kopiuj wynik\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-6\"><span class=\"field-title\"><span>Wsp\u00f3\u0142czynnik tarcia Darcy\u2019ego<\/span><span class=\"result-term\">f<\/span><\/span><span class=\"field-value\" id=\"result-6\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Kopiuj wynik\" aria-label=\"Kopiuj wynik\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><\/div><div class=\"result-actions\"><button type=\"button\" class=\"copy-link\"><svg viewBox=\"0 0 20 20\" fill=\"currentColor\" aria-hidden=\"true\"><path d=\"M12.232 4.232a2.5 2.5 0 0 1 3.536 3.536l-1.225 1.224a.75.75 0 0 0 1.061 1.06l1.224-1.224a4 4 0 0 0-5.656-5.656l-3 3a4 4 0 0 0 .225 5.865.75.75 0 0 0 .977-1.138 2.5 2.5 0 0 1-.142-3.667l3-3Z\"\/><path d=\"M11.603 7.963a.75.75 0 0 0-.977 1.138 2.5 2.5 0 0 1 .142 3.667l-3 3a2.5 2.5 0 0 1-3.536-3.536l1.225-1.224a.75.75 0 0 0-1.061-1.06l-1.224 1.224a4 4 0 1 0 5.656 5.656l3-3a4 4 0 0 0-.225-5.865Z\"\/><\/svg><span class=\"copy-link__text\">Kopiuj link do tego obliczenia<\/span><\/button><span class=\"sr-only\" role=\"status\" id=\"copy-link-status\"><\/span><\/div><\/div><a href=\"#respond\" class=\"hidden transition-opacity duration-300 opacity-0 w-50 text-sm justify-center items-center gap-2 px-4 py-2 rounded bg-gray-200 text-gray-700 hover:bg-gray-300\" id=\"leave-comment\"><span class=\"icon icon-comments\" aria-hidden=\"true\"><\/span>Zostaw komentarz<\/a><\/form><\/section><section id=\"calc-reactions\" class=\"not-prose hidden my-12 bg-gradient-to-r from-primary-50 to-gray-50 border border-indigo-100 rounded-xl px-6 py-4 shadow-sm\" data-post=\"2639\" aria-live=\"polite\" aria-labelledby=\"calc-reactions-title\"><p id=\"calc-reactions-title\" class=\"text-sm text-gray-500 text-center mb-2\">Jak oceniasz ten wynik?<\/p><div role=\"group\" aria-labelledby=\"calc-reactions-title\" class=\"grid grid-cols-3 sm:flex sm:flex-row sm:justify-around gap-4 sm:items-center sm:flex-wrap\"><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"like\"><span class=\"reaction-count\" data-reaction-count=\"like\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude00 <\/span><span class=\"reaction-description font-medium\">Lubi\u0119 to <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"helpful\"><span class=\"reaction-count\" data-reaction-count=\"helpful\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\udca1 <\/span><span class=\"reaction-description font-medium\">Pomocne <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"confused\"><span class=\"reaction-count\" data-reaction-count=\"confused\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude15 <\/span><span class=\"reaction-description font-medium\">Niejasne <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"disappointed\"><span class=\"reaction-count\" data-reaction-count=\"disappointed\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude1e <\/span><span class=\"reaction-description font-medium\">Rozczarowanie <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"inaccurate\"><span class=\"reaction-count\" data-reaction-count=\"inaccurate\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\u274c <\/span><span class=\"reaction-description font-medium\">Niedok\u0142adne <\/span><\/button><\/div><div id=\"reaction-message\" class=\"hidden mt-8 rounded-md border border-primary-100 bg-white\/50 backdrop-blur-sm px-4 py-2 text-sm text-center shadow-sm\"><\/div><\/section><div class=\"calcdash-ad not-prose calcdash-ad--calc_result calcdash-ad--in-article\"><ins class=\"adsbygoogle\" style=\"display:block\" data-ad-client=\"ca-pub-1721569815777345\" data-ad-slot=\"6317458308\" data-ad-layout=\"in-article\" data-ad-format=\"fluid\"><\/ins><script>(adsbygoogle = window.adsbygoogle || []).push({});<\/script><\/div>\n<style id=\"wpcoderpro-inline-1\">.formula-box {\r\n\tborder-bottom: none !important;\r\n}<\/style><section class=\"formula-box\" aria-labelledby=\"formula-title\">\r\n\t<div id=\"formula-title\" class=\"not-prose font-display mb-4\"><span class=\"icon icon-formula\" aria-hidden=\"true\"><\/span><h2>Wz\u00f3r na spadek ci\u015bnienia w rurze<\/h2><\/div>\r\n\t<figure class=\"not-prose formula\">\r\n\t\t<figcaption class=\"formula-title\">Wz\u00f3r<\/figcaption>\r\n\t\t<div class=\"text-base text-gray-800\" id=\"formula\">\n\\[ \\Delta p = f \\cdot \\frac{L}{D} \\cdot \\frac{\\rho v^2}{2}, \\qquad v = \\frac{4Q}{\\pi D^2} \\]\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Gdzie:<\/strong><\/p>\n<ul>\n<li>\\(\\Delta p\\) \u2014 spadek ci\u015bnienia spowodowany tarciem (Pa)<\/li>\n<li>\\(f\\) \u2014 wsp\u00f3\u0142czynnik tarcia Darcy\u2019ego (bez wymiaru)<\/li>\n<li>\\(L\\) \u2014 d\u0142ugo\u015b\u0107 rury (m)<\/li>\n<li>\\(D\\) \u2014 wewn\u0119trzna \u015brednica rury (m)<\/li>\n<li>\\(\\rho\\) \u2014 g\u0119sto\u015b\u0107 cieczy (kg\/m\u00b3)<\/li>\n<li>\\(v\\) \u2014 \u015brednia pr\u0119dko\u015b\u0107 przep\u0142ywu (m\/s)<\/li>\n<li>\\(Q\\) \u2014 przep\u0142yw obj\u0119to\u015bciowy (m\u00b3\/s)<\/li>\n<\/ul>\n<p>Wsp\u00f3\u0142czynnik tarcia Darcy\u2019ego zale\u017cy od re\u017cimu przep\u0142ywu, kt\u00f3ry opisuje liczba Reynoldsa \\(Re = \\dfrac{\\rho v D}{\\mu}\\). Dla przep\u0142ywu laminarnego (\\(Re &lt; 2300\\)) \\(f = 64\/Re\\). Dla przep\u0142ywu turbulentnego kalkulator stosuje jawn\u0105 aproksymacj\u0119 Swamee\u2013Jaina r\u00f3wnania Colebrooka\u2013White\u2019a:<\/p>\n<p>\\[ f = \\frac{0.25}{\\left[\\log_{10}\\left(\\dfrac{\\varepsilon}{3.7D} + \\dfrac{5.74}{Re^{0.9}}\\right)\\right]^2} \\]<\/p>\n<p>Strata wysoko\u015bci ci\u015bnienia, czyli r\u00f3wnowa\u017cny s\u0142up cieczy, to \\(h_l = \\dfrac{\\Delta p}{\\rho g}\\), przy czym \\(g = 9.81\\ \\text{m\/s}^2\\).<\/p>\n<p>\r\n<\/section>\n<style id=\"wpcoderpro-inline-2\">.calculation-box {\r\n\tborder-bottom: none !important;\r\n}<\/style><section id=\"calculation\" class=\"calculation-box\" aria-labelledby=\"calculation-title\">\r\n\t<div id=\"calculation-title\" class=\"not-prose font-display\"><span class=\"icon icon-unordered-list\" aria-hidden=\"true\"><\/span><h2>Spadek ci\u015bnienia w rurze \u2013 przyk\u0142ad obliczenia<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Przyk\u0142ad:<\/strong> woda o temperaturze 20 \u00b0C przep\u0142ywa przez 100 m rury ze stali handlowej o wewn\u0119trznej \u015brednicy 100 mm, z przep\u0142ywem 10 l\/s. Przyjmij \\(\\rho = 998\\ \\text{kg\/m}^3\\), \\(\\mu = 1.002\\ \\text{mPa\u00b7s}\\) oraz \\(\\varepsilon = 0.045\\ \\text{mm}\\).<\/p>\n<p>\\[ v = \\frac{4 \\times 0.01}{\\pi \\times 0.1^2} = 1.27\\ \\text{m\/s} \\]<\/p>\n<p>\\[ Re = \\frac{998 \\times 1.27 \\times 0.1}{0.001002} \\approx 126{,}800 \\quad (\\text{przep\u0142yw turbulentny}) \\]<\/p>\n<p>\\[ f = \\frac{0.25}{\\left[\\log_{10}\\left(\\dfrac{0.000045}{3.7 \\times 0.1} + \\dfrac{5.74}{126{,}800^{0.9}}\\right)\\right]^2} \\approx 0.0196 \\]<\/p>\n<p>\\[ \\Delta p = 0.0196 \\times \\frac{100}{0.1} \\times \\frac{998 \\times 1.27^2}{2} \\approx 15{,}850\\ \\text{Pa} \\]<\/p>\n<p><strong>Wynik:<\/strong> spadek ci\u015bnienia wynosi oko\u0142o 15,85 kPa (2,30 psi), co odpowiada stracie wysoko\u015bci ci\u015bnienia rz\u0119du 1,62 m s\u0142upa wody na ca\u0142ej d\u0142ugo\u015bci rury.<\/p>\n<p>\n\r\n<\/section>\n<h2>Jak korzysta\u0107 z kalkulatora<\/h2>\n<ol>\n<li>Wpisz <strong>D\u0142ugo\u015b\u0107 rury (L)<\/strong> i wybierz z listy metry albo stopy.<\/li>\n<li>Wpisz <strong>\u015arednic\u0119 wewn\u0119trzn\u0105 (D)<\/strong> rury w milimetrach lub calach. U\u017cyj \u015brednicy wewn\u0119trznej (otworu), a nie rozmiaru nominalnego ani zewn\u0119trznego.<\/li>\n<li>Wpisz <strong>Przep\u0142yw (Q)<\/strong> w litrach na sekund\u0119 lub galonach ameryka\u0144skich na minut\u0119.<\/li>\n<li>Wpisz <strong>G\u0119sto\u015b\u0107 cieczy (\u03c1)<\/strong> w kg\/m\u00b3 lub lb\/ft\u00b3. Woda w 20 \u00b0C ma oko\u0142o 998 kg\/m\u00b3.<\/li>\n<li>Wpisz <strong>Lepko\u015b\u0107 dynamiczn\u0105 (\u03bc)<\/strong> w mPa\u00b7s. Dla wody w 20 \u00b0C to w przybli\u017ceniu 1,0 mPa\u00b7s.<\/li>\n<li>Wpisz <strong>Chropowato\u015b\u0107 rury (\u03b5)<\/strong> w mm lub calach \u2014 typowe warto\u015bci znajdziesz w tabeli poni\u017cej.<\/li>\n<li>Odczytaj wyniki: <strong>spadek ci\u015bnienia na tarcie<\/strong> w kPa i psi, <strong>strat\u0119 wysoko\u015bci ci\u015bnienia<\/strong> w metrach, a tak\u017ce <strong>pr\u0119dko\u015b\u0107 przep\u0142ywu<\/strong>, <strong>liczb\u0119 Reynoldsa<\/strong> i <strong>wsp\u00f3\u0142czynnik tarcia Darcy\u2019ego<\/strong>.<\/li>\n<\/ol>\n<h2>Czym jest spadek ci\u015bnienia w rurze?<\/h2>\n<p>Gdy ciecz p\u0142ynie rur\u0105, tarcie mi\u0119dzy ciecz\u0105 a \u015bciank\u0105 rury \u2014 a tak\u017ce mi\u0119dzy warstwami cieczy poruszaj\u0105cymi si\u0119 z r\u00f3\u017cnymi pr\u0119dko\u015bciami \u2014 zamienia energi\u0119 ci\u015bnienia w ciep\u0142o. Ci\u015bnienie na ko\u0144cu rury jest zatem zawsze ni\u017csze ni\u017c na wlocie. Tej straty, nazywanej liniowym spadkiem ci\u015bnienia, musz\u0105 pokona\u0107 pompy, aby utrzyma\u0107 przep\u0142yw. R\u00f3wnanie Darcy\u2019ego\u2013Weisbacha to najcz\u0119\u015bciej stosowany model tego zjawiska; jest prawid\u0142owe zar\u00f3wno dla przep\u0142ywu laminarnego, jak i turbulentnego, dla ka\u017cdej cieczy newtonowskiej i ka\u017cdego materia\u0142u rury.<\/p>\n<p>Wynik mo\u017cna wyrazi\u0107 na dwa sposoby: jako r\u00f3\u017cnic\u0119 ci\u015bnie\u0144 \\(\\Delta p\\) (kPa lub psi) albo jako strat\u0119 wysoko\u015bci ci\u015bnienia \\(h_l\\) w metrach s\u0142upa cieczy. W instalacjach wodnych wygodniejsza bywa strata wysoko\u015bci, bo mo\u017cna j\u0105 bezpo\u015brednio odczyta\u0107 jako dodatkowy wysoko\u015b\u0107 podnoszenia pompy lub potrzebn\u0105 wysoko\u015b\u0107 statyczn\u0105. W powy\u017cszym przyk\u0142adzie pompa musi zapewni\u0107 oko\u0142o 1,62 m wysoko\u015bci podnoszenia na ka\u017cde 100 m rury, aby pokry\u0107 same tarcie.<\/p>\n<p>Liczba Reynoldsa wskazuje, w jakim re\u017cimie znajduje si\u0119 przep\u0142yw: poni\u017cej oko\u0142o 2300 przep\u0142yw jest laminarny i wsp\u00f3\u0142czynnik tarcia zale\u017cy wy\u0142\u0105cznie od \\(Re\\); powy\u017cej mniej wi\u0119cej 4000 przep\u0142yw jest turbulentny i znaczenie ma tak\u017ce chropowato\u015b\u0107 rury \\(\\varepsilon\\). W przep\u0142ywie turbulentnym mniejsze \u015brednice i wi\u0119ksze pr\u0119dko\u015bci bardzo szybko zwi\u0119kszaj\u0105 spadek ci\u015bnienia \u2014 przy sta\u0142ym przep\u0142ywie \\(\\Delta p\\) ro\u015bnie mniej wi\u0119cej z \\(v^2\\), a odwrotnie proporcjonalnie do \\(D^5\\). Podwojenie \u015brednicy rury mo\u017ce zmniejszy\u0107 straty tarcia o ponad 90%.<\/p>\n<h2>Typowe warto\u015bci chropowato\u015bci rur<\/h2>\n<table>\n<thead>\n<tr>\n<th>Materia\u0142 rury<\/th>\n<th>Chropowato\u015b\u0107 bezwzgl\u0119dna \u03b5 (mm)<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>Rury ci\u0105gnione (mied\u017a, tworzywo)<\/td>\n<td>0.0015<\/td>\n<\/tr>\n<tr>\n<td>Stal handlowa<\/td>\n<td>0.045<\/td>\n<\/tr>\n<tr>\n<td>Stal ocynkowana<\/td>\n<td>0.15<\/td>\n<\/tr>\n<tr>\n<td>\u017beliwo<\/td>\n<td>0.26<\/td>\n<\/tr>\n<tr>\n<td>Beton<\/td>\n<td>0.3 \u2013 3<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Za\u0142o\u017cenia i ograniczenia<\/h2>\n<ul>\n<li>Obliczenia obejmuj\u0105 <strong>tylko tarcie w prostej rurze<\/strong>. Kszta\u0142tki, zawory, \u0142uki, wloty i wyloty wprowadzaj\u0105 straty miejscowe, kt\u00f3re trzeba oszacowa\u0107 osobno (najcz\u0119\u015bciej jako d\u0142ugo\u015bci r\u00f3wnowa\u017cne albo wsp\u00f3\u0142czynniki strat) i doda\u0107 do tego wyniku.<\/li>\n<li>Przyj\u0119to, \u017ce ciecz jest <strong>newtonowska i nie\u015bci\u015bliwa<\/strong>, przep\u0142yw jest ustalony, a rura ma sta\u0142\u0105 \u015brednic\u0119. Gazy mo\u017cna przybli\u017ca\u0107 tylko wtedy, gdy spadek ci\u015bnienia stanowi ma\u0142y u\u0142amek ci\u015bnienia bezwzgl\u0119dnego.<br \/>\n&lt;liAproksymacja Swamee\u2013Jaina jest dok\u0142adna do oko\u0142o 1% wzgl\u0119dem r\u00f3wnania Colebrooka\u2013White\u2019a dla \\(Re &gt; 4000\\); mi\u0119dzy 2300 a 4000 (strefa przej\u015bciowa) wsp\u00f3\u0142czynnik tarcia jest z natury niepewny, wi\u0119c wyniki nale\u017cy tam traktowa\u0107 jako szacunkowe.<\/li>\n<li>Kalkulator zak\u0142ada, \u017ce podana chropowato\u015b\u0107 odpowiada stanowi rury. Stare, skorodowane lub pokryte kamieniem rury mog\u0105 mie\u0107 znacznie wi\u0119ksz\u0105 chropowato\u015b\u0107 ni\u017c czyste, nowe, a osady i mu\u0142 w praktyce dodatkowo zmniejszaj\u0105 \u015brednic\u0119.<\/li>\n<li>Zawsze u\u017cywaj <strong>\u015brednicy wewn\u0119trznej<\/strong>: nominalne rozmiary rur (np. \u201erura stalowa 2-calowa\u201d) r\u00f3\u017cni\u0105 si\u0119 od rzeczywistego otworu, a spadek ci\u015bnienia jest na t\u0119 warto\u015b\u0107 wyj\u0105tkowo wra\u017cliwy.<\/li>\n<\/ul>\n<h2>Praktyczne wskaz\u00f3wki<\/h2>\n<p>Przed dobraniem pompy zsumuj straty tarcia wszystkich odcink\u00f3w rur oraz straty miejscowe wszystkich kszta\u0142tek, i pami\u0119taj, \u017ce pompa musi te\u017c pokona\u0107 r\u00f3\u017cnic\u0119 wysoko\u015bci statycznej oraz zapewni\u0107 wymagane ci\u015bnienie resztkowe na wylocie. Powszechna zasada projektowa m\u00f3wi, aby utrzymywa\u0107 pr\u0119dko\u015b\u0107 wody w zakresie 1\u20133 m\/s: znacznie mniejsza pr\u0119dko\u015b\u0107 oznacza przewymiarowan\u0105, kosztown\u0105 rur\u0119, a znacznie wi\u0119ksza \u2014 szybki wzrost strat tarcia, ha\u0142asu i ryzyka uderzenia hydraulicznego.<\/p>\n<p>Ciekawostka: spadkiem ci\u015bnienia w rurze rz\u0105dz\u0105 r\u00f3wnania \u015bci\u015ble analogiczne do spadku napi\u0119cia w przewodzie \u2014 ci\u015bnienie zachowuje si\u0119 jak napi\u0119cie, przep\u0142yw jak nat\u0119\u017cenie pr\u0105du, a wsp\u00f3\u0142czynnik tarcia jak rezystancja. Je\u015bli zajmujesz si\u0119 te\u017c instalacjami elektrycznymi, sprawd\u017a nasze kalkulatory <a href=\"https:\/\/wpcalc.com\/pl\/inzynieria\/spadek-napiecia\/\">spadku napi\u0119cia<\/a> i <a href=\"https:\/\/wpcalc.com\/pl\/inzynieria\/prawo-ohma\/\">prawa Ohma<\/a> albo kalkulator <a href=\"https:\/\/wpcalc.com\/pl\/inzynieria\/kalkulator-awg\/\">przekroju przewodu<\/a> do doboru przewod\u00f3w wed\u0142ug obci\u0105\u017calno\u015bci pr\u0105dowej.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Oblicz spadek ci\u015bnienia i strat\u0119 wysoko\u015bci ci\u015bnienia w rurze za pomoc\u0105 r\u00f3wnania Darcy\u2019ego\u2013Weisbacha z wsp\u00f3\u0142czynnikiem tarcia wg Swamee\u2013Jaina. Wpisz d\u0142ugo\u015b\u0107 rury, \u015brednic\u0119, przep\u0142yw, w\u0142a\u015bciwo\u015bci cieczy i chropowato\u015b\u0107, aby otrzyma\u0107 \u0394p w kPa i psi, pr\u0119dko\u015b\u0107, liczb\u0119 Reynoldsa oraz wsp\u00f3\u0142czynnik tarcia.<\/p>\n","protected":false},"author":3168,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[8],"tags":[62],"class_list":["post-2639","post","type-post","status-publish","format-standard","hentry","category-inzynieria","tag-rurociagi"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/posts\/2639","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/users\/3168"}],"replies":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/comments?post=2639"}],"version-history":[{"count":0,"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/posts\/2639\/revisions"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/media?parent=2639"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/categories?post=2639"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/tags?post=2639"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}