This document discusses drag forces on objects immersed in fluids. It defines drag as the force exerted by the fluid in the direction of flow. Total drag has two components - form drag from pressure forces and wall drag from wall shear stresses. Drag coefficient is used to quantify drag and is a function of the Reynolds number. Streamlining aims to reduce drag by eliminating eddies and form drag. Potential and ideal flows are also discussed.

1. CHAPTER 7
Flow past Immersed Bodies

2. Flow Past Immersed bodies
Drag. Force exerted by the fluid on solid in the
direction of flow.
Flow parallel with the plate. Wall shear is there
Flow perpendicular to the plate. Pressure component
is there.

3. Flow parallel with plate

4. Flow perpendicular to the plate

5. Potential flow. Flow of ideal fluids.
Ideal fluids. Incompressible and has zero viscosity.

6. Wall drag and Form drag on immersed objects

7. Total drag= form Drag + wall drag
Form Drag. Total integrated drag from pressure
component
Wall drag. Total integrated drag from wall shear.
Drag Coefficient. It is a dimensionless quantity used
to quantify the drag of an object in fluid environment.
Projected Area of solid Object. Area obtained by
projecting the object on the plane perpendicular to
the direction of flow. Denoted by Ap.
Streamlining. It is the shaping of an object such as an
aircraft body or wing to reduce the amount of drag to
the motion. A perfect streamlined object has no
eddies and little or no form drag.

8. Flow past immersed Sphere

9. For spheres projected area is a circle so
Ap = π/4 Dp2
if FD is total drag, the average drag per unit area is FD/
Ap.
CD = FD/ Ap/ρ U2/2
For a given shape
CD = φ(Rep)
Rep = GoDp/μ

10. Streamlined object: AB, streamline to stagnation
point B

11. Stagnation point.
Applying B.E equation
Ps- Po/ ρ= Uo2/2
Ps is pressure on body at stagnation point
Po is pressure in undisturbed fluid
Uo is the velocity in undisturbed fluid
ρ is density of fluid.
Stagnation Pressure
(Ps/Po) 1-1/γ = Ts/To
Ts is stagnation temperature.
γ ratio of specific heats

12. Effect of Streamlining

13. Void Volume. The volume of the pores or spaces
between the solid particles of bed. Expressed as %age
of total volume occupied by fluid.
Porosity or Void Fraction. Ratio of void volume to the
total volume. 0-1. It is the measure of void(empty)
spaces in the material.
Sphericity. The roundness of 3- dimensional object.
Or it is the measure of how spherical an object is?
Superficial velocity. Velocity of a fluid in a pipe, or
column in the absence of packing or obstruction.