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square foot. Find the total force exerted on a surface 5 ft. by 6 ft. inclined at an angle of 25° to the direction of the wind.

4. Reduce 25'6, 267, and 27.8 inches of mercury to millimetres of mercury.

5. Express a pressure of 100 mm. of mercury in terms of inch of water.

6. Reduce a pressure of 600 millimetres of mercury at 0°C. to dynes per square cm. when the intensity of gravity is 981 cm. per sec. per sec.

7. Express a pressure of 760 mm. of mercury in terms of kilogramme per square metre.

8. Given the density of water as 62.5 lb. per cubic foot, and that 1·025 lb. of sea-water is equivalent in volume to one lb. of pure water. Find the pressure at a depth of 200 feet under the surface of the ocean due to the superincumbent water.

9. If the plunger of a force-pump has a cross-section of 8 square inches, and works 50 feet below the cistern, what pressure is required to force it down?

10. During a storm the barometer at sea-level stood as low as 27 466 inches. What was the pressure in lbs. per square inch?

11. What ought to be the length of a water barometer, inclined to the horizon at an angle of 30°, the mercury barometer standing at 30.5 inches?

12. The diameter of the tube of the barometer is 1 cm., and that of the cistern 4.5 cm. If the mercury in the tube rise through 2.5 cm., find the real alteration in the height of the barometer.

13. What is the theoretical height to which water can be raised by the common pump, when the mercurial barometer stands at 28 inches?

14. A barometer is observed to fall one tenth of an inch when carried up 88 feet of vertical height; how much would it fall if taken 132 yards up a hill rising 1 in 3?

15. A piece of metal of sp. gr. 8, and weighing 20 lbs. is dropped into a cylinder filled with water; find the additional pressure on the base.

16. What depth of water is required to float an iceberg one mile square by 500 feet high?

17. The neck of a wine bottle with flat bottom is 4 inches long, the total height of the bottle being 12 inches. When the bottle is filled with wine of specific gravity 0.99 to within half an inch of its mouth, what is the pressure on each square inch of the bottom?

18. What is the pressure on a sluice-gate 12 feet broad, against which the water rises 5 feet?

19. A sluice-gate is 4 feet broad and 6 feet deep, and the water rises to a height of 5 feet on one side and 2 feet on the other side. Find the pressure

in pounds on the gate.

20. Find the whole pressure upon a vertical dam of a column of water 10 feet deep and 30 feet wide. What would be the pressure of the same head of water against a dam inclined at an angle of 45° to the horizon?

21. A vessel, consisting of a decimetre cube, is filled to one third of its height

with mercury, while the rest is filled with water; determine the whole pressure against one of the sides in kilogrammes.

22. A rectangular board, one foot square, is immersed in water with its upper edge 10 feet below the surface of the water, and horizontal, the surface of the board being vertical. Find the total pressure on one side.

23. If the height of the water barometer be 1,033 centimetres, what will be the pressure on a circular disc whose radius is 7 cm. when sunk in water to a depth of 50 metres?

24. A square plate whose area is 64 square inches is immersed in sea water, its upper edge being horizontal and 12 inches below the surface. Determine the whole pressure of the water on the plate when it is inclined at 45° to the horizon, assuming a cubic inch of sea water to weigh 0'63 ounces.

SECTION XXXII.-PRESSURE OF A GAS.

ART. 154.—Height of Homogeneous Atmosphere. In the case of a vertical column of gas, the density is not uniform throughout. The gas in a horizontal layer is compressed by the weight of the superincumbent gas. It is sometimes convenient to consider what would be the height of a vertical column of gas having the density throughout which it actually has at the bottom, and producing the same pressure at the bottom. The height of such a column is called height of homogeneous atmosphere, because the conception applies to the air of the atmosphere. Prof. Everett suggests the shorter and more appropriate name, "pressure height."*

The pressure of the atmosphere is used as a convenient unit of pressure in the same way as the weight of a pound is used as a convenient unit of force. The exact unit is defined by the following equivalences—

1 atmosphere = 29.922 inches of merc. at 32° F. (British).
760 mm. of merc. at 0° C. (French).

=

ART. 155.-Dependence of Density on Pressure. The law discovered by Boyle states that the density of a portion of gas is

* Units and Physical Constants, p. 37.

proportional to the pressure of the portion, provided that the temperature be kept constant. Hence,

or

k M per VF per S,

k M=F per S by V.

The letter k is used to denote some constant number.

EXAMPLES.

Ex. 1. A litre of air at 0° C. and 760 mm. pressure contains Find the mass of 73 litres at the same temperature,

1.293 gms.

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Ex. 2. A certain quantity of air forms a small spherical bubble of a given radius, when 5 feet below the surface of water; at what depth would the same quantity of air form a bubble of half the given radius, the change of temperature being neglected.

Take the quantity of air as unit of mass M, and the first sphere as unit of volume V. The pressure of the atmosphere is equivalent to 30 feet of water.

1 M=V by (30+5) feet of water,

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Ex. 3. The content of the receiver of an air pump is 6 times that of the barrel. Find the pressure of the air in the receiver at

the end of the 8th stroke of the piston, the atmospheric pressure being 15 lbs. to the square inch.

Take the original mass of air for unit of mass, and the volume of the receiver for unit of volume; then

1 M=V by 15 lb. wt. per sq. inch.

At the end of the operations we have the same volume; hence, 1 M = 15 lb. wt. per sq. inch.

The volume of the barrel is one seventh that of the receiver and barrel conjointly. As the air will always distribute itself with uniform density, one seventh of the mass will be removed by the first double stroke, one seventh of the remainder by the second double stroke, and so on; hence after 8 strokes (1 − )8 M will be left. But

1 M=15 lb. wt. per sq. inch,

... (1–4)8 × 15 lb. wt. per sq. inch.

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1. What is the height of the homogeneous atmosphere, when the mercurial barometer is at 30 inches? The specific gravity of air at that pressure is '00125. 2. In a tube of uniform bore a quantity of air is enclosed. What will be the length of this column of air under a pressure of three atmospheres, and what under a pressure of a third of an atmosphere; its length under the pressure of a single atmosphere being 12 inches?

3. When the height of the mercurial barometer changes from 29.55 inches to 30:33 inches, what is the change in the mass of 1,000 cubic inches of air, assuming that 100 cubic inches of air weigh 31 grains at the former pressure, and that the temperature remains constantly at 0° C.?

4. A cylindrical bell 4 feet deep, whose content is 20 cubic feet, is lowered into water until its top is 14 feet below the surface of the water, and the air is forced

into it until it is three quarters full. What volume would the air occupy under the atmospheric pressure, the water-barometer being at 34 feet?

5. If the water-barometer stand at 33 feet, to what depth must a diving bell be sunk to reduce the contained air to one-third of its original volume, the height of the bell itself being neglected?

6. A diving-bell is lowered into water at a uniform rate, and air is supplied by a force-pump so as to keep the bell full, without allowing any to escape. How must the rate at which the air is supplied be varied as the bell descends?

7. An air-bubble at the bottom of a pond 10 feet deep, has a volume of 0.00006 of a cubic inch. Find what its volume becomes when it just reaches the surface, the barometer standing at 30 inches.

8. A closed indiarubber ball containing air has a volume of 4 cubic inches at a depth of 100 feet below the surface of water, whose density is unity. If the height of the water-barometer be 30 feet, determine the volume of the ball at the surface of the water, assuming the temperature to remain constant?

9. A Mariotte's tube has a uniform section of 1 square inch, and is graduatel in inches; 6 cubic inches are inclosed in the shorter (closed) limb, when the mercury is at the same level in both. What volume of mercury must be poured into the longer limb in order to compress the air into two inches? The barometer stands at 30 inches.

10. Ten cubic centimetres of air are measured off at atmospheric pressure. When introduced into the vacuum of a barometer they depress the mercury which previously stood at 76 centimetres, and occupy a volume of 15 cc. By how much has the mercurial column been depressed?

11. A cylindrical tube, 2 feet long, closed at one end, is lowered down into the sea 200 feet, open end downward like a diving-bell. The atmospheric pressure at the surface being 30 inches of mercury, find how high the water rises in the tube. A column of about 32 feet of sea-water is equal in weight to a similar column of mercury of 30 inches.

12. If the pressure inside the receiver of an air-pump were reduced to of the atmospheric pressure in 4 strokes, to what would it be reduced in 6 strokes?

13. The cylinder of a single-barrelled air-pump has a sectional area of one square inch, and the length of the stroke is 4 inches. The pump is attached to a receiver whose capacity is 36 cubic inches. Compare the pressure of the air inside the cylinder, after 8 complete strokes of the pump, with the pressure before commencing the operation.

14. If the volume of the cylinder of an air-pump be

that of the receiver, find

the density of the air in the latter at the end of the fifth stroke.

15. A receiver attached to an air-pump has the volume of 100 cubic inches, while the cylinder has the volume of 10 cubic inches. What proportion of the original air will be left in the receiver after the completion of the fourth double stroke? 16. If the barrel of the common water-pump be 3 feet long, and the tube, supposed of the same cross-section, be 16 feet long; find how high the water will rise after the first stroke, the water-barometer being at 34 feet.

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