#### Stokes law equation

## What do you mean by Stokes law?

Stokes Law, named after George Gabriel Stokes, describes the relationship between the frictional force of a sphere moving in a liquid and other quantities (such as particle radius and velocity of the particle). If a sphere or a body moves through a fluid, a friction force must be overcome.

## What are the assumptions of Stokes law?

There are several assumption associated with the Stokes’s Law: The fluid is incompressible. There is no other particle nearby that would affect the flow pattern. The motion of the particle is constant.

## Who discovered Stokes law?

Sir George Gabriel Stokes

## What is Stokes law derive the relation by the method of dimensions?

Suppose that the sphere has radius r and falls through a fluid of viscosity η. Let the terminal velocity be v (Figure 1). We can calculate the viscous drag F on the sphere by dimensional analysis. Solving this gives x = 1, y = 1 and z = 1.

## What is unit of viscosity?

Units for Dynamic Viscosity The most commonly used unit for dynamic viscosity is the CGS unit centipoise (cP), which is equivalent to 0.01 Poise (P). The SI unit for dynamic viscosity η is the Pascal-second (Pa-s), which corresponds to the force (N) per unit area (m^{2}) divided by the rate of shear (s^{–}^{1}).

## What are the SI units of viscosity?

Units. The SI unit of dynamic viscosity is the newton-second per square meter (N·s/m^{2}), also frequently expressed in the equivalent forms pascal-second (Pa·s) and kilogram per meter per second (kg·m^{−}^{1}·s^{−}^{1}). The CGS unit is the poise (P, or g·cm^{−}^{1}·s^{−}^{1} = 0.1 Pa·s), named after Jean Léonard Marie Poiseuille.

## How is viscosity calculated?

There are several formulas and equations to calculate viscosity, the most common of which is Viscosity = (2 x (ball density – liquid density) x g x a^2) ÷ (9 x v), where g = acceleration due to gravity = 9.8 m/s^2, a = radius of ball bearing, and v = velocity of ball bearing through liquid.

## What is Stokes law used for?

Knowing the terminal velocity, the size and density of the sphere, and the density of the liquid, Stokes’ law can be used to calculate the viscosity of the fluid. A series of steel ball bearings of different diameters are normally used in the classic experiment to improve the accuracy of the calculation.

## What are the limitations of Stokes law?

When the solid content of a suspension is high, Stokes’ equation may not show the real sedimentation rate. High solid content imparts additional viscosity to the system, which must be taken into consideration if the correct rate of settling is to be determined. The equation contains only the viscosity of the medium.

## How do I calculate terminal velocity?

In plain English, the terminal velocity of the object is equal to the square root of the quotient of twice the object’s weight over the product of the object’s frontal area, its drag coefficient, and the gas density of the medium through which the object is falling.

## What is terminal velocity in physics?

Terminal velocity, steady speed achieved by an object freely falling through a gas or liquid. An object dropped from rest will increase its speed until it reaches terminal velocity; an object forced to move faster than its terminal velocity will, upon release, slow down to this constant velocity.

## What is critical velocity?

Critical velocity is defined as the speed at which a falling object reaches when both gravity and air resistance are equalized on the object. Turbulent flow is defined as the irregular flow of the fluid with continuous change in magnitude and direction.

## What is the dimension of viscous force?

Coefficient of viscosity (η)= Fr/Av ——- F= tangential Force, Area, r= distance between the layers, v= velocity. Dimensional Formula of Force = M^{1}L^{1}T^{–}^{2}.

## What is meant by Reynolds number?

The Reynolds number is the ratio of inertial forces to viscous forces. The Reynolds number is a dimensionless number used to categorize the fluids systems in which the effect of viscosity is important in controlling the velocities or the flow pattern of a fluid.