Fluid Mechanics
(18AS33): Video Lectures
Prof. Ashish Kumar Gupta
1
, Incompressible Inviscid Flows
Often the flow over an aircraft or automobile is Aerodynamic force and Moments
complex and 3D in nature. The forces acting on the aircraft or the car are due to the
pressure and shear stress acting on the bodies. To understand few fundamental concepts
related to aerodynamic forces, it is sufficient to consider 2D flows such as flow over
airfoil. Airfoil is a streamlined body which acts as a lifting surface. The pressure force
acts normal to the body while the shear stress is tangential to the body surface as shown
below.
Integrating the pressure and shear forces and
over the airfoil results into a net force R and
moment M. Resolving the force R into normal
force L and parallel to free stream V∞ as D. 2
, Incompressible Inviscid Flows
The component of force perpendicular to free Aerodynamic force and Moments
stream is called lift force while the component parallel to free stream is called drag force.
Chord is defined as the line joining the leading edge and trailing edge of the airfoil.
Trailing edge is the sharp corner while the leading edge is the farthest point from the
trailing edge.
Free stream is defined as the undisturbed flow far ahead of the airfoil.
Angle of attack α, is defined as the angle between the chord and the free stream
direction.
When the forces are resolved perpendicular and parallel to Chord, it is called as N and A.
The lift and drag force can then be obtained as-
where, and N and A are given by
N=∫(p*Cos(θ)ds-τ*Sin(θ)ds) A=∫(p*Sin(θ)ds+τ*Cos(θ)ds)
M= ∫(dN*x+dA*y)= pitching moment
Nose up moment is considered to be +ve.
3
, Incompressible Inviscid Flows
Knowing the lift and drag coefficient, L and D Aerodynamic force and Moments
we can find out the non-dimensional coefficients
CL, CD, CM etc as given below-
q∞=Dynamic Pressure= 0.5*ρV∞2
S= Plan form area
l= Usually mean aerodynamic
chord, c
4
(18AS33): Video Lectures
Prof. Ashish Kumar Gupta
1
, Incompressible Inviscid Flows
Often the flow over an aircraft or automobile is Aerodynamic force and Moments
complex and 3D in nature. The forces acting on the aircraft or the car are due to the
pressure and shear stress acting on the bodies. To understand few fundamental concepts
related to aerodynamic forces, it is sufficient to consider 2D flows such as flow over
airfoil. Airfoil is a streamlined body which acts as a lifting surface. The pressure force
acts normal to the body while the shear stress is tangential to the body surface as shown
below.
Integrating the pressure and shear forces and
over the airfoil results into a net force R and
moment M. Resolving the force R into normal
force L and parallel to free stream V∞ as D. 2
, Incompressible Inviscid Flows
The component of force perpendicular to free Aerodynamic force and Moments
stream is called lift force while the component parallel to free stream is called drag force.
Chord is defined as the line joining the leading edge and trailing edge of the airfoil.
Trailing edge is the sharp corner while the leading edge is the farthest point from the
trailing edge.
Free stream is defined as the undisturbed flow far ahead of the airfoil.
Angle of attack α, is defined as the angle between the chord and the free stream
direction.
When the forces are resolved perpendicular and parallel to Chord, it is called as N and A.
The lift and drag force can then be obtained as-
where, and N and A are given by
N=∫(p*Cos(θ)ds-τ*Sin(θ)ds) A=∫(p*Sin(θ)ds+τ*Cos(θ)ds)
M= ∫(dN*x+dA*y)= pitching moment
Nose up moment is considered to be +ve.
3
, Incompressible Inviscid Flows
Knowing the lift and drag coefficient, L and D Aerodynamic force and Moments
we can find out the non-dimensional coefficients
CL, CD, CM etc as given below-
q∞=Dynamic Pressure= 0.5*ρV∞2
S= Plan form area
l= Usually mean aerodynamic
chord, c
4
