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(6) Draw also to scale on the same base an acceleration diagram

for the piston during one complete revolution of the crank.

State clearly the scales to which the two diagrams

are drawn. (c) From the acceleration diagram, determine the two positions

of the crank at which the acceleration of the piston

is zero. The first two sections of this question were fairly well answered, but very few candidates obtained the acceleration diagram correctly, and still fewer were able to determine the positions of the crank when the piston acceleration was zero.

per minute.

Q. 45. In a shale mine in order to drain one of the pits a treble ram pump,

driven by an electric motor, is employed. The rams are 94 inches
diameter by 12-inch stroke, they each make 34.75 strokes per
minute, the height to which the water is lifted is 393 feet, and
the total length of the 6-inch discharge pipe is 700 feet.
Find :-

(a) How many gallons of water are lifted
(6) How many foot-pounds of useful work are done per minute.
(c) How many foot-pounds of work are done per minute in

overcoming the friction in the pipe (the coefficient

of friction is 0.0075). (d) The B.H.P. required to lift the water and overcome the

pipe friction. Attempted by the majority of the candidates. The most frequent source of error was the mixing up of feet and inches. For example the volume pumped per minute was calculated in cubic inches, and the result was then multiplied by 6t in order to convert it into gallons. The methods employed for determining the friction in the pipe were very bad. Very few of the candidates were familiar with the ordinary formula for the frictional losses in a pipe, and a favourite method was simply to multiply the weight of the water pumped per minute by the coefficient of friction.

Q. 46. Find the maximum horse-power which can be transmitted by a

hemp rope 1 inch in diameter at a speed of 70 feet per second, if the rope is broken with a pull of 5,700 lbs., and it is desired to have a factor of safety of 30.

The angle of the groove in which the rope runs is 60°, and the coefficient of friction mav be taken as 0:25, and it is in contact with the pulley for half the circumference.

Find also the centrifugal tension in the rope if the flywheel is 10 feet in diameter, and the reduction in the horse-power transmitted due to this tension.

Weight of rope for 1 foot of length = 0·28 lbs. This question was badly answered. Many of the candidates who attempted it neglected the effect of the groove in the rim of the pulley, and worked out the problem as if it had been a flat belt running on a flat pulley. Only a few candidates obtained a correct solution to the second part of the question dealing with the centrifugal tension in the rope.

Q. 17. In the epicyclic train shown in the sketch, the wheel A, which has

30 teeth, is fixed. The rotating arm a, which rotates about the

centre A, carries a wheel B, which gears with A, and has 12 teeth, and also a second wheel C, which gears with B, and has 15 teeth. To the wheel C is rigidly fixed an arm b. Find for one revolution of the mechanism :

(a) The path of a point on the arm b, whose distance from

the centre C is equal to the distance between the two centres A and C.

(6) The path of a point on the arm b, whose distance from

the centre C is one-half that between the two centres A and C.

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Attempted by only a minority of the candidates, and the work as a rule was unsatisfactory. Most of the candidates seemed to be quite unfamiliar with such a piece of mechanism as an epicyclic train, and most absurd curves were obtained for the path of the point b.


Q. 48. A tripod has the following dimensions : The apex point is 0,

and the lengths of the three legs AO, BO, and CO are respectively 18*0 feet, 17'5 feet, and 16 feet. The lengths of the sides of the triangle formed by the feet AB, BC, and CA are 90 feet 9:5 feet and 10 feet respectively. Find graphically, or in any other

way, the forces which act down each leg of the tripod when

a load of 10 tons is suspended from it. As a rule fairly well answered, but the graphical work was often very rough and incorrect.

Q. 49. A cone clutch has an angle of 50, and a mean diameter of 10

inches. Find the thrust on the sliding part parallel to the shaft when the clutch transmits 2 horse-power at 120 revolutions per minute, if the coefficient of friction between the two parts

of the clutch is 0:35. A favourite question and well answered.

Q. 50. A steel shaft 2} inches in diameter is driven by a 20 H.P. gas

engine at 100 revolutions per minute. The shaft is supported by three bearings, spaced 15 feet apart between centres, and the centre of the driving pulley is 6 inches beyond the centre of one of the end bearings. Pulleys are arranged, as shown on the sketch, to work certain machines, and the horse-power taken off each of these pulleys is shown on the sketch ; in addition each bearing absorbs H.P. Assuming that all loads are applied at the centre of the respective pulleys and bearings, calculate the angle of twist in the shaft at each of these points, reckoning

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is 18" diameter do. B is

do. do с is 24"

do Answered by comparatively few candidates, and many of these made serious arithmetical blunders, especially in the mixing up of inch pounds and foot pounds of work.

is 10"

Q. 51. In a certain method of making shock tests of metal, a heavy

rotating disc carries a knife at a point on its circumference. The disc having been set in rapid rotation, the metal specimen to be tested, supported on two knife edges at a certain distance apart, is moved up towards the rotating disc to such a position that the knife in descending strikes the centre of the specimen and fractures it. The work absorbed in fracturing the bar is estimated from the change of velocity of rotation of the disc.

In an actual machine the diameter of the disc, which is of steel, is 12 inches, and its thickness is 4 inches. (One cubic inch of steel weighs 0-28 lbs.) The angular, velocity of the disc before impact with the specimen is 36 radians per second, and after impact, 24:3 radians per second.

Calculate the number of inch-pounds of work spent in fracturing the specimen.

Criticise this method of testing the quality of a specimen of

any material. Attempted by only a few of the candidates, but well answered.

Q. 52. Show that the Lowell formula for a rectangular gauge notch is a rational formula. It is (for sharp edges at sides and sill) –

(Q = 3:33 (L - H) H
where Q is in cubic feet per second, L and If being in feet.

Describe, with sketches, how you would measure the quantity

of water flowing down a small stream. Attempted by very few candidates, and in most cases the portion of the question dealing with the Lowell formula was badly answered.

Q. 53. Three adjacent positions, G, G., Gg of the centre of mass G of a

balance weight, at intervals of second, have been found by

geometrical construction. Referred to perpendicular axes, these positions are measured in feet as follows :

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Find approximately, by taking first and second differences, the x and y components of the velocity and acceleration of G when in the position Gg. Find also the resultant velocity and resultant acceleration for this position.

The mass of the balance weight was 351 lbs. Find the magnitude and direction of the force

corresponding to the acceleration for the position G2. Plot the points on squared paper, and on the diagram exhihit the velocity, acceleration, and force as

vectors, Attempted by very few candidates, but well answered by those who did attempt it, though in some cases the plotting was unsatisfactory.


Results ; 1st Class, 1 ; 2nd Class, 3; Failed, 18; Total, 22.

Twenty-two candidates entered for this stage, and the work was much more satisfactory than in the preceding year. Questions 61, 62, 63, 66, and 67 were the favourite ones. Most of the answers to Question 61 were very good, the bulk of the candidates selecting division (a), but the sketching in some cases was unsatisfactory, especially with regard to the details of the feed motions. In division (b), the sketching was much better, and the details were much more carefully shown by the candidates who attempted this part of the question. In Question 63 the majority of the candidates selected division (a), but most of those omitted to explain how they would test the accuracy of the instruments employed in the experiment. The answers to Question 63 were on the whole satisfactory, the diagrams were carefully drawn, but many candidates contented themselves with dealing with only one-half of a revolution of the crank, instead of one complete revolution as was asked in the question. Very few candidates attempted Question 64, and only one secured an accurate result. Question 65 was attempted by only a few candidates, but was well answered. In Question 66 most of the incorrect answers were due to faulty arithmetic, candidates showing a sound enough knowledge of the necessary formula, but making serious blunders in their calculations. Question 67 was well answered. The remaining four questions, 68-71, were each attempted by only a small number of students. “As a rule the work was fairly satisfactory.

Report on the Examination in Steam.


Results: 1st Class, 424 ; 2nd Class, 408; Failed, 496 ; Total, 1,328.

There were 1,328 candidates in this stage, being a slight increase compared with 1,300 last year.

SKETCHES. The standard reached in Questions 1 and 2 is now fairly high, and the details shown often exhibit a working knowledge of the subject. Candidates are sometimes handicapped by omitting to provide themselves with compasses and straight-edges, and suffer accordingly. The sketches in Question 3 were not so good, probably because candidates were not asked for 'good sketches' as in the previous questions. On the whole there is no need to complain of the sketching, but it is very necessary that candidates should be kept up to the mark.

CALCULATIONS The usual difficulties were noticed as soon as candidates tried to mix the Centigrade and Fahrenheit scales, but this confusion is growing less marked as men get accustomed to the former. The use of the slide rule would save many mistakes and much labour. Several candidates drew attention to the fact that the ruling of the paper into one inch squares was not accurately done. The inch was more accurately 2-5 cm. Q. 1. Describe, with good sketches, one, and only one, of the following,

(a), (6), (c), or (d):

(a) The crank shaft bearing of a horizontal or vertical engine.
(6) The crank axle of an inside cylinder locomotive.
(c) The piston of a gas or petrol engine, showing the packing,

and the pin to which the connecting rod is attached.
(d) The rotating part of a Parsons' or other steam turbine,

showing how the vanes are fixed. (a) The favourite section of this question, andstudents showed considerable familiarity with the subject.

(6) Fairly often attempted, but many had no notion where the eccentrics were put and a number showed cranks at wrong angles.

(c) Very frequently attempted, and mostly with success. There is evidently much familiarity with the petrol engine.

(d) Not often done, and attempts, when made, often sketchy and showing no familiarity with the matter. Q. 2. Describe, with good sketches, one, and only one, of the following

(a), (b), (c), (d), or (e) :

(a) A steam stop valve of the screw-down type.
(6) A locomotive regulator valve of any type.
(c) Two forms of boiler stays, stating the use of each.
(d) The front plate of a Lancashire, Cornish, or return tube

marine boiler, showing how the boiler shell is attached.

(e) The carburettor of a petrol or oil engine. (a) Often well done, but an astonishing number of sketches showed no provision whatever for the removal of the valve or indeed in certain cases for its ever having got there.

(6) A locomotive regulator valve is not an easy thing to sketch and many students got into difficulties and were unable to make their sketches clear.

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