Up: No Title Previous: No Title

Example 1: Force on a sphere accelerating (, unsteady) in an unbounded fluid at rest. (at infinity)

K.B.C on sphere:
Solution: Simply a 3D dipole (no stream)

Check:
Hydrodynamic force:

On r = a:

Finally,

General 6 degrees of freedom motions

: associated with force on body in direction due to unit acceleration in direction. For example, for a sphere:

Some added masses of simple 2D geometries
• circle figure

• ellipse figure

• plate figure

• square figure

A reasonable estimate for added mass od a 2D body is to use the displaced mass ( of an equivalent cylinder'' of the same lateral dimension or one that rounds off'' the body. For example, we consider a aquare:
1.
inscribed circle: .

2.
circumscribed circle: .

Arithmetic mean of 1) + 2) .

General 6 degrees of freedom forces and moments on a rigid body moving
in an unbounded fluid ( at rest at infinity)

Note: fixed in the body.

Then (JNN §4.13)
• forces

• moments

Einstein's notation applies.

Note:
1.
if 0 , (as expected by definition of . Also if then for any , no force in steady translation.
2.
added momentum'' due to rotation of axes, 2) where is linear momentum. (momentum from 1 coordinate into new direction)
3.
If .
Moment on a body due to pure steady translation - Munk'' moment.
Example of Munk Moment - a 2D submarine in steady translation