Bernoulli's Equation

i have given some examples. i think it is
appropriate to explain the principle that explains
how kites fly.
that is, Bernoulli's equation ( a statement of energy conservation
along the streamline of a fluid ).

m*g*h + (1/2) * (d*v^2 )+ p*(Vol1) = m*g*H + (1/2)*(dV^2) + P*(Vol2)

m*g*h and m*g*H represent gravitational potential and are equal so they can be eliminated
so:

(1/2)*(d*v^2) + p*(Vol1) = (1/2) (d*V^2) + P*(Vol2)

(1/2)*(d*v^2)-(1/2)*(d*V^2) = P*(Vol2) - p*(Vol1)

(1/2)*d*(v^2-V^2) = Vol(P-p)

d = density of air
v = initial velocity of air
V = velocity of air after it contacts the kite surface

we are going to assume that the volume of the air remains the same so

Vol = Vol1 = Vol2
p = pressure of air before it reaches the kite surface
P = pressure of air at the kite surface

we are interested in (P-p)

if the surface brings the velocity of air to a completely
perpendicular to the wind surface:
V = 0 -- that is capital V

and

(1/2) (d*v^2)= Vol*(P-p)

or, the difference in pressure DP = (P-p) is proportional to (1/2)(d*v^2)

though there is no complete analytical solution for all
shapes and orientations of surfaces, i am going to
use this equation as a starting point in the
calculations to come.