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is a crucial concept in physics, affecting objects moving through fluids like air or water. It's key in designing cars, planes, and sports equipment. Understanding drag helps engineers optimize shapes for efficiency and performance.

occurs when drag force equals an object's weight, resulting in constant speed. This happens in skydiving and affects falling raindrops. Factors like mass, shape, and fluid density influence terminal velocity, making it a fascinating study in .

Drag Force and Terminal Velocity

Drag force equation components

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Top images from around the web for Drag force equation components

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  • FD=12ρv2CDAF_D = \frac{1}{2} \rho v^2 C_D A represents the
    • FDF_D stands for the drag force experienced by an object moving through a fluid
    • ρ\rho represents the density of the fluid the object is moving through (air, water)
    • vv denotes the velocity of the object relative to the fluid it is moving through
    • CDC_D is the determined by the object's shape and surface characteristics (smoothness, roughness)
    • AA represents the of the object perpendicular to the direction of fluid flow ()

Real-world applications of drag

  • Automotive design
    • car shapes minimize drag force leading to improved fuel efficiency (sedans, sports cars)
    • Spoilers and features manipulate drag to enhance vehicle stability (racing cars, high-performance vehicles)
  • Aerospace engineering
    • Aircraft wings designed to minimize drag while generating lift for efficient flight (commercial airliners, fighter jets)
    • Drag reduction crucial for improving aircraft performance and fuel efficiency (helicopters, drones)
  • Sports
    • Drag affects the motion and trajectory of balls (golf balls, tennis balls)
    • Athletes' clothing and equipment designed to minimize drag for improved performance (swimsuits, cycling helmets)
  • Fluid dynamics
    • Drag force is a key factor in the design of fluid systems (pipelines, valves)
    • Understanding drag is essential for optimizing the flow of liquids and gases (oil pipelines, ventilation systems)
    • The helps characterize flow behavior and predict drag in different fluid systems

Terminal velocity conditions

  • Terminal velocity is the constant speed reached by an object falling through a fluid when the drag force equals the object's weight
    • At terminal velocity, the net force on the object is zero and acceleration stops (, parachuting)
  • Conditions leading to terminal velocity:
    1. The object must be falling through a fluid (air, water)
    2. The drag force must increase with the object's speed until it balances the object's weight
    3. Sufficient time must pass for the object to reach the point where the forces are balanced (skydiving, falling raindrops)

Calculating terminal velocity

  • The is derived from the drag force equation by setting FDF_D equal to the object's weight, mgmg:
    • mg=12ρvt2CDAmg = \frac{1}{2} \rho v_t^2 C_D A
    • Solving for vtv_t (terminal velocity): vt=2mgρCDAv_t = \sqrt{\frac{2mg}{\rho C_D A}}
  • Factors affecting terminal velocity:
    • Mass (mm): Objects with greater mass have higher terminal velocities (bowling ball vs. feather)
    • Drag coefficient (CDC_D): Objects with lower drag coefficients have higher terminal velocities (streamlined vs. blunt shapes)
    • Cross-sectional area (AA): Objects with smaller cross-sectional areas have higher terminal velocities (skydiver in a dive vs. spread-eagle position)
    • Fluid density (ρ\rho): Objects falling through denser fluids have lower terminal velocities (water vs. air)
  • Example calculation: Determine the terminal velocity of a skydiver with a mass of 75 kg, a drag coefficient of 1.0, and a cross-sectional area of 0.7 m^2, falling through air with a density of 1.225 kg/m^3
    • vt=2(75kg)(9.81m/s2)(1.225kg/m3)(1.0)(0.7m2)≈53m/sv_t = \sqrt{\frac{2(75 kg)(9.81 m/s^2)}{(1.225 kg/m^3)(1.0)(0.7 m^2)}} \approx 53 m/s

Types of Drag and Flow Characteristics

  • : Resistance caused by the shape of an object disrupting fluid flow
  • : Resistance due to fluid viscosity interacting with the object's surface
  • Flow regimes:
    • : Smooth, predictable fluid motion typically occurring at lower velocities
    • : Chaotic, irregular fluid motion often occurring at higher velocities
  • The is the thin region of fluid near an object's surface where viscous effects are significant

Key Terms to Review (18)

Aerodynamic: Aerodynamics is the study of the motion of air and other gases and their effects on solid bodies in motion. It is a crucial concept in understanding the forces that act on objects as they move through the air, particularly in the context of drag forces.
Boundary Layer: The boundary layer is a thin layer of fluid that forms along the surface of an object moving through a fluid, such as air or water. It is characterized by a gradual transition in velocity and other properties between the object's surface and the free stream of the surrounding fluid.
Cross-Sectional Area: The cross-sectional area of an object or flow is the area of the object or flow perpendicular to the direction of motion or flow. It is a crucial parameter in understanding the behavior of objects moving through fluids or the flow of fluids through pipes and channels.
Drag Coefficient: The drag coefficient is a dimensionless quantity that is used to quantify the drag or resistance force experienced by an object moving through a fluid, such as air or water. It is a measure of an object's aerodynamic or hydrodynamic properties and is a crucial factor in determining the motion of an object in a viscous fluid.
Drag force: Drag force is a resistive force experienced by an object moving through a fluid (such as air or water). It acts opposite to the direction of the object's motion and depends on factors like velocity, fluid density, and cross-sectional area.
Drag Force Equation: The drag force equation, also known as the drag equation, is a fundamental formula used to calculate the drag force acting on an object moving through a fluid, such as air or water. This equation is a crucial tool in the study of fluid dynamics and aerodynamics.
Fluid dynamics: Fluid dynamics is the branch of physics that studies the behavior of fluids (liquids and gases) in motion. It examines how forces affect the flow and movement of these substances, encompassing concepts like pressure, velocity, and viscosity, which are crucial in understanding phenomena in both natural and engineered systems.
Form Drag: Form drag is a type of aerodynamic drag that occurs due to the shape or geometry of an object moving through a fluid, such as air or water. It arises from the pressure differences between the front and back of the object, which create a net force opposing the object's motion.
Free Fall: Free fall is the motion of an object where gravity is the only force acting upon it, leading to uniform acceleration towards the center of a gravitational field. This concept is crucial for understanding how objects behave when they are dropped or thrown, as it allows for the application of motion equations to describe their motion under constant acceleration.
Frontal Area: Frontal area refers to the cross-sectional area of an object that is perpendicular to the direction of motion or airflow. It is a crucial parameter in determining the drag force experienced by an object moving through a fluid, such as air or water.
Laminar Flow: Laminar flow is a type of fluid flow where the fluid travels in smooth, parallel layers with no disruption between the layers. It is characterized by a high degree of order and predictability in the fluid's movement.
Reynolds number: Reynolds number is a dimensionless quantity used to predict the flow regime in fluid dynamics. It indicates whether flow will be laminar or turbulent based on the ratio of inertial forces to viscous forces.
Skin Friction Drag: Skin friction drag is a type of aerodynamic drag force that arises due to the viscous interaction between a moving object and the surrounding fluid. It is a key component of the overall drag experienced by objects moving through fluids, such as air or water.
Stokes’ law: Stokes' law describes the drag force experienced by spherical objects moving through a viscous fluid. The formula for Stokes' law is $F_d = 6 \pi \eta r v$, where $F_d$ is the drag force, $\eta$ is the dynamic viscosity of the fluid, $r$ is the radius of the sphere, and $v$ is its velocity.
Streamlined: Streamlining refers to the process of designing an object, such as a vehicle or structure, to reduce drag and improve efficiency by minimizing air resistance and turbulence. This concept is particularly important in the context of drag forces, as streamlining can significantly impact the overall performance and energy consumption of a system.
Terminal Velocity: Terminal velocity is the maximum speed an object can reach while falling through a fluid, such as air or water, under the influence of gravity. It is the point at which the drag force acting on the object exactly balances the force of gravity, resulting in a constant velocity of descent.
Terminal Velocity Equation: The terminal velocity equation describes the maximum velocity an object can reach when falling through a fluid, such as air or water. It represents the point at which the drag force acting on the object equals the gravitational force, resulting in a constant velocity.
Turbulent Flow: Turbulent flow is a type of fluid flow characterized by chaotic and unpredictable fluctuations in the velocity and pressure of the fluid. This is in contrast to laminar flow, where the fluid moves in smooth, parallel layers. Turbulent flow is an important concept in understanding various physical phenomena, including drag forces, pressures in the body, flow rate, and the motion of objects in viscous fluids.
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Glossary
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5.3 Elasticity: Stress and Strain