Air resistance formula

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Air resistance formula
Air resistance formula | Image: Learnool

Air resistance formula, also known as the drag force formula, calculates the force experienced by an object moving through a fluid medium, such as air. It is represented by the equation FD = ½ × ρ A CD v2, where FD is the drag force, ρ is the density of the fluid, A is the cross-sectional area of the object, CD is the drag coefficient, and v is the velocity of the object.

Practice problems

Problem #1

Calculate the air resistance force acting on a feather that is falling with a velocity of 8 m/s. Given the density of the air as 1.20 kg/m3, the cross-sectional area of the feather as 0.02 m2, and the drag coefficient as 0.05.

Solution

Given data:

  • Air resistance force acting on a feather, FD = ?
  • Velocity of a feather, v = 8 m/s
  • Density of the air, ρ = 1.20 kg/m3
  • Cross sectional area of a feather, A = 0.02 m2
  • Drag coefficient, CD = 0.05

Applying the formula:

  • FD = ½ × ρ A CD v2
  • FD = ½ × 1.20 × 0.02 × 0.05 × (8)2
  • FD = 0.03 N

Therefore, the air resistance force acting on a feather is 0.03 N.

Problem #2

When a skydiver jumps from a plane, the skydiver falls with a velocity of 45 m/s. Determine the air resistance force acting on the skydiver, considering the density of the air as 1.25 kg/m3, the cross-sectional area of the skydiver as 0.20 m2, and the drag coefficient as 0.70.

Solution

Given data:

  • Velocity of a skydiver, v = 45 m/s
  • Air resistance force acting on a skydiver, FD = ?
  • Density of the air, ρ = 1.25 kg/m3
  • Cross sectional area of a skydiver, A = 0.20 m2
  • Drag coefficient, CD = 0.70

Applying the formula:

  • FD = ½ × ρ A CD v2
  • FD = ½ × 1.25 × 0.20 × 0.70 × (45)2
  • FD = 177.18 N

Therefore, the air resistance force acting on a skydiver is 177.18 N.

Problem #3

A leaf is descending from a certain height with a velocity of 10 m/s while floating in the air. Find the air resistance force acting on the leaf, taking into account the density of the air as 1.22 kg/m3, the cross-sectional area of the leaf as 0.05 m2, and the drag coefficient as 0.08.

Solution

Given data:

  • Velocity of a leaf, v = 10 m/s
  • Air resistance force acting on a leaf, FD = ?
  • Density of the air, ρ = 1.22 kg/m3
  • Cross sectional area of a leaf, A = 0.05 m2
  • Drag coefficient, CD = 0.08

Applying the formula:

  • FD = ½ × ρ A CD v2
  • FD = ½ × 1.22 × 0.05 × 0.08 × (10)2
  • FD = 0.24 N

Therefore, the air resistance force acting on a leaf is 0.13 N.

Problem #4

Find the value of the air resistance force acting on a parachute bag that is falling with a velocity of 30 m/s after being thrown from a helicopter. Given the density of the air as 1.21 kg/m3, the cross-sectional area of the parachute bag as 0.10 m2, and the drag coefficient as 0.12.

Solution

Given data:

  • Air resistance force acting on a parachute bag, FD = ?
  • Velocity of a parachute bag, v = 30 m/s
  • Density of the air, ρ = 1.21 kg/m3
  • Cross sectional area of a parachute bag, A = 0.10 m2
  • Drag coefficient, CD = 0.12

Applying the formula:

  • FD = ½ × ρ A CD v2
  • FD = ½ × 1.21 × 0.10 × 0.12 × (30)2
  • FD = 6.53 N

Therefore, the air resistance force acting on a parachute bag is 6.53 N.

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Deep

Learnool.com was founded by Deep Rana, who is a mechanical engineer by profession and a blogger by passion. He has a good conceptual knowledge on different educational topics and he provides the same on this website. He loves to learn something new everyday and believes that the best utilization of free time is developing a new skill.

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