Set 9000 on B to 2,700,000 on A, and bring the cursor to 5·1 on B. Moving the slide to the left, it is found that when 11·51 on the R.H. scale of B is under the cursor, the L.H. index of C is opposite 11·51 on D. This, then, is the required diameter of the shaft.
(N.B.—The rules for the scales to be used in finding the cube root (page 42) must be carefully observed in working these examples.)
Moments of Inertia.
To find the moment of inertia of a square section about an axis
formed by one of its diagonals (I = s4
12).
Set index of C to the length of the side of square s on D; bring cursor to s on C, 12 on B to cursor, and over index of B read moment of inertia on A.
To find the moment of inertia of a rectangular section about an axis parallel to one side and perpendicular to the plane of bending.
Set index of C to the height or depth h of the section, and bring cursor to h on B. Set 12 on B to cursor, and over breadth b of the section on B read moment of inertia on A.
Ex.—Find the moment of inertia of a rectangular section of which h = 14 in. and b = 7 in.
Set index of C to 14 on D, and cursor to 14 on B. Bring 12 on B to cursor, and over 7 on B read 1600 on A.
Discharge from Pumps, Pipes, Etc.
To find the theoretical delivery of pumps, in gallons per stroke.
Set 29·4 on B to the diameter of the plunger in inches on D, and over length of stroke in feet on B read theoretical delivery in gallons per stroke on A.
(N.B.—A deduction of from 20 to 40 per cent. should be made to allow for slip.)
To find loss of head of water in feet due to friction in pipes (Prony’s rule).
Set diameter of pipe in feet on B to velocity of water in feet per second on D and bring cursor to 2·25 on B; bring 1 on B to cursor, and over length of pipe in miles on B, read loss of head of water in feet, on A.
To find velocity in feet per second, of water in pipes (Blackwell’s rule).
Set 2·3 on B to diameter of pipe in feet on A, and under inclination of pipe in feet per mile on B read velocity in feet per second on D.
To find the discharge over weirs in cubic feet per minute and per foot of width. (Discharge = 214√h3)
Set 0·00467 on C to the head in feet h on D, and under h on B read discharge on D.
To find the theoretical velocity of water flowing under a given head in feet.
Set index of B to head in feet on A, and under 64·4 on B read theoretical velocity in feet per second on D.
Horse-Power of Water Wheels.
To find the effective horse-power of a Poncelet water wheel.
Set 880 on C to cubic feet of flow of water per minute on D, and under height of fall in feet on C, read effective horse-power on D.
For breast water wheels use 960, and for overshot wheels 775, in place of 880 as above.
Electrical Engineering.
To find the resistance per mile, in ohms, of copper wire of high conductivity, at 60° F. the diameter being given in mils. (1 mil. = 0·001 in.).
Set diameter of wire in mils. on C to 54,900 on A, and over R.H. or L.H. index of B read resistance in ohms on A.
Ex.—Find the resistance per mile of a copper wire 64 mils. in diameter.
Set 64 on C to 54,900 on A, and over R.H. index of B read 13·4 ohms on A.
To find the weight of copper wire in lb. per mile.
Set 7·91 on C to diameter of wire in mils. on D, and over index of B read weight per mile on A.
Given electromotive force and current, to find electrical horse-power.
Set 746 on C to electromotive force in volts on D, and under current in ampères on C read electrical horse-power on D.
Given the resistance of a circuit in ohms and current in ampères, to find the energy absorbed in horse-power.
Set 746 on B to current on D, and over resistance on B read energy absorbed in H.P. on A.
Ex.—Find the H.P. expended in sending a current of 15 ampères through a circuit of 220 ohms resistance.
Set 746 on B to 15 on D, and over 220 on B read 66·3 H.P. on A.
Commercial.
To add on percentages.
Set 100 on C to 100 + given percentage on D, and under original number on C read result on D.
To deduct percentages.
Set R.H. index of C to 100 − the given percentage on D, and under original number on C read result on D.
Ex.—From £16 deduct 7½ per cent.
Set 10 on C to 92·5 on D and under 16 on C, read 14·8 = £14, 16s. on D.
To calculate simple interest.
Set 1 on C to rate per cent. on D; bring cursor to period on C and 1 on C to cursor. Then opposite any sum on C find simple interest on D.
For interest per annum.
Set R.H. index on C to rate on D, and opposite principal on C read interest on D.
Ex.—Find the amount with simple interest of £250 at 8 per cent., and for a period of 1 year and 9 months.
Set 1 on C to 8 on D; bring cursor to 1·75 on C, and 1 on C to cursor; then opposite 250 on C read £35, the interest, on D. Then 250 + 35 = £285 = the amount.
To calculate compound interest.
Set the L.H. index of C to the amount of £1 at the given rate of interest on D, and find the logarithm of this by reading on the reverse side of the rule, as explained on page 46. Multiply the logarithm, so found, by the period, and set the result, on the scale of equal parts, to the index on the under-side of the rule; then opposite any sum on C read the amount (including compound interest) on D.
Ex.—Find the amount of £500 at 5 per cent. for 6 years, with compound interest.
Set L.H. index of C to £1·05 on D, and read at the index on the scale of equal parts on the under-side of rule, 0·0212. Multiply by 6, we obtain 0·1272, which, on the scale of equal parts, is placed to the index in the notch at the end of the rule. Then opposite 500 on C read £670 on D, the amount required, including compound interest.
Miscellaneous Calculations.
To calculate percentages of compositions.
Set weight (or volume) of sample on C, to weight (or volume) of substance considered, on D; then under index of C read required percentage on D.
Ex.—A sample of coal weighing 1·25 grms. contains 0·04425 grm. of ash. Find the percentage of ash.
Set 1·25 on C to 0·04425 on D, and under index on C read 3·54, the required percentage of ash on D.
Given the steam pressure P and the diameter d in millimetres,
of the throat of an injector, to find the weight W, of water
delivered in lb. per hour from W = d2√̅P
0·505.
Set 0·505 on C to P on A; bring cursor to d on C and index of C to cursor. Then under d on C read delivery of water on D.
To find the pressure of wind per square foot, due to a given velocity in miles per hour.
Set 1 on B to 2 on A, and over the velocity in miles per hour on D read pressure in lb. per square foot on B.
To find the kinetic energy of a moving body.
Set 64·4 on B to velocity in feet per second on D, and over weight of body in lb. on B read kinetic energy or accumulated work in foot-lb. on A.