This document discusses aero and hydrodynamic properties relevant to transporting agricultural products using air or water. It covers drag coefficients, terminal velocity, and factors that influence drag such as particle shape, size, orientation, and fluid properties like density and viscosity. Equations are presented for calculating drag and lift forces based on these properties. The drag coefficient and terminal velocity of a particle determine the optimal air velocity for pneumatic separation of mixtures in agricultural applications.

1. AERO & HYDRODYNAMIC
PROPERTIES

2. AERO AND HYDRODYNAMIC PROPERTIES
 In handling and processing of agricultural products often air or water is used as a
carrier for transport or for separating the desirable product from the unwanted
materials.
 The pneumatic separation and conveying has been in use in agricultural machinery
and food processing equipment for many years.
 Use of water however, as a carrier for more economical transport or less injury to
such products as fruits and vegetables, is a relatively new idea in the agricultural
industry.
 DRAG COEFFICIENT AND
 TERMINAL VELOCITY

3.  When particle is immersed in stagnant fluid, buoyant forces (weight of
displaced fluid) act.
 When particle is immersed in fluid in motion, along with buoyant force
other significant forces act. These forces acting are
1) Normal to the surface of the object due to fluid flow,
2) Shear stresses, , acting tangential to the surface in the direction of flow
and resulting from frictional effects.
 The resultant force Fr may be resolved into components
a. FH, the drag and
b. FV, the lift.
Contd…

4.  Resultant force Fr may be resolved into components, Fh, the drag and Fv the lift.
The equations for calculating drag and lift have been derived by dimensional
analysis assuming :
 the smooth object having a projected area, (Ap)
 moving through a fluid of mass density, (ρf)
 viscosity, (μ)
 modulus of elasticity, (E)
 with a velocity , (V)
 Employing the methods of dimensional analysis, the equations to relate fluid and
particle properties have been established for drag and lift where CD and CL are
the (dimensionless) drag coefficient and lift coefficient of the object, respectively.
Fh = f1(Ap, ρf, μ, E,V)
Fv = f2(Ap, ρf, μ, E,V)
Contd…

5.  In most agricultural engineering applications the moving object is usually
free to assume its own random orientation. For this reason the net
resistance force Fr (resultant force) can be given in terms of an overall drag
coefficient C as follows.
where ,
Fr = resistance drag force or weight of particle at terminal velocity, kg
C = overall drag coefficient (dimensionless)
Ap = projected area of the particle normal to direction of motion, m2
ρf = mass density of the fluid, kg.s2 / m4
V = relative velocity between main body of fluid and object, m/s
Contd…

6.  The drag coefficient of the material and its resistance to air flow depend upon,
1. the bed thickness of the material,
2. type, shape and size of grain,
3. the air velocity and
4. orientation and packing of the material.
 This is quantified using Reynolds number (NRe) i.e Ratio of inertia forces To
viscous forces).
{NRe = V(dp)(ρf) /μ}
Contd…

7.  When the flow is laminar, Stokes’ law applies,
For a spherical particle, the drag force may be
approximated by
We have, Cd = 24 / NRe
Contd…

8. Terminal Velocity
 The terminal velocity of a particle may be
defined as the air velocity at which a particle
remains in suspended state in a vertical pipe. In
the condition of free fall, the particle attains a
constant terminal velocity (Vt), when the net
gravitational accelerating force ( Fg), equals the
resisting upward drag force (Fr). If V=Vt, Fg= Fr.
 Fg= Fr, Without Buoyancy
 Fg= Fr +Fb With Buoyancy

9.  In the steady state conditions, after attaining the terminal velocity, if the density of
the particle is greater than the density of the fluid, the particle will move
downward.
 If the density of the particle is lesser than the density of the fluid, the particle will
rise upward.
 If the separation of mixture of grain and foreign matters is to be achieved by air
stream, the terminal velocities of each component of mixture decide the range of air
velocity to be used for a definite extent of separation. .
Contd…

10. THANK YOU