Or, expressed by a formula, _F = Ahd_. In this formula, "F" stands for _the force which a liquid exerts against any surface_, "A" _the area of the surface_, "h," for _the average depth (or height) of the liquid pressing on the surface_, and "d", for _the weight of unit volume of the liquid_. This is the first illustration in this text, of the use of a formula to represent a law. Observe how accurately and concisely the law is expressed by the formula. When the formula is employed, however, we should keep in mind the law expressed by it. We must remember that a liquid presses not only downward and upward but sideways as well, as we see when water spurts out of a hole in the side of a vessel. Experiments have shown that at a point the pressure in a fluid is the same in all directions, hence the rule given above may be applied to the pressure of a liquid against the side of a tank, or boat, or other object, provided we are accurate in determining the _average depth of the liquid_; The following example illustrates the use of the law. _For Example_: If the English system is used, the area of the surface should be expressed in square feet, the depth in feet and the weight of the liquid in pounds per cubic foot. One cubic foot of water weighs 62.4 lbs. Suppose that a box 3 ft. square and 4 ft. deep is full of water. What force will be exerted by the water against the bottom and a side? From the law given above, the force of a liquid against a surface equals the product of the _area_ of the surface, the _depth_ of the liquid and its weight per unit volume, or using the formula, _F = Ahd_. To compute the downward force against the bottom we have the area, 9, depth, 4, and the weight 62.4 lbs. per cubic foot. 9 × 4 × 62.4 lbs. = 2246.4 lbs. To compute the force against a side, the area is 12, the average depth of water on the side is 2, the weight 62.4, 12 × 2 × 62.4 lbs. = 1497.6 lbs. Important Topics 1. Liquids exert pressure; the greater the depth the greater the pressure. 2. Difference between force and pressure. 3. Rules for finding upward and horizontal force exerted by a liquid. _F = Ahd._ 4. Weight, mass, density. Exercises 1. What is the density of water? 2. What force is pressing upward against the bottom of a flat boat, if it is 60 ft. long, 15 ft. wide and sinks to a depth of 2 ft. in the water? What is the weight of the boat? 3. If a loaded ship sinks in the water to an average depth of 20 ft., the area of the bottom being 6000 sq. ft., what is the upward force of the water? What is the weight of the ship? 4. If this ship sinks only 10 ft. when empty, what is the weight of the ship alone? What was the weight of the cargo in Problem 3? 5. What is the liquid force against one side of an aquarium 10 ft. long, 4 ft. deep and full of water?