No problem, Mark!
The pressure in a fluid such as water depends on the depth as long
as the water is not moving. Your flood defense system will need to have
additional strength if you expect waves to come crashing into it. I'll
also assume for this calculation that your defense surface is vertical.
In a stationary fluid, the pressure is P=rho*g*h, where rho is the
density of the fluid, g is Newton's gravitational constant, and h is
the depth from the surface. If you really want to be correct, we should
also add on one atmosphere's worth of pressure due to all the air on
top of the water pressing down on it. The reason that's not important
usually is that the same air pressure pushes on the back side of the
flood defense wall and the net force is just from the water.
I'll do this in SI units. The density of water rho is 1000 kg per
cubic meter. g is 9.81 m/s**2, and h is any number from zero to 1.4
meters, depending on how far down the side we are. Call the width (1
meter) W and the total height H (1.4 meters). The force on a piece of
your defense door is the area of the piece times the pressure where the
piece is. We'll think of little strips of height dh, width W, and depth
h. The area of each strip is W*dh, and so the force on the strip is
rho*g*h*W*dh. If we add all these up, we integrate over h, and get
0.5*rho*g*H*H*W (the same as finding the area of a triangle in this
case). Putting in the numbers, that's about 9614 Newtons, or about 2160
pounds.
Tom
(published on 10/22/2007)
