“Drag and Lift Force in Fluid Mechanics”

In our daily life we can feel drag when you walk in a swimming pool, water pulls us and a fisherman feels the drag on his lure as he pulls it through the water. In the Aerodynamics an airplane flies there is also concept of drag and lift force is use while designing the parts of airplane. Kites can fly because of the forces acting on the parts of the kite these force nothing other than drag and lift force. Though kites come in many shapes and sizes, the forces which act on a kite are the same for all kites. In this blog we are going to see what is drag and lift force and how it is acting on the body.

Fig.1.Fisherman feels the drag on his lure as he pulls it through the water

Fig.2. Drag force acting on body during swimming

Fluid Drag and Lift Force-

Fluid flow over solid bodies frequently occurs in practice, and it is responsible for numerous physical phenomena such as the drag force acting on automobiles, power lines, trees, and underwater pipelines and the lift force developed by airplane wings.

Drag and Lift force -

• A body meets some resistance when it is forced to move through a fluid, especially a liquid.
• Any object immersed in a viscous fluid flow experiences a net force R from the shear stresses and pressure differences caused by the fluid motion.
• A body meets some resistance when it is forced to move through a fluid, especially a liquid.

Fig.3. Drag and Lift on body

• The net force R acting on body is resolved into a component D in flow direction U and the component L in a direction normal to U as shown Fig.1
• Drag force D is defined as the resistive force acting on an immersed body in the direction of flow.
• Lift force L is defined as a lifting force acting on an immersed body perpendicular to the direction of flow and it is the component of the pressure(PdA) and wall shear forces (TdA) in the direction normal to the flow tend to move the body in that direction.

The pressure and shear forces on a two-dimensional body and the resultant lift and drag forces by resolving component of pressure and shear force.

• Addition of horizontal component in the direction of drag force gives us resultant drag force (FD) acting on the body.

Resultant Drag Force

• Addition of vertical component in the direction of lift force perpendicular to drag force gives us resultant drag force (FL) acting on the body.

Resultant Lift Force

• If we have to find net force then we have to do integration of resultant force over the area.

Drag Equation and Lift Equation –

1. Drag Equation -In fluid dynamics, the drag equation is a formula used to calculate the force of drag experienced by an object due to movement through a fully enclosing fluid. The equation is ,

Equation of Drag Force

Where,

FD = Drag force

Cd=Coefficient of drag

ρ =Mass density of fluid

V= Flow speed of the object relative to the fluid

A= Frontal area.

• This drag equation derived to within a multiplicative constant by the method of dimensional analysis. If a moving fluid meets an object, it exerts a force on the object. Suppose that the fluid is a liquid, and the variables involved under some conditions such as velocity of fluid U, density of fluid ρ, kinematic viscosity of fluid V, frontal area A, drag force FD.

2. Lift Equation -In fluid dynamics, the drag equation is a formula used to calculate the force of drag experienced by an object due to movement through a fully enclosing fluid. The equation is ,

Equation of Lift Force

Where,

FL = Lift force

Cd=Coefficient of drag

ρ =Mass density of fluid

V= Flow speed of the object relative to the fluid

A= Frontal area.

• This lift equation also derived same as that of drag equation by using dimensional analysis under same condition.

Drag coefficient and Lift Coefficient-

• The drag and lift forces depend on the density of the fluid, the upstream velocity, and the size, shape, and orientation of the body. It is more convenient to work with appropriate dimensionless numbers that represent the drag and lift characteristics of the body
• These numbers are the drag coefficient CD, and the lift coefficient CL.

Coefficient of Drag(CD) and Coefficient of lift (CL)

Application of Lift and Drag force-

We all know that gravity is a force that pulls everything towards the Earth’s surface. This pull is called the weight force. Planes and birds have to be able to provide enough lift force to oppose the weight force. Lift is caused by the variation in air pressure when air flows under and over an airplane’s wings. It acts upwards against weight and must be greater in order for the aircraft to fly.

Propulsion –Thrust and drag

The power source of a bird or plane provides the thrust. Thrust is the force that moves the object forward. Thrust is provided by:

• Muscles — for birds and other flying animals
• Engines — for flying machines
• Gravity — for gliders that actually fly by always diving at a very shallow angle (birds do this too when they glide).

Roll of drag and lift force during the playing of birds

How Birds Fly-Birds and Biomechanics

Fig.4.Drag and Lift Force Acting on Bird’s body

The four forces of flight are weight, lift, drag and thrust. These forces affect all flying things, including birds and kites! A force is a push or pull acting upon an object. Forces can help with flight, or make flight more difficult. Lift and Thrust are the forces that help flying things get off of the ground. Lift is a push upward and Thrust is a push forward. Birds get lift and thrust from flapping their wings and taking advantage of wind in a similar way to kites. The other forces of flight acting on objects are Weight and Drag. These forces pull objects down toward the ground (weight) and backward from the direction of flight (drag). In order for something to fly, its Lift and Thrust must be stronger than its Weight and Drag

The force working against thrust is called drag. It is caused by air resistance and acts in the opposite direction to the motion. The amount of drag depends on the shape of the object, the density of the air and the speed of the object. Thrust can overcome or counteract the force of drag.

An object in flight is constantly engaging in a tug of war between the opposing forces of lift, weight (gravity), thrust and drag. Flight depends on these forces whether the lift force is greater than the weight force and whether thrust is greater than drag (friction) forces.

Lift and drag are considered aerodynamic forces because they exist due to the movement of an object (such as a plane) through the air. The weight pulls down on the plane opposing the lift created by air flowing over the wing. Thrust is generated by the propeller (engine) and opposes drag caused by air resistance. During take-off, thrust must counteract drag and lift must counteract the weight before the plane can become airborne.

How it works?

If a plane or bird flies straight at a constant speed:

• lift force upwards = weight force downwards (so the plane/bird stays at a constant height)
• thrust force forwards = opposing force of drag (so the plane/bird stays at a constant speed)

If the forces are not equal or balanced, the object will speed up, slow down or change direction towards the greatest force.

If the forces are not equal or balanced, the object will speed up, slow down or change direction towards the greatest force.

Fig.5.Force Acting on Airplane

For example, if a plane’s engine produces more thrust, it will accelerate. The acceleration increases air speed past the wing, which increases lift so the plane gains altitude. Then, because the plane is moving faster, drag (air resistance) is increased, which slows the plane from speeding up as quickly until thrust and drag are equal again. The plane can now remain at a constant but greater height.
A plane can lose altitude by reducing thrust. Drag becomes greater than thrust and the plane slows down. This reduces lift and the plane descends.

Airplane wings are designed to take advantage of lift. They are shaped so that air has to travel farther over the top of the wing than underneath it. The reason for this is explained in Bernoulli’s Principle, which states that an increase in the velocity (speed) of air or any fluid results in a decrease in pressure. When the air has to travel farther over the top of the airplane wing, it must also travel faster, which results in lower pressure. The shorter distance under the wings results in higher pressure, causing the airplane to move upward.

Fig.6.Lift vs Relative Wind

​You can demonstrate Bernoulli’s Principle with a piece of notebook paper. Fold the paper in half the short way, so that you have a tent shape. Now, set the tent on a table and blow very carefully (slow and firm) through one of the open ends. The sides of the tent will stick together but the tent won’t collapse. This occurs because the velocity of your breath is more than that of the air outside of the tent, causing lower pressure. The air outside the tent has higher pressure and pushes the sides of the tent inward.

Bernoulli’s Principle

Ground Effect -

• Reduction of induced drag during takeoffs and landings
• Up-wash and Down-wash decrease
• Down-wash can hit the ground and pushes the wing from below, forming what feels like a cushion
• Causes floating if a fast approach is flown
• Increases lift while decreasing drag (induced), thrust required

Contributors:-

1. Advait Kondra
2. Satyam Kshirsagar
3. Kshitij Pargaonkar
4. Kanhaiya Kuche
5. Sohan Kulal