Fluid Pressure.-At a depth & below the surface a heavy liquid of density p the pressure is

neglecting atmospheric pressure.

When g, p, and are all expressed in the C.G. system, denotes the pressure in dynes per square cen metre; if the factor g be omitted, p will represent t pressure in grammes weight per square centimet What we have here called pressure is really intensity pressure, or pressure per unit area; and the pressure a surface of area a is P = pa, if the intensity of th pressure over the surface is uniform.

Taking into account the pressure due to the atmo phere, the pressure at a depth z is

where II denotes the atmospheric pressure on unit are of the surface of the liquid.

29. Find the pressure due to a column of mercury metre high.

Here z=100, p=13.6, and taking g=981, we have

31. Find the pressure due to a column of water I metre in depth. Express your result (1) in grammes weight per square centimetre, and (2) in dynes per square centimetre.

32. Calculate the total pressure (in grammes weight) upon the base of a cylindrical vessel one decimetre in diameter, filled with mercury to a height of 40 centi

metres.

33. What must be the height of a column of mercury to exert a pressure of 1 kilogramme per square centimetre?

34. The specific gravity of sea-water is 1.025; calculate the pressure in grammes weight per square centimetre at a depth of 40 metres below the surface of the sea.

35. Mercury is poured into a vessel until the layer is Io centimetres deep, and then water is added until the depth of the water-column is 75 centimetres: determine the pressure on the base in dynes per square centi

metre.

36. What must be the height of a column of water in order that the pressure at its base may be a megadyne (106 dynes) per square centimetre?

37. Find the equivalent in dynes per square centimetre of a 'pressure of 1000 kilogrammes weight per square metre.

38. Determine the pressure in grammes weight exerted upon a horizontal area of 2 square decimetres sunk to a depth of 75 centimetres below the surface of oil of specific gravity 0.85.

39. If the inch be the unit of length, and the second the unit of time, what must be the density of the standard substance in order that the equation p=gpz may give the pressure in pounds weight?

40. Express in pounds weight per square foot the pressure at the bottom of a lake 300 feet deep.

per square inch) in a laboratory which is supplied fro a tank at a height of 40 feet.

42. To what depth must a surface be sunk in wat in order that the pressure upon it may be 60 pounds p square inch?

43. If a cubic foot of sea-water weighs 64 pounds, wh is the pressure at a depth of a mile under the surface the sea?

44. If the atmospheric pressure be 15 pounds p square inch, what is the pressure at the bottom of pond 30 feet deep?

45. At what depth below the surface of water wi the pressure be equal to two atmospheres, if the atmo pheric pressure is 1 megadyne per square centimetre?

46. Show that if two liquids which do not mix me in communicating tubes, their heights above the com mon surface of separation will be inversely as the densities.

If the heights of the two liquids above the surface separation are 15 and 18 inches, and the density of th first is 1.08, what is the density of the second?

47. I wish to discover what the water pressure at particular tap is, and, in order to do so, I connect with a mercury manometer; on opening the tap th mercury is forced to a height of 110 centimetres : e press the "head of water" in feet.

48. Calculate the available water pressure in pound per square inch in Example 47.

49. A uniform U-tube is about half filled with water how much oil of specific gravity 0.8 must be poured int one limb in order to make the water rise 4 inches in th other?

50. The limbs of a V-tube are inclined at an angle 60°. A length of the tube is filled with water; it i then held upright with its limbs equally inclined to th vertical, and as much oil of specific gravity s is poure

m

er

er

at

of

er

a

11

et

r

of

e

a

t

S

S

of it: find the differ

ence of level of the liquids in the two sides.

[In Examples 51-55 the result is to be expressed in grammes
weight, neglecting atmospheric pressure.]

51. What is the pressure on an area of 10 square
centimetres immersed in water, the centre of gravity of
the area being at a depth of 15 centimetres?

52. Calculate the pressure on a circular disc 16 centimetres in diameter immersed in mercury, the centre of the circle being at a depth of 25 centimetres below the surface.

53. A rectangular plate 30 centimetres long and 10 centimetres broad is immersed horizontally at a depth of 3 metres in brine of density II: what is the pressure upon its surface ?

54. What would be the pressure upon the plate in the preceding example, if it were held in a vertical plane with its lower and higher corners 60 and 50 centimetres respectively below the surface?

55. A cube, the edge of which is one decimetre, is suspended in water with its sides vertical and its upper surface at a depth of 1 metre below the surface: find the pressure on each of its faces.

56. Prove that if a cubical box be filled with water, the total pressure to which it is subjected is equal to three times the weight of the water which it contains.

57. Prove that a body immersed in a liquid sustains an upward pressure which is equal to the weight of the liquid displaced and describe any practical applications of this fact.

::

58. Describe how you would demonstrate experimentally the truth of the principle of Archimedes; and explain what is meant by the apparent weight of a body

in water.

A body weighs 62 grammes in vacuo and 42 grammes water find its volume and specific gravity.

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59. What will be the apparent weight in water of piece of rock-crystal (density 2.7) which weighs grammes in vacuo?

60. A bar of aluminium (density 2.6) weighs 54 grammes in vacuo: what will be the loss of weig when it is weighed in water?

61. An irregular solid is found to weigh 98 gramm in vacuo and 64 grammes in water: what is its volume

62. A solid cube, 4 inches in the side, is formed of substance of specific gravity 12.5: what will its appare weight in water be?

63. A body which weighs 24 grammes in air 1 found to weigh 20 grammes in water; what will be i apparent weight in alcohol of specific gravity o.8?

64. A body which weighs 35 grammes in air is foun to weigh 30 grammes in one fluid and 25 grammes i another what will be its weight when immersed in mixture containing equal volumes of the two fluids?

65. Two bodies are in equilibrium when suspende in water from the arms of a balance: the mass of th one body is 28 and its density is 5.6; if the mass of th other is 36, what is its density?