Terminal Velocity

Terminal velocity refers to the speed achieved by a freely falling object cutting through the fluids like water and air. It happens when the whole additional sum of the drag force (F d) and the buoyancy equals the falling force of gravity where the acceleration is zero and the net force acting on the object is zero.

The terminal velocity formula is used to calculate the terminal velocity as well as the acceleration due to gravity and height if any two of these quantities are known. And terminal velocity is computed in metres per second, i.e. ms-1.

Terminal Velocity Meaning

The falling body attains the uniform limiting velocity when the resistance of the air has become equal to the force of gravity.

In other words, we can say the maximum velocity attained by the body is called terminal velocity.

Terminal Velocity Speed

These are some examples of the terminal velocity:

 Terminal Velocity Formula

In terms of mathematics used in physics, the terminal speed can be calculated by following without considering the buoyancy of the fluid:

Terminal Velocity Formula Is: vt= √2mgρAcd

Here,

●  Vt represents terminal velocity

●  m represents the mass of the falling object

●  g represents the acceleration due to gravitation

● Cd represents the drag coefficient

●  p represents the density of the fluid through which the object is falling down

●  A represents the projected area of the object

If a real-life situation is considered, the object approaches its velocity asymptotically.

The effect of buoyancy on the object can be taken into effect by using the Archimedes principle.

The terminal speed of an object can change due to the following:

1.      properties of the fluid

2.      the mass of the object

3.      Its cross-sectional area

As we know, air density always increases with decreasing altitude, at about 1% for every 80 metres. Objects are falling, cutting through the atmosphere; for every 160 metres of fall, the terminal speed always decreases by about 1%. After reaching the local terminal velocity, speed decreases to adjust with the local terminal speed while still falling.

Terminal Velocity In The Presence Of Buoyancy Force

The buoyancy force is taken into consideration if the object falls into the fluid. If the object falls into the fluid by its own net weight attains its terminal velocity (settling velocity) when the net force acting on the object becomes zero.

If the upward buoyancy force and drag force are exactly balanced by the object’s weight where the terminal velocity is reached.

W=Fb+D (equation-1)

where

• W  is the weight of the object

• Fb is the buoyancy force acting on the object, and

• D is the drag force acting on the object.

If the spherical object falls in the fluid, three forces will act in it. The three equations are given below

W=Π/6d³sg (equation 2)

Fb=Π/6d³ρg (equation 3)

D= Cd^1/2V²A (equation 4)

where

• d  is the diameter of the spherical object

• g is the gravitational acceleration

•  is the density of the fluid

• s is the density of the object

• A≤A= 1 / 4 πd²  is the projected area of the sphere

• Cd is the drag coefficient, and

• V is the characteristic velocity (taken as terminal velocity, Vt).

Substitute equations 2,3,4 in equation 1 and solve the equation to get the terminal velocity Vt

Vt=√4gd3Cds-ρ (equation 5)

Equation 1 represents the objects falling in the denser liquid. If the object doesn’t fall in the denser liquid, the drag force should be made negative as the object moves upwards against gravity. Some examples: bubbles formed at the bottom of the  champagne  bottle and helium balloons where terminal velocity will be negative as it is against gravity.

Drag Force

Similar to friction, the drag force tends to always oppose the motion of an object in which it is falling. The drag force is always proportional to the function of the velocity of the object in the given fluid. This functionality always tends to depend on the shape, size, and velocity of the object and the fluid. For large objects like cyclists, cars, and baseballs not moving too slow, the magnitude of the drag force FDFD is always proportional to the square of the speed of the object.

We can express it mathematically by the following:

FD∝v²

Keeping check of the other factors, this could be expressed as

FD=1/2 CρAv²

Here C is expressed as the drag coefficient, A is the area of the object in the fluid, and ρ refers to the density of the fluid.

This equation can also be written more broadly as FD=bv², where b is a constant equivalent to 0.5CρA.

Conclusion

We have discussed the terminal velocity definition and formula. We also covered drag force; the terminal speed of an object can change due to the property of the fluid, mass, and cross-sectional area.