Name: terminal velocity in a viscous fluid
Uploaded: 2025-05-22T09:06:09.000Z
Duration: 1 min 20 s
Channel: JoVE

Bir sıvının içinde hareket eden bir cismi düşünün. Nesnenin yakınındaki sıvı katmanları onunla birlikte sürüklenir ve bağıl hıza maruz kalır, bu da nesne üzerinde viskoz bir kuvvete neden olur. Viskoz kuvvet, nesnenin şekline, boyutuna, hızına ve sıvı özelliklerine bağlıdır. 
Bir sıvının içinde hareket eden küresel bir cisim için viskoz kuvvet, kürenin yarıçapı, hızı ve sıvı viskozitesi ile orantılıdır.
Denklemi boyutsal olarak çözmek, viskoz kuvvetin bu parametrelere bağımlılığını verir. Elde edilen ifade, viskoz kuvvetin cismin hızıyla doğru orantılı olduğunu gösteren Stokes yasasıdır.
Bir küre bir sıvının içinden düşürülürse, cismin ağırlığı onu aşağı doğru çekerken, viskoz ve kaldırma kuvvetleri yukarı doğru hareket eder.
İvmeye bağlı olarak hız arttıkça viskoz kuvvet artar. Viskoz kuvvet ağırlığı ve kaldırma kuvvetini dengelediğinde, küre terminal hız adı verilen sabit bir hızla düşer.
Yüksek viskoziteli bir sıvı için terminal hız deneysel olarak ölçülebilir. Daha sonra Stokes yasası kullanılarak viskozite elde edilebilir.

<ol>
	<li>Verma, H.C. (2008). Fizik kavramları. Cilt 1, Bharati Bhawan Pub. & Dis.: bölüm 14.17, 14.18; sayfa 291–292.</li>
</ol>

stokes yasası

Stokes' Law

Viskoz kuvvetler, sürtünme gibi moleküllerin birbirine göre olan göreceli hareketine direnen atomlararası kuvvetlerdir. Bir katı cisim bir sıvıdan geçerken, viskoz kuvvetler onu ters yönde sürükler. Bu kuvvetin büyüklüğü, katının şekline, boyutuna, hızına ve sıvının viskozite katsayısına, yoğunluğuna ve sıcaklığına bağlıdır.

Bir sıvı içindeki katı bir küresel nesne üzerindeki kuvvetin ifadesine Stokes yasası denir. Stokes yasası yalnızca düşük Reynolds sayısı sıvıları için geçerlidir, yani sıvı akışı yalnızca düzgün ve hareketli olmadığında uygulanır. Katı nesne üzerindeki kuvvet, nesnenin yarıçapı ve hızı ile birlikte sıvının viskozite katsayısına bağlı olarak deneysel olarak bulunur. Her bir değişkenin bağımlılık düzeni boyut analizi yoluyla elde edilebilir. Orantı sabiti deneysel olarak elde edilir.

Bir sıvı içindeki bir küresel katının hareketi, Newton'un ikinci hareket yasası kullanılarak analiz edilebilir. İlk olarak, katı hareketsiz olduğunda viskoz drag yoktur. Aşağı doğru etkiyen net kuvvet, ağırlık farkı ve sıvının yüzer kuvvetiyle verilir ve hızını artırır. Ancak, hız arttıkça, viskoz drag artar. Büyük bir yukarı doğru viskoz drag olduğunda, aşağı yönlü ağırlık, yukarı doğru kaldırma kuvveti ve yukarı doğru viskoz drag kuvveti birbirini dengelediğinden net bir kuvvet oluşmaz. Katı nihayetinde terminal hız denilen sabit bir hıza ulaşır.

Stokes Yasası

Viskoz kuvvetler, sürtünme gibi, moleküllerin birbirleri üzerindeki bağıl hareketine direnen moleküller arası kuvvetlerdir. Katı bir cisim bir ...

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Education

JoVE Core

Physics

Fizik

Unit 1

Ünite 1

Fluid Mechanics

Akışkanlar Mekaniği

KEY TERMS AND CONCEPTS

TEMEL TERİMLER VE KAVRAMLAR

terminal velocity in a viscous fluid

Viscous forces act like friction in a liquid. They resist the relative motion of molecules and pull back on a solid body moving through the fluid. The size of this force depends on the body’s shape and size, its speed, and the liquid’s viscosity, density, and temperature.

For a spherical solid object, the force in a fluid is described by Stokes’ law. This law applies only at low Reynolds number, when the flow is laminar and not turbulent. Experiments show that the force is proportional to the sphere’s radius, its speed, and the liquid’s viscosity coefficient. Dimensional analysis helps determine how these variables depend on one another, while the proportionality constant is found experimentally.

A sphere moving through a liquid can also be studied with Newton’s second law. At first, the sphere has no viscous drag because it is at rest. The downward net force, which comes from the difference between its weight and the liquid’s buoyant force, makes it speed up.

As the speed increases, the viscous drag also increases. Eventually, the upward viscous drag becomes large enough to balance the downward weight and the upward buoyant force. When these three forces balance, there is no net force, and the sphere continues at a steady speed called terminal velocity.

Terminal Velocity in a Viscous Fluid

characteristics of fluids

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density

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pascal's law

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application of pascal's law

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viscosity

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stokes' law

Viscous forces act like friction in a liquid. They resist the relative motion of molecules and pull back on a solid body moving through the fluid. The size of this force depends on the body’s shape and size, its speed, and the liquid’s viscosity, density, and temperature. For a spherical solid object, the force in a fluid is described by Stokes’ law. This law applies only at low Reynolds number, when the flow is laminar and not turbulent. Experiments show that the force is proportional to the...

key terms and concepts

Learn how viscous drag, buoyancy, and weight act on a sphere in a liquid, and how Stokes’ law leads to terminal velocity in low Reynolds number flow.

Terminal Velocity in a Viscous Fluid | JoVE K12

physics

JoVE Temel Fizik, kinematik, dinamik, akışkanlar mekaniği, statik, dalgalar ve akustik dahil olmak üzere temel fizik konularının teorisini ve uygulamasını kısa ve anlaşılması kolay animasyonlu videolarla tanıtıyor. Ek olarak, sektör içindeki bilim insanı videoları, dünya çapındaki günümüz laboratuvarlarında gerçekleştirilen klasik ve orijinal araştırma deneylerinde ilgili kavramların uygulanmasını göstermektedir.

Terminal Velocity in a Viscous Fluid

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