Welcome to Physics Forums.anooop said:Homework Statement
Derive an expression for frictional force
acting on a spherical objects of radius R
moving with velocity V
in a continuous viscous fluid of fluid's viscosity η .
Homework Equations
please do not use dimension analysis to prove.
The Attempt at a Solution
Then I suggest you look through your lecture notes and textbooks. You will not be spoon fed answers here. However, if you are willing to put some effort in, we are more than happy to help you.anooop said:Apart from "Mechanics of Continuous Media",i have good understanding of other undergraduate physics topics as well.
I do not have enough time to go through the whole of fluid dynamics.
i want to know only 3 things in Mechanics of Continuous Media fo my exam.
(a) proof of stokes's law,poiseuille equation,elastic constants and their inter-relation.
please help with these topics.
Stokes' law is a physical law that describes the relationship between the frictional force acting on a small spherical object moving through a fluid at a constant velocity and the fluid's viscosity and the size and velocity of the object.
Stokes' law states that the frictional force acting on a particle in a fluid is directly proportional to the particle's velocity and the fluid's viscosity, and inversely proportional to the particle's radius. It also states that the frictional force must be equal and opposite to the force of gravity acting on the particle for it to move at a constant velocity.
Stokes' law is important in fluid dynamics because it helps us understand and predict the behavior of small particles in a fluid, such as in sedimentation or the motion of microscopic organisms. It also provides a way to measure the viscosity of a fluid.
According to Stokes' law, the frictional force acting on an object is directly proportional to its size and shape, specifically its radius. This means that smaller and more streamlined objects will experience less frictional force compared to larger and more irregularly shaped objects.
Stokes' law is most accurate for low Reynolds number fluids, which are fluids with slow-moving particles. It is commonly used for liquids, such as water and oil, but can also be applied to gases at low velocities. For high Reynolds number fluids, other equations, such as the Navier-Stokes equation, are more appropriate.