{"id":2546,"date":"2026-10-14T17:05:00","date_gmt":"2026-10-14T16:05:00","guid":{"rendered":"https:\/\/wpcalc.com\/pl\/chemia\/wzniesienie-kapilarne-kalkulator\/"},"modified":"2026-10-14T17:05:00","modified_gmt":"2026-10-14T16:05:00","slug":"wzniesienie-kapilarne-kalkulator","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/pl\/chemia\/wzniesienie-kapilarne-kalkulator\/","title":{"rendered":"Kalkulator wzniesienia kapilarnego"},"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\">Oblicz wzniesienie kapilarne na podstawie napi\u0119cia powierzchniowego, g\u0119sto\u015bci i promienia rurki<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"2546\" data-favorite-title=\"Wzniesienie kapilarne\" data-favorite-url=\"https:\/\/wpcalc.com\/pl\/chemia\/wzniesienie-kapilarne-kalkulator\/\" data-favorite-excerpt=\"Oblicz, jak wysoko ciecz podniesie si\u0119 (lub opadnie) w kapilarze, korzystaj\u0105c z prawa Jurina. Wpisz napi\u0119cie powierzchniowe, g\u0119sto\u015b\u0107 cieczy, promie\u0144 rurki, k\u0105t zwil\u017cania i przyspieszenie grawitacyjne, aby otrzyma\u0107 wzniesienie kapilarne w mm, cm, m lub calach.\" aria-label=\"Dodaj do ulubionych\" data-favorite-icon=\"icon icon-molecule\">\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\/chemia\/wzniesienie-kapilarne-kalkulator\/\" method=\"POST\" class=\"calculator\" id=\"calculator-2546\" data-post=\"2546\"><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\">Napi\u0119cie powierzchniowe (\u03b3)<\/label><div class=\"term\">\u03b3<\/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=\"napicie_powierzchniowe_\" id=\"field-1\" aria-describedby=\"calc-info-1\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 72.8\" min=\"0\" value=\"72.8\"\/><div class=\"grid grid-cols-1\"><select id=\"field-2\" name=\"jednostka\" aria-label=\"Jednostka\"><option value=\"mN_m\" selected>mN\/m<\/option><option value=\"N_m\">N\/m<\/option><option value=\"dyn_cm\">dyn\/cm<\/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-1\">Napi\u0119cie powierzchniowe cieczy wzgl\u0119dem powietrza. Woda \u2248 72,8 mN\/m, etanol \u2248 22,3 mN\/m, rt\u0119\u0107 \u2248 486 mN\/m (wszystkie przy 20 \u00b0C).<\/small><\/div><div class=\"field has-term\" id=\"input-2\"><label for=\"field-3\">G\u0119sto\u015b\u0107 cieczy (\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_cieczy_\" id=\"field-3\" aria-describedby=\"calc-info-3\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 998\" min=\"0\" value=\"998\"\/><div class=\"grid grid-cols-1\"><select id=\"field-4\" name=\"jednostka\" aria-label=\"Jednostka\"><option value=\"kg_m3\" selected>kg\/m\u00b3<\/option><option value=\"g_cm3\">g\/cm\u00b3<\/option><option value=\"lb_ft3\">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><small id=\"calc-info-3\">G\u0119sto\u015b\u0107 samej cieczy, a nie otaczaj\u0105cego powietrza. Woda \u2248 998 kg\/m\u00b3 przy 20 \u00b0C, rt\u0119\u0107 \u2248 13 546 kg\/m\u00b3.<\/small><\/div><div class=\"field has-term\" id=\"input-3\"><label for=\"field-5\">Promie\u0144 rurki (r)<\/label><div class=\"term\">r<\/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=\"promie_rurki_r\" id=\"field-5\" aria-describedby=\"calc-info-5\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 0.5\" min=\"0\" value=\"0.5\"\/><div class=\"grid grid-cols-1\"><select id=\"field-6\" name=\"jednostka\" aria-label=\"Jednostka\"><option value=\"mm\" selected>mm<\/option><option value=\"um\">\u00b5m<\/option><option value=\"cm\">cm<\/option><option value=\"m\">m<\/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-5\">Promie\u0144 wewn\u0119trzny rurki kapilarnej. Rurka o \u015brednicy wewn\u0119trznej 1 mm ma promie\u0144 0,5 mm.<\/small><\/div><div class=\"field has-term\" id=\"input-4\"><label for=\"field-7\">K\u0105t zwil\u017cania (\u03b8)<\/label><div class=\"term\">\u03b8<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"kt_zwilania_\" id=\"field-7\" aria-describedby=\"calc-unit-7 calc-info-7\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 0\" min=\"0\" max=\"180\" value=\"0\"\/><div class=\"unit\" id=\"calc-unit-7\">\u00b0<\/div><small id=\"calc-info-7\">K\u0105t mi\u0119dzy powierzchni\u0105 cieczy a \u015bciank\u0105 rurki. Woda w czystym szkle \u2248 0\u00b0 (zwil\u017canie), rt\u0119\u0107 w szkle \u2248 140\u00b0 (niezwil\u017canie, powoduje obni\u017cenie menisku).<\/small><\/div><div class=\"field has-term\" id=\"input-5\"><label for=\"field-8\">Przyspieszenie grawitacyjne (g)<\/label><div class=\"term\">g<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"przyspieszenie_grawitacyjne_g\" id=\"field-8\" aria-describedby=\"calc-unit-8 calc-info-8\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 9.81\" min=\"0\" value=\"9.81\"\/><div class=\"unit\" id=\"calc-unit-8\">m\/s\u00b2<\/div><small id=\"calc-info-8\">Ziemia \u2248 9,81 m\/s\u00b2, Ksi\u0119\u017cyc \u2248 1,62 m\/s\u00b2. Wi\u0119ksze g zmniejsza wzniesienie.<\/small><\/div><div class=\"field is-single\" id=\"input-6\"><label for=\"field-9\">Poka\u017c wzniesienie kapilarne w<\/label><div class=\"grid grid-cols-1\"><select id=\"field-9\" name=\"poka_wzniesienie_kapilarne_w\"><option value=\"mm\" selected>milimetrach (mm)<\/option><option value=\"cm\">centymetrach (cm)<\/option><option value=\"m\">metrach (m)<\/option><option value=\"in\">calach (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><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Przelicz ponownie\" id=\"calculate-button\" data-post=\"2546\">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 wzniesienia kapilarnego<\/h3><div class=\"result-box\"><div class=\"field-result\" id=\"output-1\"><span class=\"field-title\"><span>Wzniesienie lub obni\u017cenie kapilarne (h)<\/span><span class=\"result-term\">h<\/span><\/span><span class=\"field-value\" id=\"result-1\"><\/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 is-column\" id=\"output-2\"><span class=\"field-title\"><span>Wzniesienie lub obni\u017cenie w innych jednostkach<\/span><\/span><span class=\"field-value\" id=\"result-2\"><\/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 is-column\" id=\"output-3\"><span class=\"field-title\"><span>Szczeg\u00f3\u0142y oblicze\u0144<\/span><\/span><span class=\"field-value\" id=\"result-3\"><\/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 is-column\" id=\"output-4\"><span class=\"field-title\"><span>O zjawisku kapilarnym<\/span><\/span><span class=\"field-value\" id=\"result-4\"><\/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=\"2546\" 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>Wzniesienie kapilarne<\/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\\[ h = \\frac{2\\,\\gamma\\,\\cos\\theta}{\\rho\\, g\\, r} \\\\\\]\n\\[ \\Delta p = \\frac{2\\,\\gamma\\,\\cos\\theta}{r} \\]\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Gdzie:<\/strong><\/p>\n<ul>\n<li>\\(h\\) \u2014 wzniesienie lub obni\u017cenie s\u0142upa cieczy (m)<\/li>\n<li>\\(\\gamma\\) \u2014 napi\u0119cie powierzchniowe cieczy na granicy z powietrzem (N\/m)<\/li>\n<li>\\(\\theta\\) \u2014 k\u0105t zwil\u017cania mi\u0119dzy ciecz\u0105 a \u015bciank\u0105 rurki (\u00b0)<\/li>\n<li>\\(\\rho\\) \u2014 g\u0119sto\u015b\u0107 cieczy (kg\/m\u00b3)<\/li>\n<li>\\(g\\) \u2014 przyspieszenie grawitacyjne (m\/s\u00b2)<\/li>\n<li>\\(r\\) \u2014 promie\u0144 wewn\u0119trzny kapilary (m)<\/li>\n<\/ul>\n<p>Pierwsze r\u00f3wnanie to <strong>prawo Jurina<\/strong>: wynika ono z r\u00f3wnowagi mi\u0119dzy si\u0142\u0105 kapilarn\u0105 skierowan\u0105 w g\u00f3r\u0119 \\(2\\pi r\\,\\gamma\\cos\\theta\\) a ci\u0119\u017carem \\(\\rho g \\pi r^2 h\\) s\u0142upa cieczy. Drugie r\u00f3wnanie opisuje skok ci\u015bnienia kapilarnego (Laplace'a) na zakrzywionym menisku, kt\u00f3ry nap\u0119dza ruch cieczy.<\/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>Wzniesienie kapilarne \u2013 przyk\u0142ad obliczenia<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Przyk\u0142ad:<\/strong> woda o temperaturze 20 \u00b0C (napi\u0119cie powierzchniowe 72,8 mN\/m, g\u0119sto\u015b\u0107 998 kg\/m\u00b3) podnosi si\u0119 w czystej kapilarze szklanej o promieniu wewn\u0119trznym 0,5 mm. Woda doskonale zwil\u017ca czyste szk\u0142o, wi\u0119c k\u0105t zwil\u017cania wynosi 0\u00b0, a przyspieszenie grawitacyjne 9,81 m\/s\u00b2.<\/p>\n<p>\\[ \\gamma = 72.8\\ \\text{mN\/m} = 0.0728\\ \\text{N\/m}, \\quad r = 0.5\\ \\text{mm} = 5\\times10^{-4}\\ \\text{m} \\]<br \/>\n\\[ h = \\frac{2 \\times 0.0728 \\times \\cos 0\u00b0}{998 \\times 9.81 \\times 5\\times10^{-4}} = \\frac{0.1456}{4.895} \\approx 0.02974\\ \\text{m} \\]<br \/>\n\\[ h \\approx 29.74\\ \\text{mm} \\approx 2.97\\ \\text{cm} \\approx 1.17\\ \\text{in} \\]\n<\/p>\n<p><strong>Wynik:<\/strong> woda podnosi si\u0119 mniej wi\u0119cej o <strong>29,74 mm<\/strong> (\u2248 2,97 cm) ponad poziom otaczaj\u0105cej cieczy \u2014 dok\u0142adnie to pokazuje kalkulator przy domy\u015blnych warto\u015bciach.<\/p>\n<p>\n\r\n<\/section>\n<h2>Jak korzysta\u0107 z kalkulatora wzniesienia kapilarnego<\/h2>\n<ol>\n<li>Wpisz <strong>napi\u0119cie powierzchniowe (\u03b3)<\/strong> cieczy i wybierz jednostk\u0119 (mN\/m, N\/m lub dyn\/cm). Dla wody w 20 \u00b0C wynosi ono oko\u0142o 72,8 mN\/m.<\/li>\n<li>Podaj <strong>g\u0119sto\u015b\u0107 cieczy (\u03c1)<\/strong> wraz z jednostk\u0105 (kg\/m\u00b3, g\/cm\u00b3 lub lb\/ft\u00b3). U\u017cyj g\u0119sto\u015bci cieczy, a nie otaczaj\u0105cego powietrza.<\/li>\n<li>Wpisz wewn\u0119trzny <strong>promie\u0144 rurki (r)<\/strong> \u2014 pami\u0119taj, \u017ce to promie\u0144, wi\u0119c rurka o \u015brednicy wewn\u0119trznej 1 mm to 0,5 mm. Wybierz mm, \u00b5m, cm, m lub in.<\/li>\n<li>Ustaw <strong>k\u0105t zwil\u017cania (\u03b8)<\/strong> w stopniach: 0\u00b0 dla wody w czystym szkle, oko\u0142o 140\u00b0 dla rt\u0119ci w szkle (wtedy nast\u0119puje obni\u017cenie zamiast wzniesienia).<\/li>\n<li>Dostosuj w razie potrzeby <strong>przyspieszenie grawitacyjne (g)<\/strong>; 9,81 m\/s\u00b2 to warto\u015b\u0107 domy\u015blna dla Ziemi, a 1,62 m\/s\u00b2 przybli\u017ca warunki panuj\u0105ce na Ksi\u0119\u017cycu.<\/li>\n<li>Wybierz jednostk\u0119 wyniku w polu <strong>Poka\u017c wzniesienie kapilarne w<\/strong> (mm, cm, m lub in) \u2014 im w\u0119\u017csza rurka, tym wi\u0119ksze wzniesienie, wi\u0119c zmie\u0144 jednostk\u0119, gdy liczba stanie si\u0119 niepor\u0119czna.<\/li>\n<\/ol>\n<p>Wynik ma znak: warto\u015b\u0107 dodatnia oznacza wzniesienie ponad poziom otaczaj\u0105cej cieczy, a ujemna \u2014 obni\u017cenie poni\u017cej niego.<\/p>\n<h2>Czym jest wzniesienie kapilarne i dlaczego wyst\u0119puje?<\/h2>\n<p>Wzniesienie kapilarne to zjawisko, w kt\u00f3rym ciecz wznosi si\u0119 w w\u0105skiej rurce (kapilarze) zanurzonej w niej, pozornie sprzeciwiaj\u0105c si\u0119 grawitacji. Nap\u0119dza je <strong>napi\u0119cie powierzchniowe<\/strong>: cz\u0105steczki na powierzchni cieczy ci\u0105gn\u0105 menisk wzd\u0142u\u017c \u015bcianki rurki, a je\u015bli ciecz zwil\u017ca \u015bciank\u0119 (k\u0105t zwil\u017cania poni\u017cej 90\u00b0), menisk jest wkl\u0119s\u0142y i jego krzywizna wytwarza niedob\u00f3r ci\u015bnienia, kt\u00f3ry zasysa ciecz w g\u00f3r\u0119. S\u0142up przestaje rosn\u0105\u0107, gdy jego ci\u0119\u017car dok\u0142adnie r\u00f3wnowa\u017cy si\u0142\u0119 kapilarn\u0105 \u2014 ta r\u00f3wnowaga to w\u0142a\u015bnie prawo Jurina.<\/p>\n<p>Najbardziej uderzaj\u0105ca cecha wzoru to odwrotna proporcjonalno\u015b\u0107 do promienia rurki: <em>zmniejszenie promienia o po\u0142ow\u0119 podwaja wzniesienie<\/em>. Woda w rurce o promieniu 0,5 mm podnosi si\u0119 tylko o oko\u0142o 3 cm, ale w porze o \u015brednicy 10 \u00b5m wspi\u0105 si\u0119 mniej wi\u0119cej na 1,5 m. Ta zale\u017cno\u015b\u0107 wyja\u015bnia, dlaczego r\u0119czniki papierowe wch\u0142aniaj\u0105 rozlane p\u0142yny, dlaczego dzia\u0142aj\u0105 knoty i g\u0105bki, a tak\u017ce jak drzewa transportuj\u0105 wod\u0119 na dziesi\u0105tki metr\u00f3w przez mikroskopijne naczynia drewnne \u2014 kapilarno\u015b\u0107, obok osmozy i transpiracji, to jeden z kluczowych mechanizm\u00f3w transportu u ro\u015blin.<\/p>\n<p>K\u0105t zwil\u017cania decyduje o kierunku zjawiska. Ciecze zwil\u017caj\u0105ce (\\(\\theta &lt; 90\u00b0\\), woda w szkle) si\u0119 podnosz\u0105; przy \\(\\theta = 90\u00b0\\) powierzchnia pozostaje p\u0142aska; a ciecze niezwil\u017caj\u0105ce (\\(\\theta &gt; 90\u00b0\\), rt\u0119\u0107 w szkle) zostaj\u0105 <strong>obni\u017cone<\/strong> poni\u017cej poziomu otoczenia, poniewa\u017c \\(\\cos\\theta\\) jest ujemny. Kalkulator sam ustala znak i podpowiada, czy mamy do czynienia z wzniesieniem, czy z obni\u017ceniem. Pokazuje te\u017c promie\u0144 krzywizny menisku (\\(R = r\/\\cos\\theta\\)) oraz ci\u015bnienie kapilarne \\(\\Delta p\\), czyli to, co \u201eczuje<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Oblicz, jak wysoko ciecz podniesie si\u0119 (lub opadnie) w kapilarze, korzystaj\u0105c z prawa Jurina. Wpisz napi\u0119cie powierzchniowe, g\u0119sto\u015b\u0107 cieczy, promie\u0144 rurki, k\u0105t zwil\u017cania i przyspieszenie grawitacyjne, aby otrzyma\u0107 wzniesienie kapilarne w mm, cm, m lub calach.<\/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":[4],"tags":[21],"class_list":["post-2546","post","type-post","status-publish","format-standard","hentry","category-chemia","tag-wiazania-chemiczne"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/posts\/2546","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=2546"}],"version-history":[{"count":0,"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/posts\/2546\/revisions"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/media?parent=2546"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/categories?post=2546"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/tags?post=2546"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}