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Hukum Bernoulli
Oleh : Meli (1106550)
Rindu Nurani (1204513)
Fluida
Fluida berbeda dengan zat padat, yaitu tidak
dapat menopang tegangan geser (gaya geser
terhadap luas). Jadi, fluida berubah bentuk
bagaimanapun ruang yang diisinya. Bila sebuah
benda tercelup dalam fluida seperti air, fluida
mengadakan sebuah gaya tegak lurus permukaan
benda di setiap titik pada permukaan benda
tersebut.
P
F
A
Fluida Bergerak dalam Beda Luasan
Pipa dan Ketinggian
𝑦1
𝑦2
∆𝑥1
𝐴2
𝐴1
∆𝑥2
∆𝑚 = 𝜌. ∆𝑉
𝑦1 → 𝑦2
𝑣1 → 𝑣2
∆𝑡 = 𝑠𝑎𝑚𝑎/𝑘𝑜𝑛𝑠𝑡𝑎𝑛
∆𝑈 (𝑃𝑒𝑟𝑢𝑏𝑎ℎ𝑎𝑛 𝐸𝑃)
∆𝐾 (𝑃𝑒𝑟𝑢𝑏𝑎ℎ𝑎𝑛 𝐸𝐾)
𝜌 =
∆𝑚
∆𝑉
∆U=∆𝑚 . 𝑔. 𝑦2- ∆𝑚 . 𝑔 . 𝑦1
∆U=𝜌. ∆𝑉. 𝑔. 𝑦2-𝜌. ∆𝑉. 𝑔. 𝑦1
∆U=𝜌. ∆𝑉. 𝑔. (𝑦2-𝑦1)
∆𝑈 (𝑃𝑒𝑟𝑢𝑏𝑎ℎ𝑎𝑛 𝐸𝑛𝑒𝑟𝑔𝑖 𝑃𝑜𝑡𝑒𝑛𝑠𝑖𝑎𝑙)
∆𝐾 (𝑃𝑒𝑟𝑢𝑏𝑎ℎ𝑎𝑛 𝐸𝑛𝑒𝑟𝑔𝑖 𝐾𝑖𝑛𝑒𝑡𝑖𝑘)
∆K=
1
2
. ∆𝑚 . 𝑣2
2
-
1
2
. ∆𝑚. 𝑣1
2
∆K=
1
2
. 𝜌. ∆𝑉. 𝑣2
2
-
1
2
𝜌. ∆𝑉. 𝑣1
2
∆K=
1
2
. 𝜌. ∆𝑉. (𝑣2
2
-𝑣1
2
)
∆U + ∆K=𝜌. ∆𝑉. 𝑔. (𝑦2-𝑦1) +
1
2
. 𝜌. ∆𝑉. (𝑣2
2
-𝑣1
2
)
𝑊𝑡𝑜𝑡𝑎𝑙=𝜌. ∆𝑉. 𝑔. (𝑦2-𝑦1) +
1
2
. 𝜌. ∆𝑉. (𝑣2
2
-𝑣1
2
)
Energi dan Usaha
Gaya dan Usaha
𝑊1 = 𝐹1. ∆𝑥1
𝑊1 = 𝑃1. 𝐴1. ∆𝑥1
𝑊1 = 𝑃1. ∆𝑉
𝑊2 = 𝐹2. ∆𝑥2
𝑊2 = 𝑃2. 𝐴2. ∆𝑥2
𝐹 = 𝑃. 𝐴
𝑊2 = 𝑃2. ∆𝑉
𝑊𝑡𝑜𝑡𝑎𝑙 = 𝑊1 + 𝑊2
𝑊𝑡𝑜𝑡𝑎𝑙 = 𝑃1. ∆𝑉 + 𝑃2. ∆𝑉
𝑊𝑡𝑜𝑡𝑎𝑙 = 𝑃1 + 𝑃2 . ∆𝑉
𝑊𝑡𝑜𝑡𝑎𝑙=𝜌. ∆𝑉. 𝑔. (𝑦2-𝑦1) +
1
2
. 𝜌. ∆𝑉. (𝑣2
2
-𝑣1
2
)𝑊𝑡𝑜𝑡𝑎𝑙 = 𝑃1 + 𝑃2 . ∆𝑉
Energi dan Usaha
Gaya dan Usaha
𝑃1 + 𝑃2 . ∆𝑉=𝜌. ∆𝑉. 𝑔. (𝑦2-𝑦1) +
1
2
. 𝜌. ∆𝑉. (𝑣2
2
-𝑣1
2
)
𝑃1 + 𝑃2 =𝜌. 𝑔. (𝑦2-𝑦1) +
1
2
. 𝜌. (𝑣2
2
-𝑣1
2
)
𝑃1 + 𝜌. 𝑔. 𝑦1 +
1
2
. 𝜌. 𝑣1
2
=𝑃2 + 𝜌. 𝑔. 𝑦2 +
1
2
. 𝜌. 𝑣2
2
P+𝜌. 𝑔. 𝑦 +
1
2
. 𝜌. 𝑣2= konstan
Fluida Bergerak dalam Beda Luasan
Pipa dan Ketinggian
P+𝜌. 𝑔. 𝑦 +
1
2
. 𝜌. 𝑣2
= konstan
P +
1
2
. 𝜌. 𝑣2
= konstan
𝑃1 + 𝜌. 𝑔. 𝑦1 +
1
2
. 𝜌. 𝑣1
2
=𝑃2 + 𝜌. 𝑔. 𝑦2 +
1
2
. 𝜌. 𝑣2
2
𝑦1
𝑦2
∆𝑥1
𝐴2𝐴1
∆𝑥2
y yy
𝐴1
𝐴2
Sayap Pesawat
Mengapa Pesawat Bisa Terbang?
P +
1
2
. 𝜌. 𝑣2= konstan

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Hukum bernoulli

  • 1. Hukum Bernoulli Oleh : Meli (1106550) Rindu Nurani (1204513)
  • 2. Fluida Fluida berbeda dengan zat padat, yaitu tidak dapat menopang tegangan geser (gaya geser terhadap luas). Jadi, fluida berubah bentuk bagaimanapun ruang yang diisinya. Bila sebuah benda tercelup dalam fluida seperti air, fluida mengadakan sebuah gaya tegak lurus permukaan benda di setiap titik pada permukaan benda tersebut.
  • 4. Fluida Bergerak dalam Beda Luasan Pipa dan Ketinggian
  • 5. 𝑦1 𝑦2 ∆𝑥1 𝐴2 𝐴1 ∆𝑥2 ∆𝑚 = 𝜌. ∆𝑉 𝑦1 → 𝑦2 𝑣1 → 𝑣2 ∆𝑡 = 𝑠𝑎𝑚𝑎/𝑘𝑜𝑛𝑠𝑡𝑎𝑛 ∆𝑈 (𝑃𝑒𝑟𝑢𝑏𝑎ℎ𝑎𝑛 𝐸𝑃) ∆𝐾 (𝑃𝑒𝑟𝑢𝑏𝑎ℎ𝑎𝑛 𝐸𝐾) 𝜌 = ∆𝑚 ∆𝑉
  • 6. ∆U=∆𝑚 . 𝑔. 𝑦2- ∆𝑚 . 𝑔 . 𝑦1 ∆U=𝜌. ∆𝑉. 𝑔. 𝑦2-𝜌. ∆𝑉. 𝑔. 𝑦1 ∆U=𝜌. ∆𝑉. 𝑔. (𝑦2-𝑦1) ∆𝑈 (𝑃𝑒𝑟𝑢𝑏𝑎ℎ𝑎𝑛 𝐸𝑛𝑒𝑟𝑔𝑖 𝑃𝑜𝑡𝑒𝑛𝑠𝑖𝑎𝑙) ∆𝐾 (𝑃𝑒𝑟𝑢𝑏𝑎ℎ𝑎𝑛 𝐸𝑛𝑒𝑟𝑔𝑖 𝐾𝑖𝑛𝑒𝑡𝑖𝑘) ∆K= 1 2 . ∆𝑚 . 𝑣2 2 - 1 2 . ∆𝑚. 𝑣1 2 ∆K= 1 2 . 𝜌. ∆𝑉. 𝑣2 2 - 1 2 𝜌. ∆𝑉. 𝑣1 2 ∆K= 1 2 . 𝜌. ∆𝑉. (𝑣2 2 -𝑣1 2 ) ∆U + ∆K=𝜌. ∆𝑉. 𝑔. (𝑦2-𝑦1) + 1 2 . 𝜌. ∆𝑉. (𝑣2 2 -𝑣1 2 ) 𝑊𝑡𝑜𝑡𝑎𝑙=𝜌. ∆𝑉. 𝑔. (𝑦2-𝑦1) + 1 2 . 𝜌. ∆𝑉. (𝑣2 2 -𝑣1 2 ) Energi dan Usaha
  • 7. Gaya dan Usaha 𝑊1 = 𝐹1. ∆𝑥1 𝑊1 = 𝑃1. 𝐴1. ∆𝑥1 𝑊1 = 𝑃1. ∆𝑉 𝑊2 = 𝐹2. ∆𝑥2 𝑊2 = 𝑃2. 𝐴2. ∆𝑥2 𝐹 = 𝑃. 𝐴 𝑊2 = 𝑃2. ∆𝑉 𝑊𝑡𝑜𝑡𝑎𝑙 = 𝑊1 + 𝑊2 𝑊𝑡𝑜𝑡𝑎𝑙 = 𝑃1. ∆𝑉 + 𝑃2. ∆𝑉 𝑊𝑡𝑜𝑡𝑎𝑙 = 𝑃1 + 𝑃2 . ∆𝑉
  • 8. 𝑊𝑡𝑜𝑡𝑎𝑙=𝜌. ∆𝑉. 𝑔. (𝑦2-𝑦1) + 1 2 . 𝜌. ∆𝑉. (𝑣2 2 -𝑣1 2 )𝑊𝑡𝑜𝑡𝑎𝑙 = 𝑃1 + 𝑃2 . ∆𝑉 Energi dan Usaha Gaya dan Usaha 𝑃1 + 𝑃2 . ∆𝑉=𝜌. ∆𝑉. 𝑔. (𝑦2-𝑦1) + 1 2 . 𝜌. ∆𝑉. (𝑣2 2 -𝑣1 2 ) 𝑃1 + 𝑃2 =𝜌. 𝑔. (𝑦2-𝑦1) + 1 2 . 𝜌. (𝑣2 2 -𝑣1 2 ) 𝑃1 + 𝜌. 𝑔. 𝑦1 + 1 2 . 𝜌. 𝑣1 2 =𝑃2 + 𝜌. 𝑔. 𝑦2 + 1 2 . 𝜌. 𝑣2 2 P+𝜌. 𝑔. 𝑦 + 1 2 . 𝜌. 𝑣2= konstan
  • 9. Fluida Bergerak dalam Beda Luasan Pipa dan Ketinggian
  • 10. P+𝜌. 𝑔. 𝑦 + 1 2 . 𝜌. 𝑣2 = konstan P + 1 2 . 𝜌. 𝑣2 = konstan 𝑃1 + 𝜌. 𝑔. 𝑦1 + 1 2 . 𝜌. 𝑣1 2 =𝑃2 + 𝜌. 𝑔. 𝑦2 + 1 2 . 𝜌. 𝑣2 2 𝑦1 𝑦2 ∆𝑥1 𝐴2𝐴1 ∆𝑥2 y yy 𝐴1 𝐴2
  • 12. Mengapa Pesawat Bisa Terbang? P + 1 2 . 𝜌. 𝑣2= konstan