"Goofball_star_dot_etal" wrote in message
...
On Mon, 18 Dec 2006 11:41:53 -0700, "Gilligan"
wrote:

Frictional resistance varies as the wetted surface area.
ok

Frictional resistance varies with the square of speed.

ok (force)

Power to overcome skin friction (speed x force) varies with the cube
of speed.


The speed will change as of the square root of wetted surface area change.


Not "for a fixed power input"

V=(P/k * A)^1/3
V speed, P power k a constant

For small increases in area, the decrease in speed will be a third. 3%
increase in area will give 3/3 = 1% decrease in speed.

k is a drag coefficient and A is wetted surface area?

If so then and P is constant:

dV/dA = .333*P/k*A^(-2/3)

Simplifying:

dV/dA ~ 1/(A^0.6)

If A is very large then dV/dA ~ 0

If A = 1 then dV/dA = A

If A1 then dV/dA ~ large

Since in real units (ft^2, meter^2) A is not near unity, lets throw out that
case. Also toss A=1 for same reason. In reality then A1. If so then:

dV/dA = 1/(A^0.6) * some constant. The curve approaches zero for A large.

The speed will change as the 2/3 power of wetted surface area rather than
the square root (1/2 power).