Physics Part 26

16. How heavy a cake of ice can be dragged over a floor by a horizontal force of 20 lbs., if the coefficient of friction is 0.06?

17. The coefficient of friction of iron on iron is 0.2. What force can a switch engine weighing 20 tons exert before slipping?

18. Using a system of pulleys with a double movable block a man weighing 200 lbs. is just able to lift 600 lbs. What is the efficiency of the system?

19. What is the horse-power of a pump that can pump out a cellar full of water 40 ft. 20 ft. by 10 ft. deep, in 30 minutes?

20. How many tons of coal can a 5 horse-power hoisting engine raise in 30 minutes from a barge to the coal pockets, a height of 50 ft.?

(7) WATER POWER

=136. Energy of Falling Water.=--The energy of falling and running water has been used from the earliest times for developing power and running machinery. The energy is derived from the action of the moving water in striking and turning some form of _water-wheel_, several varieties of which are described below.

=The Overshot Wheel.=--The overshot wheel (Fig. 112) is turned by the weight of the water in the buckets. It was formerly much used in the hilly and mountainous sections of this country for running sawmills and grist mills as it is very easily made and requires only a small amount of water. Its efficiency is high, being from 80 to 90 per cent., the loss being due to friction and spilling of water from the buckets. To secure this high efficiency the overshot wheel must have a diameter equal to the height of the fall which may be as much as 80 or 90 ft.

[Ill.u.s.tration: FIG. 112.--Overshot water wheel.]

[Ill.u.s.tration: FIG. 113.--Undershot water wheel.]

[Ill.u.s.tration: FIG. 114.--Diagram ill.u.s.trating the principle of the Pelton wheel.]

=The Undershot Wheel.=--The old style undershot wheel (Fig. 113) is used in level countries, where there is little fall, often to raise water for irrigation. Its efficiency is very low, seldom rising more than 25 per cent. The principle of the undershot wheel, however, is extensively used in the water motor and the Pelton wheel (Fig. 114). In these the water is delivered from a nozzle in a jet against the lower buckets of the wheel. They have an efficiency of about 80 per cent. and are much used in cities for running small machines, washing machines, pipe organ blowers, etc., and in mountainous districts where the head is great.

[Ill.u.s.tration: FIG. 115.--Diagram of a hydro-electric power house showing a vertical turbine _A_ with penstock _B_ and tail race _C_.]

[Ill.u.s.tration: FIG. 116.--The outer case of a turbine showing the mechanism for controlling the gates.]

[Ill.u.s.tration: FIG. 117.--Inner case of a turbine showing the gates and the lower end of the runner within.]

[Ill.u.s.tration: FIG. 118.--The runner of a turbine.]

[Ill.u.s.tration: FIG. 119.--Turbine and generator of the Tacoma hydro-electric power plant.]

=137. The Turbine.=--The turbine is now used more than any other form of water-wheel. It was invented in 1827 by De Fourneyron in France. It can be used with a small or large amount of water, the power depending on the head (the height of the water, in the reservoir above the wheel). It is the most efficient type of water-wheel, efficiencies of 90 per cent.

often being obtained. The wheel is entirely under water (Fig. 115). It is enclosed in an outer case (Fig. 116) which is connected with the reservoir by a penstock or pipe and is always kept full of water. The wheel itself is made in two parts, a rotating part called the runner (see Fig. 118) and an inner case (Fig. 117) with gates that regulate the amount of water entering the wheel. This case has blades curved so that the water can strike the curved blades of the rotating part (Fig.

118) at the angle that is best adapted to use the energy of the water.

The water then drops through the central opening into the tail race below (see Fig. 115). The energy available is the product of the weight of the water and the head. The turbine is extensively used to furnish power for generating electricity at places where there is a sufficient fall of water. The electrical energy thus developed is transmitted from 50 to 200 miles to cities where it is used in running street cars, electric lighting, etc. Turbines can be made to revolve about either vertical or horizontal axes. Fig. 119 represents a _horizontal_ water turbine connected to a dynamo. Compare this with the _vertical_ turbine in Fig. 115.

Exercises

1. Does a person do more work when he goes up a flight of stairs in 5 seconds than when he goes up in 15 seconds? Explain.

2. A motorcycle has a 4 horse-power motor and can go at a rate of 50 miles per hour. Why cannot 4 horses draw it as fast?

3. What is the efficiency of a motor that is running fast but doing no useful work?

4. What horse-power can be had from a waterfall, 12 ft. high, if 20 cu.

ft. of water pa.s.s over it each second?

5. What is the horse-power of a fire engine if it can throw 600 gallons of water a minute to a height of 100 ft.?

6. Why are undershot wheels less efficient than the overshot wheel or turbine?

7. A revolving electric fan is placed on the stern of a boat. Does the boat move? Why? Place the fan under water. Does the boat now move? Why?

8. Why does an electric fan produce a breeze?

9. Explain the action of the bellows in an organ.

10. At Niagara Falls the turbines are 136 ft. below the surface of the river. Their average horse-power is 5000 each. 430 cu. ft. of water each second pa.s.s through each turbine. Find the efficiency.

11. At Laxey on the Isle of Man is the largest overshot wheel now in use. It has a horse-power of 150, a diameter of 72.5 ft., a width of 10 ft., and an efficiency of 85 per cent. How many cubic feet of water pa.s.s over it each second?

12. The power plant at the Pikes Peak Hydro-electric Company utilizes a head of 2150 ft., which is equal to a pressure of 935 lbs. per square inch, to run a Pelton wheel. If the area of the nozzle is 1 sq. in. and the jet has a velocity of 22,300 ft. per minute, what is the horse-power developed if the efficiency is 80 per cent.?

13. A test made in 1909 of the turbines at the Centerville power house of the California Gas and Electric Corporation showed a maximum horse-power of 9700, speed 400 r.p.m. under a head of 550 ft. The efficiency was 86.25 per cent. How many cubic feet of water pa.s.sed through the turbines each second?

14. The turbine in the City of Tacoma Power Plant (see Fig. 120) uses a head of 415 ft. 145 cu. ft. a second pa.s.s through the turbine. Calculate the horse-power.

15. In problem 14, what is the water pressure per square inch at the turbine?

16. The power plant mentioned in problem 13 develops 6000 kw. What is the efficiency?

Review Outline: Work and Energy

Work; how measured, units, foot-pound, kilogram meter, erg.

Energy; how measured, units, potential, _P.E._ = _w h_, or _f s_.

Kinetic = _(wv)/(2g)_.

Power; how measured, units, horse power, watt, 5 forms of energy, conservation. H.p. = (lbs. ft.)/(550 sec.).

Machines; 6 simple forms, 2 groups, advantages, uses, Law: _W D_{w}_ = _F D_{f}_.

Lever; moments, mechanical advantage, uses and applications.

Wheel and Axle and Pulley; common applications, mechanical advantage.

Inclined Plane, Wedge, and Screw; mechanical advantage and efficiency.

Friction; uses, how reduced, coefficient of, laws (3).

Water Wheels; types, efficiency, uses.