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Ayrıca, eşit hacım bölmeli kaplardan oluşan sistemlerin denge durumları ve vanaların açılmasıyla oluşan basınç değişimleri adım adım gösterilmektedir."]},"endTime":2328,"title":"Pascal Prensibi ve Bileşik Kaplar Dersi","beginTime":0}],"fullResult":[{"index":0,"title":"Pascal Prensibi ve Sıvı Basıncı Temel Kavramları","list":{"type":"unordered","items":["Pascal prensibi, sıvı basıncı konusunun temel kavramlarından biridir.","Sıvı moleküller arasındaki boşluklar çok az ve moleküller birbiri üzerinden kayarak hareket eder, kısa mesafelerde birbirini iterler.","Sıvılar üzerine uygulanan kuvvet neticesinde hacimdeki küçülme yok denecek kadar az olduğundan, pratikte sıvılar sıkıştırılamaz olarak kabul edilir."]},"beginTime":0,"endTime":56,"href":"/video/preview/9826775519115478086?parent-reqid=1769659453118804-17902819513526056680-balancer-l7leveler-kubr-yp-vla-163-BAL&text=pascal62&t=0&ask_summarization=1"},{"index":1,"title":"Pascal Prensibinin Tanımı ve Uygulamaları","list":{"type":"unordered","items":["Fransız bilim insanı Blaise Pascal'ın araştırmalarından biri, kapalı bir kapta bulunan sıvının herhangi bir noktasına uygulanan basınçın, sıvı tarafından temas ettiği her noktaya aynen iletildiği idi.","Pascal prensibi, sıvıların üzerine uygulanan dış basınçın, temas ettiği her noktaya aynen iletildiği ve her noktada basınç artışı meydana geldiği prensibidir.","Pistonlu sistemde, piston tarafından uygulanan basınç (F/S) sıvının temas ettiği her noktaya iletilir ve kabın içindeki basınç artışları (ΔP) uygulanan dış kuvvete eşittir."]},"beginTime":56,"endTime":165,"href":"/video/preview/9826775519115478086?parent-reqid=1769659453118804-17902819513526056680-balancer-l7leveler-kubr-yp-vla-163-BAL&text=pascal62&t=56&ask_summarization=1"},{"index":2,"title":"Pascal Prensibinin Uygulamaları","list":{"type":"unordered","items":["Havasız ortamda bulunan bir kapta, K, L ve M noktalarındaki toplam basınçlar sırasıyla 3hdg, 2hdg ve hdg'dir.","Havasız ortamdan vakumlanmış ortamdan çıkarılıp açık hava basıncı (P0) olan ortama getirildiğinde, K, L ve M noktalarındaki toplam basınçlar sırasıyla 3hdg+P, 2hdg+P ve hdg+P olur.","Sıvının üst kısmına yerleştirilen piston, F büyüklüğündeki kuvvetle itildiğinde, K, L ve M noktalarındaki toplam basınçlar sırasıyla 3hdg+P+F/S, 2hdg+P+F/S ve hdg+P+F/S olur."]},"beginTime":165,"endTime":346,"href":"/video/preview/9826775519115478086?parent-reqid=1769659453118804-17902819513526056680-balancer-l7leveler-kubr-yp-vla-163-BAL&text=pascal62&t=165&ask_summarization=1"},{"index":3,"title":"ÖSYM Soruları ve Çözümleri","list":{"type":"unordered","items":["İçinde hava ve h yüksekliğinde su bulunan bir kaptaki K cismi, sızdırmaz piston K düzeyinden L düzeyine kadar itilerek kaptaki hava sıkıştırıldığında, suyun yüksekliği değişmez çünkü K cisminin batan hacminde değişim olmaz.","K cisminin tabanındaki A noktasındaki sıvı basıncı değişmez çünkü K cisminin batan hacmi sabit kalır.","Kabın tabanındaki B noktasındaki toplam basınç artar çünkü havanın basıncı artar ve bu basınç tabana iletilir."]},"beginTime":346,"endTime":698,"href":"/video/preview/9826775519115478086?parent-reqid=1769659453118804-17902819513526056680-balancer-l7leveler-kubr-yp-vla-163-BAL&text=pascal62&t=346&ask_summarization=1"},{"index":4,"title":"Basınç Ölçerlerinin Gösterdiği Değerler","list":{"type":"unordered","items":["İkinci durumda pistonlara uygulanan basınç kuvveti olduğunda, A noktasındaki yeni basınç HDG olur ve sıvı basıncında değişim yoktur çünkü sıvılar sıkıştırılamaz olarak alınır.","K basınç ölçerinin gösterdiği değer 15B olarak verilmiş, L basınç ölçerinin gösterdiği değer ise HDG + 2F/S olarak hesaplanır.","A noktasında iki durum arasındaki basınç farkı 2F/S'den F/S'yi çıkardığımızda F/S'lik bir basınç farkı olur ve bu 7P'ye eşittir."]},"beginTime":700,"endTime":791,"href":"/video/preview/9826775519115478086?parent-reqid=1769659453118804-17902819513526056680-balancer-l7leveler-kubr-yp-vla-163-BAL&text=pascal62&t=700&ask_summarization=1"},{"index":5,"title":"Basınç Farkının Hesaplanması","list":{"type":"unordered","items":["L'de de sıvı basınçları HDG her iki durumda aynı olup, ilk durumda F/S'lik dış basınç etki ederken ikinci durumda uygulanan kuvvet 2F/S olduğu için basınç farkı yine F/S'lik olur ve 7P'ye eşittir.","İlk durumda basınç 10P iken basınç farkı 7P olması gerekir, bu nedenle L basınç ölçerinin gösterdiği değer 17P olur.","Kahveli basıncı ölçerlerin gösterdiği değerler arasındaki fark pistona uygulanan kuvvetin büyüklüğüne bağlı olarak değişmez, bu Ascal prensibini gösterir."]},"beginTime":791,"endTime":952,"href":"/video/preview/9826775519115478086?parent-reqid=1769659453118804-17902819513526056680-balancer-l7leveler-kubr-yp-vla-163-BAL&text=pascal62&t=791&ask_summarization=1"},{"index":6,"title":"Sıvı Basıncının Hesaplanması","list":{"type":"unordered","items":["A noktasına etki eden sıvı basıncı 3B'ye eşittir çünkü toplam basınç ile basınç ölçeğinin gösterdiği değer toplam basınçtır.","F/S ifadesinde 7P olarak bulunan değer, toplam basınç ifadesini verdiğinde sıvı basıncının 3P olduğunu gösterir.","Tüm öncüllerin doğru olduğu sonucuna varılır."]},"beginTime":952,"endTime":1024,"href":"/video/preview/9826775519115478086?parent-reqid=1769659453118804-17902819513526056680-balancer-l7leveler-kubr-yp-vla-163-BAL&text=pascal62&t=952&ask_summarization=1"},{"index":7,"title":"Bileşik Kaplar","list":{"type":"unordered","items":["Kolları açık bileşik kaplar türdeş sıvı ile doldurulurken, boruların kesit alanına, şekline, eğimine bağlı olmaksızın sıvı kollarda eşit miktar yükselir.","Türdeş sıvı kollarda dengedeyken KLM noktalarındaki toplam basınçlar birbirine eşittir çünkü akışkanların basıncın büyük olduğu yerden küçük olduğu yere doğru hareket etmesi gerekir.","Kollardaki basınçlar kabın tabanından okunur ve açık kollara etki eden açık hava basınçları sistemin denge noktasında dengesine etki etmez."]},"beginTime":1024,"endTime":1217,"href":"/video/preview/9826775519115478086?parent-reqid=1769659453118804-17902819513526056680-balancer-l7leveler-kubr-yp-vla-163-BAL&text=pascal62&t=1024&ask_summarization=1"},{"index":8,"title":"Pistonlu Bileşik Kaplar","list":{"type":"unordered","items":["Bir kolunda sürtünmesiz piston bulunan kaptaki türdeş sıvı dengedeyken K ve L noktalarındaki toplam basınçlar birbirine eşittir.","Türdeş bir sıvı içerisinde kollarda eşit miktar aşağı inerse basıncı eşit miktar arttırmış, eşit miktar yukarı çıkarsan da basıncı eşit miktar azaltmış olursun.","M ve N noktalarındaki basınçlar birbirine eşittir çünkü kahvelerdeki basınçlar birbirine eşittir ve kollardaki basınçları eşit miktar azaltmış oluruz."]},"beginTime":1217,"endTime":1370,"href":"/video/preview/9826775519115478086?parent-reqid=1769659453118804-17902819513526056680-balancer-l7leveler-kubr-yp-vla-163-BAL&text=pascal62&t=1217&ask_summarization=1"},{"index":9,"title":"Örnek Soru","list":{"type":"unordered","items":["Şekildeki düzenek ağızları açık R ve 2R yarıçaplı silindirik borularla oluşturulmuş olup K noktasındaki sıvı basıncı P'dir.","K noktasının üzerinde başlangıçta var olan sıvı yüksekliği H olarak ifade edilir.","R yarıçaplı borunun kesit alanı πR², 2R yarıçaplı borunun kesit alanı ise 4πR² olur."]},"beginTime":1370,"endTime":1426,"href":"/video/preview/9826775519115478086?parent-reqid=1769659453118804-17902819513526056680-balancer-l7leveler-kubr-yp-vla-163-BAL&text=pascal62&t=1370&ask_summarization=1"},{"index":10,"title":"Bileşik Kaplarda Sıvı Basıncı Hesaplama","list":{"type":"unordered","items":["Bileşik kaplarda, kollardaki sıvı seviyeleri birbirine eşit olmak zorundadır.","Başlangıçta 4S kesit alanına yerleştirilmiş sıvı, vana açıldığında 5S kesit alanına dağılır ve yüksekliği h'ye eşitlenir.","İlk durumdaki sıvı basıncı Pd = hdg, ikinci durumdaki basıncı P' = 4hdg olarak hesaplanır ve P' = 4P/5 olarak bulunur."]},"beginTime":1426,"endTime":1553,"href":"/video/preview/9826775519115478086?parent-reqid=1769659453118804-17902819513526056680-balancer-l7leveler-kubr-yp-vla-163-BAL&text=pascal62&t=1426&ask_summarization=1"},{"index":11,"title":"Eşit Hacim Bölmeli Kaplarda Sıvı Basıncı","list":{"type":"unordered","items":["Eşit hacim bölmeli kaplardan biri türdeş sıvı ile dolu, diğeri boş olduğunda, vana açıldığında sıvı seviyeleri eşitlenir.","İlk durumda A noktasındaki sıvı basıncı Pd = 4hdg, vana açıldıktan sonra A noktasındaki basınç P' = 3P/8 olarak hesaplanır."]},"beginTime":1553,"endTime":1754,"href":"/video/preview/9826775519115478086?parent-reqid=1769659453118804-17902819513526056680-balancer-l7leveler-kubr-yp-vla-163-BAL&text=pascal62&t=1553&ask_summarization=1"},{"index":12,"title":"Bileşik Kaplarda Sıvı Denge Durumu","list":{"type":"unordered","items":["Bileşik kaplarda dengenin sağlanması için kollardaki sıvı basınçlarının birbirine eşit olması gerekir.","Sıvıların özkütleleri farklı olduğunda, özkütlesi daha büyük olan sıvının bulunduğu koldan daha küçük özkütleli sıvının bulunduğu kola doğru sıvı hareketi olur.","Edirne şıkkında, sıvı düzeyleri arasındaki çizgiye kadar her iki tarafta aynı sıvı bulunurken, kalan kısımlarda özkütlesi ve yüksekliği farklı olan sıvılar bulunur ve bu durumda basınç dengesi kurulabilir."]},"beginTime":1754,"endTime":2071,"href":"/video/preview/9826775519115478086?parent-reqid=1769659453118804-17902819513526056680-balancer-l7leveler-kubr-yp-vla-163-BAL&text=pascal62&t=1754&ask_summarization=1"},{"index":13,"title":"Bileşik Kap Problemi","list":{"type":"unordered","items":["Düşey kesileri şekilli eşit hacım bölmeli kaplardan KLM ise boş olup, A noktasındaki sıvı basıncı P'dir.","Vana açılıp denge sağlandıktan sonra B noktasındaki sıvı basıncı kaç P olur sorusu inceleniyor.","Bağlantı borularının hacmi önemsiz olarak verilmiştir."]},"beginTime":2077,"endTime":2095,"href":"/video/preview/9826775519115478086?parent-reqid=1769659453118804-17902819513526056680-balancer-l7leveler-kubr-yp-vla-163-BAL&text=pascal62&t=2077&ask_summarization=1"},{"index":14,"title":"Bileşik Kap Mantığı","list":{"type":"unordered","items":["Bileşik kap mantığı uygulanarak A noktasının basıncı P = 5hhdg olarak ifade edilmiştir.","Vanayı açarak sistemin yeni görünümü oluşturulmuştur.","Sıvı akışı sonucunda L ve M kabının bağlantı borusuna kadar sıvı seviyesi ulaşmıştır."]},"beginTime":2095,"endTime":2191,"href":"/video/preview/9826775519115478086?parent-reqid=1769659453118804-17902819513526056680-balancer-l7leveler-kubr-yp-vla-163-BAL&text=pascal62&t=2095&ask_summarization=1"},{"index":15,"title":"Denge Durumu","list":{"type":"unordered","items":["L'ye dökülen sıvı direkt olarak bağlantı borusundan M'ye gidecek ve M'nin iki birimi gelen suyla doldurulacaktır.","A kabından hala akması gereken bir birimlik sıvı var ve bu sıvı LM kaplarına gittiğinde iki birime dağılacaktır.","Son durumda sıvı yüksekliği h/2 olacak şekilde sistem dengeye gelecektir."]},"beginTime":2191,"endTime":2261,"href":"/video/preview/9826775519115478086?parent-reqid=1769659453118804-17902819513526056680-balancer-l7leveler-kubr-yp-vla-163-BAL&text=pascal62&t=2191&ask_summarization=1"},{"index":16,"title":"Sonuç","list":{"type":"unordered","items":["Yeni durumda B noktasının üzerinde 5h/2 yüksekliğinde d özkütleli sıvı var ve basıncı 5hdg/2 olacaktır.","Yukarıdaki basınç P olduğuna göre, B noktasındaki basınç P/2 olacaktır.","Pascal prensibi ve bileşik kaplar konuları öğrenilmiş olup, konu tamamlanmıştır."]},"beginTime":2261,"endTime":2323,"href":"/video/preview/9826775519115478086?parent-reqid=1769659453118804-17902819513526056680-balancer-l7leveler-kubr-yp-vla-163-BAL&text=pascal62&t=2261&ask_summarization=1"}],"linkTemplate":"/video/preview/9826775519115478086?parent-reqid=1769659453118804-17902819513526056680-balancer-l7leveler-kubr-yp-vla-163-BAL&text=pascal62&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"Ders 92 - Pascal Prensibi ve Bileşik 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İlk bölümde Pascal üçgeninin yapısı, sıfırıncı satırın bir ile başlaması, her satırın bir ile devam etmesi ve alt küme sayıları ile ilişkisi anlatılmaktadır. İkinci bölümde ise iki'nin sıfırlısı, bir lisesi, ikilisi ve üçlüsü gibi kavramlar ve beş'in üstüne eşit olan ifadeyi bulma konusu işlenmektedir.","Videoda Pascal özdeşliği (n'in r'li kombinasyonu ile n'in r+1'li kombinasyonunun toplamı) detaylı olarak açıklanmakta ve örneklerle gösterilmektedir. Ayrıca, bu konunun bir sonraki konu olan binom katsayıları için temel olduğu belirtilmektedir."]},"endTime":793,"title":"Matematik Dersi: Pascal Üçgeni ve Sayılar","beginTime":0}],"fullResult":[{"index":0,"title":"Pascal Üçgeni ve Özellikleri","list":{"type":"unordered","items":["Pascal üçgeni (hayyam üçgeni olarak da bilinir) bir ile başlayıp bir üçgen şeklinde bir-bir şeklinde devam eden ve bir ile sonlanan bir sayı dizisidir.","Pascal üçgeninde sayılar, üstteki iki sayının toplamı olarak hesaplanır (örneğin 1+1=2, 1+2=3, 2+3=5).","Pascal üçgeninde sıfırıncı satır birinci satıra gelir ve sıfırıncı satırdaki eleman 1'dir (2⁰=1)."]},"beginTime":1,"endTime":103,"href":"/video/preview/16937830401907207508?parent-reqid=1769659453118804-17902819513526056680-balancer-l7leveler-kubr-yp-vla-163-BAL&text=pascal62&t=1&ask_summarization=1"},{"index":1,"title":"Pascal Üçgeninin Kombinasyon İlişkisi","list":{"type":"unordered","items":["Pascal üçgenindeki sayılar kombinasyon sayılarını temsil eder; örneğin beşinci satırda 1, 5, 10, 10, 5, 1 sayıları sırasıyla 5'ün 0'lısı, 1'lisi, 2'lisini, 3'lüsü, 4'lüsü ve 5'lisini gösterir.","Herhangi bir n elemanlı kümenin tüm alt kümelerinin sayısı 2ⁿ'dir ve bu sayı Pascal üçgenindeki n. satırdaki sayıların toplamına eşittir.","Pascal üçgenindeki bir sayı, aynı satırdaki bir sonraki sayı ile birlikte toplandığında bir sonraki satırdaki karşılık gelen sayıya eşittir (örneğin 4C1 + 4C2 = 5C2)."]},"beginTime":103,"endTime":336,"href":"/video/preview/16937830401907207508?parent-reqid=1769659453118804-17902819513526056680-balancer-l7leveler-kubr-yp-vla-163-BAL&text=pascal62&t=103&ask_summarization=1"},{"index":2,"title":"Pascal Özdeşliği ve Uygulamaları","list":{"type":"unordered","items":["Pascal özdeşliği, ardışık gelen kombinasyonların toplamının bir sonraki satırdaki karşılık gelen kombinasyona eşit olduğunu gösterir (nCr + nC(r+1) = (n+1)C(r+1)).","Pascal özdeşliği, ardışık kombinasyonların toplamını hesaplamak için kullanılır ve binom 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prensibi, sıvı basıncı, kapalı kaplarda sıvı basıncı, pascal prensibine örnekler, gaz basıncı, basınç, 8.sinif kapalı kaplarda sıvı basıncı, 8.sinif Pascal prensibi...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/3008607/f8c1317cf662029f790307ccd225f0bd/564x318_1"},"target":"_self","position":"2","reqid":"1769659453118804-17902819513526056680-balancer-l7leveler-kubr-yp-vla-163-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1769659453118804-17902819513526056680-balancer-l7leveler-kubr-yp-vla-163-BAL&text=videoid:11774646654785520127","teaser":[{"list":{"type":"unordered","items":["Bu video, bir eğitim içeriği olup, konuşmacı Pascal prensibini açıklamak ve deney yapmak için gerekli malzemeleri göstermektedir.","Videoda öncelikle Pascal prensibinin tanımı yapılmakta, ardından deney için gerekli malzemeler (plastik şişe, pipet, esnek balon ve kap) tanıtılmaktadır. Deneyde balonun şişenin ağız kısmına yerleştirilmesi, balonun içindeki havanın şişenin içine doldurulması ve bu sayede pipetin içindeki suyun kaba boşaltılması gösterilmektedir. Son olarak, bu prensibin günlük hayattaki uygulamaları (pompalı damacanalar, basmalı sıvı sabunluklar, parfüm şişeleri, cam sil şişeleri) anlatılmaktadır."]},"endTime":253,"title":"Pascal Prensibi Deneyi","beginTime":0}],"fullResult":[{"index":0,"title":"Pascal Prensibi Nedir?","list":{"type":"unordered","items":["Pascal prensibi, kapalı kaplardaki sıvıların üzerine uygulanan basıncın her yöne eşit büyüklükte ve dik bir şekilde iletimini ifade eder.","Pascal prensibine göre, kapalı kaplardaki sıvılar üzerine uygulanan basıncın her yöne aynı büyüklükte ve kabın her tarafına dik bir şekilde iletildiği belirtilir."]},"beginTime":2,"endTime":43,"href":"/video/preview/11774646654785520127?parent-reqid=1769659453118804-17902819513526056680-balancer-l7leveler-kubr-yp-vla-163-BAL&text=pascal62&t=2&ask_summarization=1"},{"index":1,"title":"Deney Malzemeleri ve Amacı","list":{"type":"unordered","items":["Deney için plastik şişe, pipet, esnek balon ve suyu boşaltmak için kullanılan bir kap gereklidir.","Deneyde balonun içerisine hava doldurulup şişenin ağız kısmına yerleştirilerek, balonun içerisindeki havanın şişenin içerisine dolması gözlemlenecektir.","Balonun içerisindeki hava şişenin içerisine geldiğinde, şişenin içerisindeki sıvıya basınç uygulayacak ve kapalı bir ortam oluşturacaktır."]},"beginTime":43,"endTime":117,"href":"/video/preview/11774646654785520127?parent-reqid=1769659453118804-17902819513526056680-balancer-l7leveler-kubr-yp-vla-163-BAL&text=pascal62&t=43&ask_summarization=1"},{"index":2,"title":"Deneyin Gerçekleştirilmesi","list":{"type":"unordered","items":["Balonun içerisi hava ile doldurulup ağzı şişenin ağız kısmına yerleştirilir.","Balonun içerisindeki hava şişenin içerisine serbest bırakıldığında, suyun her tarafına eşit büyüklükte ve dik bir şekilde basınç uygular.","Pipetin en alt kısmındaki kısma uygulanan basınç, pipetin içerisindeki havayı dışarıya doğru ittirip suyun şişenin içerisinden kaba doğru boşalmasını 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14: • [Pascal] Optimizing Bubble Sort (Tuto... 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