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72. When the injection orifice in a steam-vessel becomes by any means choked up, the usual mode adopted for clearing is that of blowing through by the force of the steam; how is the necessary force of the steam to be ascertained?

A column of water whose base equal one square inch and height one lineal foot is 434 pounds, hence multiply 434 by the depth in feet from the surface of the water to the centre of the pipe, and the product equal the pressure of steam in pounds that will equipoise that column; but an overwhelming force of two or three pounds must be applied by which to remove the obstruction.

73. Suppose a steam-vessel to be propelled through the water at a certain rate of speed by a known amount of power; how is the proportionate increase or decrease of speed ascertained by any other amount of power given?

The power required to propel a vessel through the water is as the cube of the velocity; hence, if 300 horses' power propel a vessel at a velocity of 91 knots per hour, the velocity by 450 horses' power will be

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74. Is the increase or decrease of fuel with a difference of the vessel's speed as the cube of the velocity also?

No; steam-vessels, to be propelled at an increased velocity through the water, require an augmentation of fuel equal to the square of the increased speed, multiplied by the distance steamed, or to be steamed over; hence, suppose 80 tons of coal be a sufficient quantity for a voyage of 1000 miles, at a speed of eight knots per hour, the quantity requisite to complete a distance of 1500 miles at a speed of ten knots per hour, will be

82:102: 80:125, and 1000: 125:: 1500: 187.5

tons.

Again: Suppose 400 tons of coal be a sufficient quantity for generating steam at a rate of ten knots per hour, at what rate per hour must the vessel steam, so that 300 tons will complete the voyage?

400:102: 30075, and 75 8.66 knots per

hour.

=

75. The distance run or passed over by vessels at sea is commonly computed in knots or nautical

miles of 2028 yards, English, the statute mile being 1760; 9.84 knots are nearly equal to 11.34 statute miles. Hence, if a vessel be going at a rate of 8 knots per hour, how many English or statute miles is that corresponding to?

9.84: 11.34::8.5:9.79 miles, or 1.1522 × 8.5 = 9.79 as before.

But the knot sometimes causes confused estimation of a vessel's speed or distance run, because of its length being made to depend upon the length of a measured degree on the earth's surface, which varies in different latitudes, as under:

The length of a degree as measured at

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76. Relative to a screw for the propelling purpose of a steam-vessel, how is the pitch ascertained from the dimensions that are left accessible after a considerable portion of the helix being cut away? From the square of either blade's extremity

subtract the square of either's height, and the square root of the remainder is to the height as the circumference of the screw is to the pitch or lineal distance passed through by one revolution, providing there was no slip.

Suppose the section of a screw as follows:Breadth at extremity of either blade 4 feet; height, or twist of each, 1 feet; and diameter 13 feet:

4.5-1.752-4.13, and 13 x 3.1416-4084; hence 3.13: 1.75:: 40.84: 17.3 feet, pitch of the

screw.

77. The revolutions and pitch of a screw being known, and also the speed of the vessel, how is the amount of slip ascertained?

If the speed of the vessel is observed in knots or nautical miles per hour, multiply the pitch of the screw in feet by the number of its revolutions. per minute; subtract from the product 101.5 times the speed of the vessel in knots per hour, multiply the remainder by .00985, and the product is the loss by slip per hour in equal terms of unity. The same rule is equally suitable if observed and required in English statute miles, only instead of

101.5 the speed, take 88; and instead of multiplying by .00985, multiply by .0114.

Thus, suppose the pitch of a screw propeller equal 13 feet, the number of revolutions being 70 per minute, and it is found that the vessel's speed is 8 knots an hour, the amount of slip will be the following:

13.5 x 70 - 101.5 × 8 = 133 x .00985

=

1.29

knots slip per hour. Again, if the speed be

taken in statute miles:

13.5 × 70 88 x 8

miles slip per hour.

= 241 x .0114 = 2.74

78. When any curve or portion of a circle is given, how is the corresponding radius obtained? RULE. Take any length of straight line, or chord in the curve, and to the square of half its length add the square of the height, or versed sine, divide the sum by twice the versed sine, and the quotient is the radius.

Ex. Suppose a portion of a paddle-wheel ring, in which a line may be stretched 5 feet in length, and the height from the line to the ring measuring 2 inches, what is the radius?

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