6. What is the liquid force on one side of a liter cube full of water?

Full of alcohol? Full of mercury? What force is pressing on the bottom in each case?

7. What depth of water will produce a pressure of 1 g. per square centimeter? 10 g. per square centimeter? 1000 g. per square centimeter?

8. What depth of water will produce a pressure of 1 lb. per square inch?

10 lbs. per square inch? 100 lbs. per square inch?

9. What will be the force against a vertical dam-breast 30 meters long, the depth of the water being 10 meters?

10. A trap door with an area of 100 sq. dcm. is set in the bottom of a tank containing water 5 meters deep. What force does the water exert against the trap door?

11. What is the force on the bottom of a conical tank, filled with water, the bottom of which is 3 meters in diameter, the depth 1.5 meters?

12. If alcohol, density 0.8 were used in problem 11, what would be the force? What would be the depth of alcohol to have the same force on the bottom as in problem 11?

13. What is the pressure in pounds per square inch at a depth of 1 mile in sea water, density 1.026 grams per cc.?

14. Find the force on the sides and bottom of a rectangular cistern filled with water, 20 ft. long, 10 ft. wide, and 10 ft. deep?

15. Find the force on the bottom of a water tank 14 ft. in diameter when the water is 15 ft. deep, when full of water.

16. Find the force on one side of a cistern 8 ft. deep and 10 ft.

square, when full of water.

17. Find the force on a vertical dam 300 ft. long and 10 ft. high, when full of water.

18. Find the pressure at the bottom of the dam in question 17.

19. Why are dams made thicker at the bottom than at the top?

20. A ship draws 26 ft. of water, _i.e._, its keel is 26 ft. under water. What is the liquid force against a square foot surface of the keel? Find the pressure on the bottom.

(2) TRANSMISSION OF LIQUID PRESSURE

=40. Pascal's Principle.=--Liquids exert pressure not only due to their own weight, but when confined, may be made to transmit pressure to considerable distances. This is a matter of common knowledge wherever a system of waterworks with connections to houses is found, as in cities.

The transmission of liquid pressure has a number of important applications. The principle underlying each of these was first discovered by Pascal, a French scientist of the seventeenth century.

Pascal's Principle, as it is called, may be ill.u.s.trated as follows:

Suppose a vessel of the shape shown in Fig. 18, the upper part of which we may a.s.sume has an area of 1 sq. cm., is filled with water up to the level _AB_. A pressure will be exerted upon each square centimeter of area depending upon the depth. Suppose that the height of _AB_ above _CD_ is 10 cm., then the force upon 1 sq. cm.

of _CD_ is 10 g., or if the area of _CD_ is 16 sq. cm., it receives a force of 160 g.

[Ill.u.s.tration: FIG. 18.--The force increases with the depth.]

If now a cubic centimeter of water be poured upon _AB_ it will raise the level 1 cm., or the head of water exerting pressure upon _CD_ becomes 11 cm., or the total force in _CD_ is 1611 g., _i.e._, each square centimeter of _CD_ receives an additional force of 1 g. _Hence the force exerted on a unit area at_ _AB_ _is transmitted to every unit area within the vessel._

The usual form in which this law is expressed is as follows: _Pressure applied to any part of a confined liquid is transmitted unchanged, in all directions, and adds the same force to all equal surfaces in contact with the liquid_.

[Ill.u.s.tration: FIG. 19.--The force is proportional to the area.]

The importance of this principle, as Pascal himself pointed out, lies in the fact that by its aid we are able to exert a great force upon a large area by applying a small force upon a small area of a confined liquid, both areas being in contact with the same liquid. Thus in Fig. 19 if the area of the surface _CD_ is 2000 times the area of the surface _AB_, then 1 lb. applied to the liquid on _AB_ will exert or sustain a force of 2000 lbs. on _CD_.

=41. Hydraulic Press.=--An important application of Pascal's principle is the _hydraulic press_. See Fig. 20. It is used for many purposes where great force is required, as in pressing paper or cloth, extracting oil from seeds, lifting heavy objects, etc. Many high school pupils have been seated in a _hydraulic chair_ used by a dentist or barber. This chair is a modified hydraulic press.

[Ill.u.s.tration: FIG. 20.--Cross-section of a hydraulic press.]

The hydraulic press contains two movable pistons, _P_ and _p_ (see Fig.

20). The larger of these, _P_, has a cross-sectional area that may be 100 or 1000 times that of the smaller. The smaller one is moved up and down by a lever; on each upstroke, liquid is drawn in from a reservoir, while each down-stroke forces some of the liquid into the s.p.a.ce about the large piston. Valves at _V_ and _V'_ prevent the return of the liquid. If the area of _P_ is 1,000 times that of _p_, then the force exerted by _P_ is 1000 times the force employed in moving _p_. On the other hand, since the liquid moved by the small piston is distributed over the area of the large one, the latter will move only 1/1000 as far as does the small piston. The relation between the motions of the two pistons and the forces exerted by them may be stated concisely as follows: The _motions_ of the two _pistons_ of the hydraulic press are inversely proportional to the forces exerted by them. The _cross-sectional areas_ of the two pistons are, on the other hand, directly proportional to the forces exerted by them.

An application of Pascal's principle often employed in cities is the hydraulic elevator. In this device a long plunger or piston extends downward from the elevator car into a cylinder sunk into the earth, sometimes to a depth of 300 ft. Water forced into this cylinder pushes the piston upward and when the water is released from the cylinder the piston descends.

Fig. 21 represents another form of hydraulic elevator, where the cylinder and piston are at one side of the elevator shaft. In this type, to raise the elevator, water is admitted to the cylinder pushing the piston downward.

=42. Artesian Wells.=--Sometimes a porous stratum containing water in the earth's crust is inclined. Then if there are impervious strata (see Fig. 22), both above and below the water-bearing one, and the latter comes to the surface so that rain may fill it, a well sunk to the water-bearing stratum at a point where it is below the surface will usually give an artesian well, that is, one in which the water rises to or above the surface. Many are found in the United States.

[Ill.u.s.tration: FIG. 21.--A hydraulic freight elevator.]

[Ill.u.s.tration: FIG. 22.--Conditions producing an artesian well.]

[Ill.u.s.tration: FIG. 23.--A standpipe.]

=43. Standpipes and Air Cushions.=--Many who have lived in cities where water is pumped into houses under pressure know that the water pressure is changed when several faucets are opened at the same time. Again, if several persons are using a hose for sprinkling, the pressure may be lessened so as to be insufficient to force the water above the first floor. In order to allow for these changes some flexibility or spring must be introduced somewhere into the water-pipe system. Water is nearly incompressible and if no means were employed to take care of the pressure changes, the sudden stopping and starting of the flow would cause serious jars and start leaks in the pipes. Two common devices for controlling sudden changes in the water pressure are the _standpipe_ and the _air cushion_.

The _standpipe_ is simply a large vertical tube connected to the water mains from which and into which water readily flows. When many faucets are opened the water lowers; when most faucets are closed the water rises, giving a simple automatic control of the surplus water and a supply of water for a short time during a shut-down of the pumps. Standpipes are often used in towns and small cities. Fig. 23 represents the standpipe at Jerome, Idaho.

The _air cushion_ (Fig. 24) is a metal pipe or dome filled with air attached to a water pipe where sudden changes in pressure are to be controlled. At many faucets in a city water system such an air cushion is employed. It contains air; this, unlike water, is easily compressible and the confined air when the tap is suddenly closed receives and checks gradually the rush of water in the pipe. Even with an air cushion, the "pound" of the water in the pipe when a tap is suddenly closed is often heard. If air cushions were not provided, the "water hammer" would frequently crack or break the pipes.

[Ill.u.s.tration: FIG. 24.--The short pipe above the faucet contains air forming an air cushion.]

Important Topics

1. Pascal's law.

2. Hydraulic press.

3. Artesian wells.

4. Standpipes and air cushions.

Exercises

1. Where have you _seen_ an air cushion? Describe it and its use.

2. Where have you _seen_ an hydraulic press? Why and how used?

3. Where have you _seen_ hydraulic elevators? What moves them?