A cubic foot of water weighs 62½ pounds. Take a hollow column with an internal cross-sectional area of one square foot and if it be filled with water to a depth of ten feet there will be a weight of 625 pounds of water in the column and hence a pressure of 625 on the bottom of the tube or 4.34 pounds on every square inch of the bottom. But the water presses on the sides of the tube as well and the amount of this pressure depends upon the depth or “head” of water and not upon the quantity of water. At the bottom of the tube the pressure on the side walls is 625 pounds per square foot or 4.34 pounds per square inch; at a depth of one foot the pressure on the side walls is 62.5 pounds per square foot or .434 pound per square inch; at a depth of two feet it will be .864 pound per square inch, etc. The pressure on each square inch depends not upon the mass of the water but upon its depth. If the column of water had a cross-sectional area of a mile or a thousand miles, the pressure at a depth of one foot would always be .434 pound per square inch. (Of course there are slight variations from this figure due to salt or other substances dissolved in water or to changes in density produced by variations of temperature, but we need not consider such minute differences here.) That is why a dam which is strong enough to hold back the waters of a pond will be just as able to hold back the waters of the whole ocean if it be placed in a sheltered bay where ocean waves cannot tear it to pieces. The ocean, despite its enormous mass, can exert no more pressure per foot of depth than the water in a cistern.
WHY A SHIP FLOATS
It is because the pressure of water at a given depth is exerted upward, as well as laterally and downward, that a ship floats. It is the upward pressure of the water that holds up the boat. When an object is placed in a reservoir of water it sinks into zones of increasing pressure until it finally reaches a depth at which the pressure on the bottom of the object balances the weight of the body. If the body is entirely submerged before reaching such a point, it will continue to sink to the bottom of the reservoir because water will flow over the top of the object and keep adding downward pressure to offset the increasing upward pressure. The amount of water in the reservoir makes no difference. A battleship will float just as high in a flooded dry dock as it will in the open ocean. If the dry dock were so narrow as to leave a clearance of but a few inches of water around the ship, the latter would still float even though the ship weighed considerably more than the water in the dock.
There is a big difference, then, between the weight of water and the pressure it exerts. In Figure 38 we have an L-shaped receptacle with the lower arm of the L terminating in a chamber A. The top wall B of this chamber measures ten square inches. The tube C has a cross sectional area of one square inch. If tube C is filled to a height of twelve inches above wall B we shall have an upward pressure of 0.434 pound on every square inch of wall B, or a total of 4.34 pounds. If by means of a plunger D we add a hundred pounds of pressure to the column of water in tube C, we shall be adding a thousand pounds to the pressure on the wall B. The side walls and bottom of the chamber A will also be subjected to a pressure of 1,000 pounds per inch plus the pressure due to the depth or head of water.
FIG. 38.—DIAGRAM ILLUSTRATING HYDROSTATIC PRESSURE
THE AIR-LOCK OF A PNEUMATIC CAISSON
SUBAQUEOUS TUNNEL, SHOWING THE SHIELD IN THE BACKGROUND