what is terminal velocity Related: Terminal velocity - Mechanical Properties of Fluids

Question

what is terminal velocity Related:  Terminal velocity - Mechanical Properties of Fluids

Answer

Terminal Velocity

Terminal velocity is the maximum velocity of a body moving through a viscous fluid.It is attained when force of resistance of the medium is equal and opposite to the force of gravity.

As the velocity is increasing the retarding force will also increase and a stage will come when the force of gravity becomes equal to resistance force.

After that point velocity won’t increase and this velocity is known as terminal velocity.It is denoted by ‘vt’.Wheret=terminal.

Mathematically:-Terminal velocity is attained when Force of resistance = force due to gravitational attraction.6πηrv =mg6πηrv = densityxVg (Because density=m/V), density=ρ – σ where ρ and σ are the densities of the sphere and the
viscous medium resp.6πηrv = (ρ – σ)x4/3πr3g where Volume of the sphere(V) =4/3πr3By simplifying=(ρ – σ)gx4/3r2x1/(6η)vt =2r2(ρ – σ)g/9 η .This is the terminal velocity. Where(v=vt)

Answer

If  a  particle is moving  inside a liquid then  after  some  time its velocity will become  constant as  net  force will  become  zero  is  called  terminal  velocity

Answer

Terminal Velocity:

Definition:
Terminal velocity is the maximum velocity that an object can attain when falling through a fluid, such as air or water. At terminal velocity, the gravitational force acting on the object is equal to the drag force exerted by the fluid, resulting in a net force of zero and constant velocity.

Explanation:
When an object falls through a fluid, it experiences two main forces: gravity and drag. Initially, as the object starts to fall, the gravitational force is greater than the drag force, causing the object to accelerate. However, as the object's velocity increases, the drag force also increases.

Drag Force:
The drag force exerted by the fluid on the object depends on several factors, including the object's shape, size, and the properties of the fluid. The drag force can be expressed as:

F_d = 0.5 * ρ * A * C_d * v²

Where:
- F_d is the drag force
- ρ is the density of the fluid
- A is the cross-sectional area of the object
- C_d is the drag coefficient
- v is the velocity of the object

Terminal Velocity:
As the object's velocity increases, the drag force eventually becomes equal to the gravitational force. At this point, the net force on the object becomes zero, resulting in a constant velocity. This maximum velocity is known as the terminal velocity.

Factors affecting Terminal Velocity:
Several factors influence the terminal velocity of an object, including:
1. Object's shape and size: Objects with larger surface areas experience greater drag forces, resulting in lower terminal velocities.
2. Fluid properties: The density and viscosity of the fluid affect the magnitude of the drag force and, consequently, the terminal velocity.
3. Gravitational force: The strength of the gravitational force determines the acceleration of the object and, consequently, how quickly it reaches its terminal velocity.

Conclusion:
Terminal velocity is the maximum velocity that an object can attain when falling through a fluid. It occurs when the gravitational force is balanced by the drag force exerted by the fluid. Factors such as the object's shape, size, fluid properties, and gravitational force influence the terminal velocity. Understanding terminal velocity is crucial in various fields, including physics, engineering, and skydiving, as it helps predict the behavior of objects in fluid environments.

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