of the reservoir. When the water begins to escape over the edge of the funnel close the cock, and read very carefully the level by the gauge. Read also the height of the liquid in B, which should be nearly empty. At the beginning of a minute open E by removing the rod K, when the water will begin to flow into B in a clear transparent steam, marked, when the aperture is not circular, by alternate swellings and contractions. As the liquid will at once descend in A, the valve C should be opened at the same time, and adjusted so that the water shall slowly trickle over the edge of the funnel, or outlet tube, or the latter may be dispensed with, and the surface kept just at the point of the hook. When B is nearly full, which should take at least five minutes, close E and note the time. It is best to make this come at the end of a minute. Now read the height of the water in B, empty it, and repeat to see if the same results are obtained twice in succession. Make the experiment again with other pressures, also changing the orifices.

To reduce the scale-readings of H to cubic inches, the reservoir B must next be calibrated. If nearly rectangular, a direct measurement will give its horizontal cross-section, but if the sides are at all curved it is safer to use some other method. A plan much used in practice is to mount it on a platform scale and weigh it when empty, and when filled with water to various heights, and reduce the weight of the water in each case to cubic inches, by dividing by .03614, the weight in pounds of one cubic inch of water. A curve should then be constructed, in which ordinates represent the scale-readings and abscissas the volumes. If greater accuracy is required, the tenth of a cubic foot used in Experiment 19 should be employed. A T is placed between its valve and the glass, the branch of which is connected with the hydrant by a rubber tube. It is then hung over the reservoir B, as in the figure. To use it, admit water until it is filled to the top of the hook in its upper end. Shut off the water, and open the valve below. When the water level has reached the lower point, close the valve and read the gauge in B, thus taking a series of readings which will correspond to intervals of precisely one tenth of a cubic foot. In this case it is best to construct a residual curve to show more clearly the irregularities in form of the reservoir.

The area of the orifices must next be measured with a fine scale,

reading to tenths of a division by the eye, or if greater accuracy is required, using the dividing engine.

Finally, to compute the theoretical flow, we have the following data. By the theorem of Torricelli the velocity/2gh, in which g 32.2 ft., or the acceleration of gravity, and h is the height of the liquid above the centre of pressure of the orifice. This equals the difference in the two readings of the hook gauge in A, before and after the experiment, correcting for the position of the centre of pressure, which will sensibly coincide with the centre of gravity of the orifice. Thus with a circular orifice one-half its diameter must be subtracted. A stream of water will then flow out having a volume equal to that of a prism with cross-section s equal to that of the orifice, and a length v for each second, or in t seconds, the observed time, the volume V should be stv = st/2gh. The observed volume is obtained directly from the calibration of B, of which either a curve or a table should be furnished. This quantity divided by V gives m, the coefficient of efflux.

49. JETS OF WATER.

Apparatus. A cylindrical brass tube is used as an orifice, and is mounted at a height of three or four feet from the floor, with a hinge and graduated circle, so that it can be set at any given angle. A deal rod divided into inches is attached to it to measure the range, and the whole is connected with the hydrant by a rubber tube and valve, so that water may flow through it at any required velocity. The water is collected as it escapes in a large vessel, which is weighed in a spring balance before and after the experiment, and thus the amount of water determined. A second scale of inches is also required to measure the vertical descent of

the curve.

Experiment. Almost all the laws of projectiles may be proved by this apparatus. 1st. The form of the jet is a parabola. Set the tube horizontal, and allow the water to flow through it, with such a velocity that in moving three feet horizontally it will descend about the same distance. Take care that this velocity is unchanged during the experiment by noticing that the horizontal range remains the same. Now measure the vertical fall of the jet for every two inches on the horizontal scale, and construct a curve with these distances as coördinates. Next, to measure the veloc

ity, allow the water to flow into the vessel for one minute, and weigh it. The weight in grammes equals the number of cubic centimetres, and this divided by the area of the orifice (found by measuring the diameter of the tube), gives the velocity of the water per minute. Divide this by 60, for the velocity per second, and construct the parabola given by theory, in which x =

gt2

2

gx2
2v2,

= vt, and Y and the acceleration of gravity g = 386 inches. Great care must be taken to reduce all these quantities to the same measure, as inches or metres, several different units being purposely employed in these measurements. Repeat the latter part of this experiment with three or four different velocities, and see if for a given value of y, x is proportional to v.

2d. The horizontal range for a velocity v, and angle of projec

22

tion a, equals sin 2a.

Prove this by measuring the range for

every 5° from 0° to 90°. Evidently the maximum is when x = 45°. In a similar manner we may prove that the maximum range on an inclined plane is attained when the direction of the jet bisects the angle between it and the vertical, and again, that the curve of safety or envelope to all the parabolas formed with a given velocity when the jet is turned in different directions, is a parabola, with the orifice for a focus.

50. RESISTANCE OF PIPES.

8

Apparatus. A " brass tube six feet in length has five holes drilled in it at intervals of exactly a foot, taking care that no burr or roughness remains on the inside. Short pieces of brass tubing are soldered on over them, and long glass tubes are attached by pieces of rubber hose. The whole is mounted on a stand, so that the brass pipe is horizontal, and the glass tubes vertical and a foot apart. Each tube is graduated, or has a paper scale attached, to show the height at which the water stands in it. ter may be passed through the brass pipe at different velocities by connecting it with the hydrant, and regulating the flow by the faucet. To keep the pressure regular, it is better to connect with a separate reservoir, and to measure the velocity, the water may be received in a large graduated vessel.

Wa

Experiment. When water flows through the brass pipe it will rise in the glass tubes owing to the friction, and the latter may be

FLOW OF LIQUIDS THROUGH SMALL ORIFICES.

99

very accurately measured by the height of the liquid. On trying the experiment it will be noticed that the top of the liquid columns lie very nearly in a straight line, passing through the open end of the pipe, where of course the pressure is zero. The exact pressure should be measured by the attached scale, and observations of all of them taken for several different heights. A second series of experiments should also be made to determine the velocity corresponding to these heights. In this case the escaping liquid is received in the graduated vessel for a known time, or the time required to fill it is noted, and from this, knowing the volume and cross-section of the pipe, the velocity is readily determined. The results should be represented by curves, first making abscissas distances, and ordinates pressures, and secondly, using velocities as abscissas, and the heights of the liquid in the most distant tube for ordinates. From these curves the laws and coefficients of liquid friction are readily determined.

51. FLOW OF LIQUIDS THROUGH SMALL ORIFICES.

Apparatus. A Mariotte's flask is placed about three feet above the table and a rubber tube is connected with its outlet. To this is fastened a brass tube with a perforated screw cap, so arranged that small circles of platinum foil may be inserted, with holes of various sizes. A vertical scale shows the height of the orifice, and a balance serves to measure the quantity of water received.

Experiment. Fill the Mariotte's flask with water. For this purpose it is often convenient to have a third tube, which is closed by a rubber cap, except when the flask is to be filled. It is then opened to allow the air to escape, and water is admitted by one of the other tubes. Raise the orifice so that water is just on the point of flowing out of it, and measure its height. Insert one of the platinum diaphragms and lower it, so that the water shall flow out drop by drop. Collect what escapes during a minute, and weigh it. Lower the orifice and repeat at intervals, until it is as low as possible. Measure also at the point where the drops begin to unite into a continuous stream. For all lower points measure. the length of the stream, that is, the distance before it begins to divide into drops.

Compute the coefficient of efflux by means of the usual formula,

V = mstv = mst√2gh, hence m =

V st✅2gh'

in which s equals the

cross section

πα

4, calling d the diameter of the orifice, t = the

time of flow 60, h the head, or the reading first taken minus that corresponding to the given observation, and V is obtained from the weight, remembering that 1 gramme of water = 1 cm3 = .061 inches. Finally, construct a curve in which ordinates represent the coefficients m, and abscissas the heads h.

By this simple apparatus, interesting results could be obtained by measuring the flow of various liquids with different pressures and orifices. Their relative viscosity might thus be compared.

Apparatus. In Fig. 42, A is a tall bell-glass set in a glass jar B containing water. Cis a glass tube drawn out to a point and connected with A by a rubber tube; it is immersed in a test tube D, containing the liquid to be tried. A may be filled with air by blowing through the bent tube E. Paper scales divided into millimetres are attached to B and D to measure the pressure, and D is supported in such a way that it may be raised or lowered at will.

D

B

Fig. 42.

A

E

Experiment. Draw out a piece of glass tubing to a fine point, break off a small piece and grind the end flat so that the orifice shall be circular and smooth. Connect it as at C, by a rubber tube, with the bell-glass A, and fill the latter with air by blowing into E. Raise the test-tube D containing the liquid to be employed, so that the air escaping from C shall bubble up through it. Soon the pressure in A is so far diminished that it becomes insufficient to overcome the resistance opposed to it, the flow will then stop, and the top of the liquid in C will be found to be very much curved. Record the pressure of the air in A which equals the difference in level of the water within and without it. Call it h, and call ' the difference in level within and without C. Repeat this observation several times, either by blowing into E, or by lowering D so that the flow shall recommence. Next remove the tube from the liquid, break off the end, and stick it carefully into