194. Find the horse-power of a 10 in. by 12 in. steam engine running 250 R. P. M. with a M. E. P. of 60 lb.

195. What will be the horse-power of a single cylinder, four cycle gas engine with the following data:

Size of cylinder, 12 in. by 16 in.

Rev. per minute, 225

Mean effective pressure, 78 lb. per square inch?

Number of working strokes of the number of revolutions.

196. A body can do as much work in descending as is required to raise it. Knowing this fact, calculate the horse-power that could be developed by a water-power which discharges 800 cu. ft. of water per second from a height of 13.6 ft., assuming that 25% of the theoretical power is lost in the wheel and in friction.

197. What would be the brake horse-power of a steam engine which exerted a net pressure of 100 lb. on the scales, at a radius of 4 ft., when running at 250 R. P. M.?

198. How many foot-pounds of work per hour would be obtained from a 60 H. P. engine?

199. A centrifugal pump is designed to pump 3000 gallons of water per minute to a height of 70 ft. If the efficiency of the pump is 60%, what horse-power will be required to drive it?

200. The pump of problem 199 is to run 1500 R. P. M. and is to be beltdriven from a 48 in. pulley on a high speed automatic engine, running 275 R. P. M. What should be the diameter and width of face of the pulley on the pump, if the pulley is to be 1 in. wider than the belt?

CHAPTER XVIII

MECHANICS OF FLUIDS

115. Fluids. Nearly every shop of any size contains some devices which are operated by water or air pressure, so every upto-date mechanic should have a knowledge of how these machines work.

A Fluid is any substance which has no particular form, but always shapes itself to the vessel which contains it. Water, oil, air, steam, gas-all are fluids. In some ways water, oil, and similar substances are different from the lighter substances―air, steam, etc. To separate these, we give the name of Liquids to such substances as water and oil; while air, steam, etc., are given the general name of Gases. In some respects liquids and gases are alike and in others they are different. The chief difference is that liquids have definite volumes; they cannot be compressed or expanded any visible amount, while gases can be readily compressed or expanded to almost any extent. For all practical purposes we can say that liquids cannot be compressed. The third form of matter-Solids-needs no explanation. The differences in these three forms can be stated as follows:

A Solid has a definite shape and volume.

A Liquid has no definite shape, but has a definite volume. A Gas has neither a definite shape nor volume.

There are some substances that exist in states in between the solid and the liquid form. Among these are tar, glue, putty, gelatine, etc.

116. Specific Gravity.-By Specific Gravity of a substance we mean its relative weight as compared with the same volume of water. Thus we say that the specific gravity of cast iron is 7.21, meaning that cast iron is 7.21 times as heavy as water. A cubic foot of water weighs 62.4 lb. and a cubic foot of cast iron weighs about 450 lb. The quotient 450 -7.21 is the specific gravity of the iron.

62.4

In many hand books we find tables of specific gravities and, when we wish to get the actual weight per cubic inch or per cubic

foot of some substance, we must multiply the weight of the unit of water by the specific gravity of the substance.

Example:

The specific gravity of alcohol is .8. How many pounds would there be to a gallon of alcohol?

One gallon of water =83 lb.

One gallon of alcohol=.8×8}=6} lb., Answer.

If a substance has a specific gravity less than 1, it will float in water, because it is lighter than the same volume of water. If the specific gravity is greater than 1, the substance is heavier than water and will sink. A substance that will float in water may sink in some other liquid if it has a greater specific gravity than the liquid in question. For example, a piece of apple-wood will float in water but will sink when placed in gasoline, the specific gravity of the wood being about .76 and that of gasoline about .71. A piece of iron will sink in water but will float when placed in mercury (quick silver), the specific gravity of mercury being 13.6 and that of iron about 7.21.

117. Transmission of Pressure Through Fluids.-One of the most useful properties of all fluids is the ability to transmit

W

FIG. 73.

pressure in all directions. If we have a vessel filled with water, as shown in Fig. 73, and apply a pressure to the water by means of a piston, as shown, this pressure will be transmitted through the water in all directions. If the sides of the vessel are flat, they will bulge out, showing that there is a pressure on the sides; and if the piston is loose, the water will escape upward around it, showing that there is a pressure in this direction also.

If the total force on the piston is W lb. and the area on the bottom of the piston is A sq. in., then there will be a pressure W

of lb. exerted on each square inch of the water beneath the A piston. This pressure will be transmitted equally in all directions and the pressure on each square inch of the top, sides, and bottom of the vessel will be

Example:

W

lb.

A

If the piston of Fig. 73 is 6 in. in diameter, and has a total weight of 1000 lb., what would be the water pressure per square inch?

W

1000

Ρ

=

A .7854×62

1000

28.27

Explanation: As the piston rests on the water, the pressure of the water on the bottom of the piston must be sufficient to =35.4 lb. per sq. in., Answer. support the weight. The area of the bottom is 28.27 sq. in.,

1000 28.27

and the pressure on each sq. in. will be or 35.4 lb. persquare inch. This pressure is transmitted throughout the water and is exerted by it with equal force in all directions.

118. The Hydraulic Jack.-This property of water of transmitting pressure in any direction is made use of in many ways. The same property is, of course, common to other fluids such as

P

W

FIG. 74.

oil, air, etc. Wherever we find a powerful, slow-moving force required in a shop, we usually find some hydraulic machine. (The word "hydraulic" refers to the use of water but it is often applied to machines using any liquid-water, oil, or alcohol.) Fig. 74 shows the principle of all these hydraulic machines.

A small force P is exerted on a small piston and this produces a certain pressure in the water. This pressure is transmitted to the larger cylinder where the same pressure per square inch is exerted on the under side of the large piston. If the large piston has 100 times the area of the small piston, the weight supported (W) will be 100 times P. If the water pressure produced by P is 100 lb. per square inch and the large piston has an area of 100 sq. in., then the weight W that can be raised will be 10,000 lb.

Like the lever, the jackscrew, and the pulley, this increase in force is obtained only by a decrease in the distance the weight is moved. The work done on the small piston is theoretically the same as the work obtained from the large piston. For example, suppose that the large piston has 100 times the area of the small one and we shove the small piston down 1 in.; the water that is thus pushed out of the small cylinder will have to spread out over the entire area of the large piston; the large piston will, therefore, be raised only one one-hundredth of the distance that the small piston was moved. Thus, we have, here also, an application of the law that the work put into a machine is equal, neglecting friction, to the work done by it.

Force X distance moved = weight distance raised.

The Mechanical Advantage of such a machine will be seen to be the ratio of the areas of the pistons. In the case just mentioned, the ratio of the areas of the pistons was 100:1; hence, the mechanical advantage was 100.

In Fig. 74, the motion that can be given to W is very limited, but by using a pump with valves, instead of the simple plunger P, we can continue to force water into the large cylinder and thus secure a considerable motion to W.

Fig. 75 shows a common form of hydraulic jack which operates on this principle. The top part contains a reservoir for the liquid, and also has a small pump operated by a hand lever on the outside of the jack. By working the lever, the liquid is pumped into the lower part of the jack between the plunger and the casing, thus raising the load. The load may be lowered by slacking the lowering screw Y. This opens a passage to the reservoir, and the load on the jack forces the liquid to flow back through this passage to the reservoir.

In calculating the mechanical advantage of a hydraulic jack, we must consider the mechanical advantage of the lever which