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I found this http://web.mit.edu/2.972/www/reports/hydrofoil/hydrofoil.html on MIT webisite.

There are two explanation for how it works:

1. The conservation of linear momentum or Newton's third law.If water is pushed down, the water pushes back on the hydrofoil.

http://web.mit.edu/2.972/www/reports/hydrofoil/hydrofoil-1.gif

For the change for momentum of water, their is a equal but opposite change in momentum of the hydrofoil, directed upward.

2. Bernoulli'principles: $$P_o=P+1/2dv^2+dgy$$

$P_o$ is called the stagnation of pressure and is a constant. P is pressure. d is density. v is velocity of fluid. and g is gravitational acceleration. So if v increases on top, the top pressure will decreases, and as v of fluid decreases on the bottom, the pressure with increase. The hydrofoil then starts to rise when the bottom pressure overcomes the top pressure. It rises till there is no water on top.

**QUESTION**

1. Why the velocity of fluid on top is greater than that of the fluid on bottom? The link says "this is due in part to viscous effects which lead to formation of vertices at the end of foil." But I am not sure what those "effect" and "vertices" are.

2. What keeps the top velocity increasing, and the bottom velocity decreasing?

I guess it's this enlarging difference in velocities that produces larger and larger pressure difference, and thus larger net force.