Pressure Drag: What, How, Working, Formula, Examples:


In this article very interring topic “Pressure drag” is discusses. The cause of the pressure drag is pressure comparison intermediate surface of a matter. Pressure drag related everything is prate here.

Pressure drag derive as, when the molecules of the air being more pushed to each other on the surface of the matter’s front face and space is out more than the usual to the back face of the surface matter. The condition for a matter pressure drag more happened in the air particles for the flow of the turbulent.

What is pressure drag?

The relation between the velocity and pressure drag is directly proportional to each other. For the lower amount of velocity the amount of pressure drag is low and for the higher velocity pressure drag is high.

In a matter when force is acting that time the motion of the matter can stand against that known as pressure drag. When the matter is actually a gaseous matter is known as Air resistance or Aerodynamic drag and as the same time when the matter is actually a liquid matter is known as Hydrodynamic drag.

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Pressure drag
Image – Pressure drag;
Image Credit – Wikimedia Commons

What is air pressure drag?

The main reason of the air pressure drag is size and shape of a matter. In the air pressure drag the layers of the air in not stays one directional due to the force for this reason turbulent flow is appear.

The meaning of the air pressure drag is the particles which are present in the air shoving more in the face of the substance and a huge placed diversion is produce in the back of the substance. Mainly the air pressure drags reason of the division of the border placer from a certain surface.

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How does pressure drag work?

Pressure drag work when the molecules present in the air more compressed on the face of the front plane and not more compressed on the face of the back plane for this reason the layers present in the air molecules being separate to each other and start to swirl, this condition known as turbulent flow.

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How to calculate pressure drag?

The equation of pressure drag state that, pressure drag which denoted as D is equal to the coefficient of drag which denoted as [latex]C_d[/latex] multiplied the fluid density which denoted as r multiplied half of fluid velocity which denoted as V is square multiplied the area of reference which denoted as A.

Pressure drag can be calculate using this formula,

[latex]Pressure drag = Pressure drag coefficient \times \frac{Density\times Velocity squred}{2} \times Reference area[/latex]

Mathematically can written,

[latex]D = C_d \frac{\rho \times v^2}{2}\times A[/latex]

Where,

D = Pressure drag

[latex]C_d[/latex] = Pressure drag coefficient

[latex]\rho[/latex] = Density

 v = Velocity

 A = Reference area

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How to reduce pressure drag?

The zone of the pressure low is appear behind the head, arms, back, and legs of the cyclists. It is very hard to reshape the parts from where the flow of the air is pass for reduce pressure drag.

The pressure drag can reduce in some ways, they are listed below,

  • Apply aero helmet
  • Body should be keep as low as possible
  • Hiding some equipment
  • The body should be keep in align
  • Head should be keep down
  • Double cap
  • Keep the kick tight
  • Point toes
  • Low profile goggles should be wearing
  • Hair should be shaving

How does air pressure affect drag?

The relationship with air pressure and drag is proportional to each other. Means the air pressure is increases then the drag amount is also increases and the air pressure is decreases then the drag amount is also decreases.

Pressure drag coefficient:

For any object which is moves in a motion due to force is applied that time drag is produce.

Pressure drag coefficient is the quantities resistance or drag of a particular matter in an environment which is based on liquid substance when force is exerted. The amount of the net force is act in the direction of the liquid substance flow due to shear stress and pressure on the plane of the particular matter.

Pressure drag coefficient
Image – Drag coefficient;
Image credit – Wikipedia

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Pressures drag coefficient formula:

The formula of the coefficient of pressure drag is given below,

[latex]F_d = c_d \frac{1}{2}\rho v^2A[/latex]

or, [latex]c_d = \frac{2F_d}{\rho u^2A}[/latex]

Where,

[latex]F_d[/latex] = Drag force express in Newton

[latex]c_d[/latex] = Drag coefficient

[latex]\rho[/latex] = Density of a liquid substance express in kilogram per cubic meter

 v = Flow velocity of a liquid substance express in meter per second

A =Reference area for a particular body shape substance expressed in square meter The pressure drag coefficient depend upon some several facts of the parameters such as size and shape of any matter’s body, Flow of the liquid matter which is depend on Reynolds number, Mach number, Froude number and unevenness of the body.

How to calculate drag pressure coefficient?

Drag pressure coefficient can calculated using this formula,

[latex]c_d = \frac{2F_d}{\rho v^2 A}[/latex] …………. eqn(1)

=> [latex]c_d = c_p + c_r[/latex]

=> [latex]c_d = \frac{2}{\rhov^2A}\int_{S}^{}dS (p – p_o)(\hat{n}.\hat{i}) + \frac{2}{\rho v^2A}\int_{S}^{}dS (\hat{t}).\hat{i}T_w[/latex] …………. eqn (2)

In eqn (2),

[latex]c_p = \frac{2}{\rho v^2A}\int_{S}^{}dS (p – p_o)(\hat{n}.\hat{i})[/latex]

[latex]c_r = \frac{2}{\rho v^2A}\int_{S}^{}dS[/latex]

Where,

[latex]c_d[/latex] = Drag pressure coefficient

[latex]F_d[/latex] = Drag force

A = Plan form area for a particular matter body

S = Wet surface for a particular matter body

[latex]c_p[/latex] = Pressure drag coefficient

[latex]c_f[/latex] = Friction drag coefficient

[latex]\hat{n}[/latex] = Perpendicular direction of a matter body which surface is dS. This is denoted the point from the fluid state to solid state

[latex]\hat{t}[/latex] = Denoted the direction where shear stress is exerted on the matter of a body surface dS

[latex]\hat{i}[/latex] = Denoted the direction where vector is exerted in the flow of the stream

p = Pressure acted on the body of the matter at the dS surface

[latex]p_o[/latex] = Far away pressure from the matter at the dS surface

[latex]T_w[/latex] = Magnitude of the shear stress acted on the body of the matter at the dS surface

[latex]\rho[/latex] = Density

v = Viscosity

Pressure drag vs. friction drag:

The compression between pressure drag and friction drag describe below,

ParameterFriction drag  Pressure drag
DefinitionWhen an object is flow in a liquid substance that time friction is appear between the liquid substance surface and the body of the matter and drag is produce. This type of drag is known as friction drag.Pressure drag is produce when the materials of a matter is resolved the force because of pressure is applied normally to the all points of the surface of a matter’s body.
Formula[latex]C_f = \frac{T_w}{\frac{1}{2}\rho _\infty v^2_\infty }[/latex]
Where,
[latex]C_f[/latex] = Skin friction coefficient
[latex]T_w[/latex] = Skin shear stress which is applied in the surface plane of the body
[latex]v_\infty[/latex] = Free stream speed for velocity of the body
[latex]\rho _\infty[/latex] = Free stream speed for density of the body
[latex]{\frac{1}{2}\rho _\infty v^2_\infty } \equiv  q_\infty[/latex] = Free stream dynamic pressure for the body of the matter
[latex]F_d = c_d \frac{1}{2}\rho v^2A[/latex]
or, [latex]c_d = \frac{2F_d}{\rho u^2A}[/latex]
Where,
[latex]F_d[/latex] = Drag force express in Newton
[latex]c_d[/latex] = Drag coefficient
[latex]\rho[/latex] = Density of a liquid substance express in kilogram per cubic meter
v = Flow velocity of a liquid substance express in meter per second
A =Reference area for a particular body shape substance expressed in square meter  
DependentFriction between the surface and the body of the matterSize of the body
Image – Pressure drag and Friction drag;
Image Credit – Wikimedia Commons

Pressure drag vs. skin friction drag:

The compression between pressure drag and skin friction drag describe below,

ParameterSkin friction drag  Pressure drag
DefinitionThe skin friction drag actually is an example of the state of aerodynamic drag. The skin friction drag can prevent force applied of a particular matter which is flowing in a motion in liquid substances.Pressure drag is mainly causes because of increasing pressure in front of a particular object and decreasing pressure in the back portion of the object.
Equation[latex]C_f = \frac{T_w}{q}[/latex]
Where,
[latex]C_f [/latex]= Skin friction coefficient
[latex]T_w [/latex]= Shear stress for the local wall
q = Dynamic pressure for the free stream
[latex]C_f = 2\frac{d\theta }{dx}[/latex]
Now layers of boundary where pressure gradient is not applied in the direction of x that time momentum thickness can be express as,
[latex]C_f = 2\frac{d\theta }{dx}[/latex]
For the particularly turbulent flow the skin friction coefficient can be estimate using following equation,
[latex]C_f,t_u_r = \frac{0.074}{R_e^0^.^2}[/latex]
For the particularly laminar flow the skin friction coefficient can be estimate using following equation,
[latex]C_f,l_a_m = \frac{1.32}{\sqrt{R_e}}[/latex]  
[latex]F_d = c_d \frac{1}{2}\rho v^2A[/latex]
or, [latex]c_d = \frac{2F_d}{\rho u^2A}[/latex]
Where,
[latex]F_d[/latex] = Drag force express in Newton
[latex]c_d[/latex] = Drag coefficient
[latex]\rho[/latex] = Density of a liquid substance express in kilogram per cubic meter
v = Flow velocity of a liquid substance express in meter per second
A =Reference area for a particular body shape substance expressed in square meter  
DependentViscosityShape and size of the matter
RelationshipDirectly proportional to the viscosityDirectly proportional to shape and size of the matter
ExampleMotion of a airplane in air Motion of a matter in liquid substanceAir resistance Riding of a bicyclist Motion of a boat in water
Image – Skin friction drag;
Image Credit – Wikimedia commons

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Pressure drag vs. induced drag:

The compression between pressure drag and induced drag describe below,

ParameterPressure dragInduced drag
DefinitionWhen air molecules are compressed pressure drag produce.The position of the wing drag initiated by or working from the nature of the lift.
Relationship with speedThe relation between airspeed and pressure drag is directly proportional to each other.  The relation between airspeed and induced drag is indirectly proportional each other.  
Factor depend  1. Size and shape of the body of a object
2. Surrounding pressure
3.Motion of the liquid  
1. Size and shape of the body of a object
2. Inclination of a object
3. In the air flow condition of a object  
Image – Induced drag;
Image Credit – Wikipedia

Pressure drag example:

Examples of the pressure drag is listed below,

  1. Airfoil
  2. Hummer H2 SUV
  3. Skydiver
  4. Bicycle
  5. Sphere
  6. Circular flat plate
  7. Honda civic
  8. Dodge ram pickup
  9. Toyota Camry
  10. Object moving in a liquid substance
  11. Speedboat

Indrani Banerjee

Hi..I am Indrani Banerjee. I completed my bachelor's degree in mechanical engineering. I am a enthusiastic person and I am a person who is positive about every aspect of life. I like to read Books and listening to music.

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