Given the stroke and number of revolutions per minute, to find the
piston speed.
Set stroke in inches on C to 6 on D, and over number of revolutions on D
read piston speed in feet per minute on C.
To find cubic feet of steam in a cylinder at cut-off, given diameter of
cylinder and period of admission in inches.
Set 2200 on B to cylinder diameter on D, and over period of admission on
B read cubic feet of steam on A.
EX.—Cylinder diameter 26 in., stroke 40 in., cut-off at ⅝ of stroke.
Find cubic feet of steam used (theoretically) per stroke.
Set 2200 on B to 26 on D, and over 40 × ⅝ or 25 in. on B, read 7·68
cub. ft. on A, as the number of cubic feet of steam used per stroke.
Given the diameter of a cylinder in inches, and the pressure in lb. per
square inch, to find the load on the piston in tons.
Set pressure in lb. per square inch on B to 2852 on A, and over cylinder
diameter in inches on D read load on piston in tons on B.
EX.—Steam pressure 180 lb. per square inch; cylinder diameter, 42 in.
Find load in tons on piston.
Set 180 on B to 2852 on A, and over 42 on D read 111 tons, the gross
load, on B.
Given admission period and absolute initial pressure of steam in a
cylinder, to find the pressure at various points in the expansion period
(isothermal expansion).
Invert the slide and set the admission period, in inches, on Ɔ to the
initial pressure on D; then under any point in the expansion stroke on Ɔ
find the corresponding pressure on D.
EX.—Admission period 12 in., stroke 42 in., initial pressure 80 lb.
per square inch. Find pressure at successive fifths of the expansion
period.
Set 12 on Ɔ to 80 on D, and opposite 18, 24, 30, 36 and 42 in. of the
whole stroke on Ɔ find the corresponding pressures on D:—53·3, 40, 32,
26·6 and 22·8 lb. per square inch.
To find the mean pressure constant for isothermally expanding steam,
given the cut-off as a fraction of the stroke.
Find the logarithm of the ratio of the expansion _r_, by the method
previously explained (page 46). Prefix the characteristic and to the
number thus obtained, on D, set 1 on C. Then under 2·302 on C read _x_
on D. To _x_ + 1 on D set _r_ on C, and under index of C read mean
pressure constant on D. The latter, multiplied by the initial pressure,
gives the mean forward pressure throughout the stroke. (N.B.—Common log.
× 2·302 = hyperbolic log.)
EX.—Find the mean pressure constant for a cut-off of ¼th, or a ratio
of expansion of 4.
Set (L.H.) index of C to 4 on D, and on the reverse side of the slide
read 0·602 on the logarithmic scale. The characteristic = 0; hence to
0·602 on D set (R.H.) index of C, and under 2·302 on C read 1·384 on
D. Add 1, and to 2·384 thus obtained on D set _r_ (= 4) on C, and
under 1 on C read 0·596, the mean pressure constant required.
Mean pressure constants for the most usual degrees of cut-off are given
below:—
Cut-off in fractions of stroke Mean pressure constant
¾ 0·968
⁷⁄₁₀ 0·952
⅔ 0·934
⅝ 0·919
⅗ 0·913
½ 0·846
⅖ 0·766
⅜ 0·750
⅓ 0·699
³⁄₁₀ 0·664
¼ 0·596
⅕ 0·522
⅙ 0·465
⅐ 0·421
⅛ 0·385
⅑ 0·355
⅒ 0·330
¹⁄₁₁ 0·309
¹⁄₁₂ 0·290
¹⁄₁₃ 0·274
¹⁄₁₄ 0·260
¹⁄₁₅ 0·247
¹⁄₁₆ 0·236
To find mean pressure:—Set 1 on C to constant on D, and under initial
pressure on C read mean pressure on D.
Given the absolute initial pressure, length of stroke, and admission
period, to find the absolute pressure at any point in the expansion
period, it being assumed that the steam expands adiabatically. (P_{2} =
(P_{1})/(R^{¹⁰⁄₉}) in which P_{1} = initial pressure and P_{2} the
pressure corresponding to a ratio of expansion R.)
Set L.H. index of C to ratio of expansion on D, and read on the back of
the slide the decimal of the logarithm. Add the characteristic, and to
the number thus obtained on D set 9 on C, and read off the value found
on D under the index of C. Set this number on the logarithmic scale to
the index mark, in the opening on the back of the rule, and under L.H.
index of C read the value of R^{¹⁰⁄₉} on D. The initial pressure divided
by this value gives the corresponding pressure due to the expansion.
EX.—Absolute initial pressure 120 lb. per square inch; stroke, 4 ft.;
cut-off ¼. Find the respective pressures when ½ and ¾ths of the stroke
have been completed.
In the first case R = 2. Therefore setting the L.H. index of C to 2 on
D, we find the decimal of the logarithm on the back of the slide to be
0·301. The characteristic is 0, so placing 9 on C to 0·301 on D, we
read 0·334 as the value under the R.H. index of C. (N.B.—In locating
the decimal point it is to be observed that the log. of R has been
multiplied by 10, in accordance with the terms of the above
expression.) Setting this number on the logarithmic scale to the back
index, the value of R^{¹⁰⁄₉} is found on D, under the L.H. index of C,
to be 2·16. Setting 120 on C to this value, it is found that the
pressure at ½ stroke, read on C over the R.H. index of D, is 55·5 lb.
per square inch. In a similar manner, the pressure when ¾ths of the
stroke is completed is found to be 35·4 lb. per square inch.
For other conditions of expanding steam, or for gas or air, the method
of procedure is similar to the above.
To find the horse-power of an engine, having given the mean _effective_
pressure, the cylinder diameter, stroke, and number of revolutions per
minute.
To cylinder diameter on D set 145 on C; bring cursor to stroke in feet
on B, 1 on B to cursor, cursor to number of revolutions on B, 1 on B to
cursor, and over mean effective pressure on B find horse-power on A.
(N.B.—If stroke is in inches, use 502 in place of 145 given above.)
EX.—Find the indicated horse-power, given cylinder diameter 27 in.,
mean effective pressure 38 lb. per square inch, stroke 32 in.,
revolutions 57 per minute.
Set 502 on C to 27 on D, bring cursor to 32 on B, 1 on B to cursor,
cursor to 57 on B, 1 on B to cursor, and over 38 on B read 200 I.H.P.
on A.
To determine the horse-power of a compound engine, invert the slide and
set the diameter of the _high_-pressure cylinder on Ɔ to the cut-off in
that cylinder on A. Use the number then found on A over the diameter of
the _low_-pressure cylinder on Ɔ as the cut-off in that cylinder,
working with the same pressure and piston speed, and calculate the
horse-power as for a single cylinder.
To find the cylinder ratio in compound engines, invert the slide and set
index of Ɔ to diameter of the low-pressure cylinder on D. Then over the
diameter of the high-pressure cylinder on C, read cylinder ratio on A.
EX.—Diameter of high-pressure cylinder 7¾in., low-pressure 15 in. Find
cylinder ratio.
Set index on Ɔ to 15 on D, and over 7·75 on Ɔ read 3·75, the required
ratio, on A.
The cylinder ratios of triple or quadruple-expansion engines may be
similarly determined.
EX.—In a quadruple-expansion engine, the cylinders are 18, 26, 37, and
54 inches in diameter. Find the respective ratios of the high, first
intermediate, and second intermediate cylinders to the low-pressure.
Set (R.H.) index of Ɔ to 54 on D, and over 18, 26, and 37 on Ɔ read 9,
4·31, and 2·13, the required ratios, on A.
Given the mean effective pressures in lb. per square inch in each of the
three cylinders of a triple-expansion engine, the I.H.P. to be developed
in each cylinder, and the piston speed, to find the respective cylinder
diameters.
Set 42,000 on B to piston speed on A; bring cursor to mean effective
pressure in low-pressure cylinder on B, index of B to cursor, and under
I.H.P. on A read low-pressure cylinder diameter on C. To find the
diameters of the high-pressure and intermediate-pressure cylinders,
invert the slide and place the mean pressure in the low-pressure
cylinder on ᗺ to the diameter of that cylinder on D. Then under the
respective mean pressures on ᗺ read corresponding cylinder diameters on
D.
EX.—The mean effective pressures in the cylinders of a
triple-expansion engine are:—L.P., 10·32; I.M.P., 27·5; and H.P., 77·5
lb. per square inch. The piston speed is 650 ft. per minute, and the
I.H.P. developed in each cylinder, 750. Find the cylinder diameters.
Set 42,000 on B to 650 on A, and bring cursor to 10·32 on B. Bring
index of B to cursor, and under 750 on A read 68·5 in. on C, the L.P.
cylinder diameter. Invert the slide, and placing 10·32 on ᗺ to 68·5 on
D, read, under 27·5 on ᗺ, the I.M.P. cylinder diameter = 42 in., on D;
also under 77·5 on ᗺ read the H.P. cylinder diameter = 25 in., on D.
To compute brake or dynamometrical horse-power.
Set 525 on C to the total weight in lb. acting at the end of the lever
(or pull of spring balance in lb.) on D; set cursor to length of lever
in feet on C, bring 1 on C to cursor, and under number of revolutions
per minute on C find brake horse-power on D.
Given cylinder diameter and piston speed in feet per minute, to find
diameter of steam pipe, assuming the maximum velocity of the steam to be
6000 ft. per minute.
Set 6000 on B to cylinder diameter on D, and under piston speed on B
read steam pipe diameter on D.
Given the number of revolutions per minute of a Watt governor, to find
the vertical height in inches, from the plane of revolution of the balls
to the point of suspension.
Set revolutions per minute on C to 35,200 on A, and over index of B read
height on A.
Given the weight in lb. of the rim of a cast-iron fly-wheel, to find the
sectional area of the rim in square inches.
Set the mean diameter of the wheel in feet on C to 0·102 on D, and under
weight of rim on C find area on D.
Given the consumption of coal in tons per week of 56 hours, and the
I.H.P., to find the coal consumed per I.H.P. per hour.
Set I.H.P. on C to 40 on D, and under weekly consumption on C read lb.
of coal per I.H.P., per hour on D.
EX.—Find coal used per I.H.P. per hour, when 24 tons is the weekly
consumption for 300 I.H.P.
Set 300 on C to 40 on D, and under 24 on C read 3·2 lb. per I.H.P. per
hour on D.
(N.B.—For any other number of working hours per week divide 2240 by the
number of working hours, and use the quotient in place of 40 as above.)
To find the tractive force of a locomotive.
Set diameter of driving wheel in inches on B to diameter of cylinder in
inches on D, and over the stroke in inches on B read on A, tractive
force in lb. for each lb. of effective pressure on the piston.