Water pressure increases with depth because the water up above weighs down on the water below. Pressure can be measured in a variety of ways. Water pressure can be easily calculated with a simple equation involving depth, density and gravity.
TL;DR (Too Long; Didn't Read)
The deeper you go into the water, the more water is above you -- and the weight of all that water applies pressure.
Water Pressure and Depth
Water, like all things on Earth, is pulled downward by the force of gravity. Every body of water has a certain weight, and this weight pushes downward on whatever is below it. Water pressure is the result of the weight of all the water above pushing down on the water below. As you go deeper into a body of water, there is more water above, and therefore a greater weight pushing down. This is the reason water pressure increases with depth. The pressure depends only upon the depth, and is the same anywhere at a given depth and in every direction.
Units of Pressure
Pressure is measured in units of force (such as pounds, lb.) divided by area (square inches, in2). Other ways of measuring pressure are also common. An often convenient unit is the atmosphere, atm, equal to the pressure of the atmosphere at sea level. Traditionally, pressure is measured using a barometer, a device in which a column of liquid (mercury, typically) is pushed up by the air pressure outside. Because of this, pressure is often given in units of millimeters of mercury (mm Hg), corresponding to the displacement along the barometer’s column.
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Calculating Water Pressure
The calculation of water pressure is very straightforward. Imagine a flat surface at the depth for which you want to calculate the pressure. All you have to do is find the weight of all the water on top of that surface, then divide it by the area of the surface.
p = W÷ A where p is pressure, W is weight, and A is area.
Finding the Weight of a Body of Water
In a gravitational field, such as on the surface of Earth, everything is accelerated downward by the Earth’s gravity, giving it weight. If you know the mass of an object, you can find the weight by multiplying the mass by the acceleration due to gravity. Remember Newton’s second law: force (weight) equals mass times acceleration (gravity).
You can find the mass, m, of a body of water by multiplying its volume, V, by its density, r.
m = Vr
Now, to find the weight, multiply it by the gravitational acceleration, g (about 9.80 m/s2 at the Earth’s surface).
W = gVr
Putting It All Together
We now have all the pieces to find the water pressure at a certain depth. Substituting our equation for the weight, W, into our original pressure equation, we get:
p = gVr ÷ A
V is the volume of the water above our imagined surface. Remember, volume is just length times width times height. The length times width portion is simply the area, A. The height is the depth, d. So, the volume V can be rewritten as:
V = dA
Substituting this into our pressure equation, we get:
p = gdAr ÷ A
Now we can cancel the A out of the top and bottom to get:
p = gdr
Pressure is equal to the gravitational acceleration, g, times the depth, d, times the density of water, r. The gravitational acceleration is 9.80 m/s^2, and the density of water is 1 g/cm^3, or 1000 kg/m^3. Putting these numbers in, we get a final equation of:
p = d (in meters, m)(9.80 m/s2)(1000 kg/m3)