Question

what is stokes law and velocity gradient

Answer 1

Stokes' law defines the drag force that exists between a sphere moving through a fluid with constant velocity. Viscosity is the resistance of a fluid to flow, and with increasing viscosity, the sphere's velocity drops.

for gradient it is just rate of change (with respect to distance here) And here is the definition. The difference in velocity between adjacent layers of the fluid is known as a velocity gradient and is given by v/x, where v is the velocity difference and x is the distance between the layers.

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Answer 2

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✒ Stokes Law

• Stokes’s law, mathematical equation that expresses the settling velocities of small spherical particles in a fluid medium.
• The law, first set forth by the British scientist Sir George G. Stokes in 1851, is derived by consideration of the forces.
• Acting on a particular particle as it sinks through a liquid column under the influence of gravity.
• The force acting in resistance to the fall is equal to 6πrηv, in which r is the radius of the sphere, η is the viscosity of the liquid, and v is the velocity of fall.
• The force acting downward is equal to 4/3πr3 (d1 - d2)g, in which d1 is the density of the sphere, d2 is the density of the liquid, and g is the gravitational constant.

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✒ Velocity Gradient

• The difference in velocity between adjacent layers of the fluid is known as a velocity gradient and is given by v/x, where v is the velocity difference and x is the distance between the layers.
• To keep one layer of fluid moving at a greater velocity than the adjacent layer, a force F is necessary.
• Resulting in a shearing stress F/A, where A is the area of the surface in contact with the layer being moved.
• In the same way if we are talking about gradient that means how the physical quantity varies with distance.
• For example : potential gradient gives you Vector field.

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