In both cases we shall have Q-cub. ft. per minute. But if by any chance we cannot find Va, we only have to compute it by finding Q from Equation 327, and dividing by the sectional area of the stream at which h is measured. Instead of rectangular notches, triangular ones have been used as in fig. 522. The formula to use, which will give a value of Q=cub. ft. per second,

the values of B and H being shown on the diagram. Due to end contraction, however, we have to modify the equation, its new value being

c being a coefficient = 59 when the notch is a 90° one. On the other hand, when B=4H (very flat), C =

='62.

Again, when the notch is 90° we can have another modification, that is,

Q=cs √2gH!

The edges are assumed to be levelled off sharp.

(329)

Take now a circular hole in a tank discharging freely into the atmosphere.

We now have to treat a submerged rectangular opening such as the sluices illustrated by figs. 492 and 493. Referring to fig. 523, we see two values h, and h, and the discharge

c being a coefficient equal to 70 if the sluice stands vertically, or 75 if inclined to the horizontal (see previous reasoning). Now it will be seen that it is a comparatively easy matter to transpose any of the foregoing equations to give other required values. For instance, such an equation as Q=8025 c A/h would be transposed so as to give A so

and so on.

A =

Q 8.025c /h

(332)

When treating the subject of water pipes we assumed these to be new pipes, fresh from the works, the bore being quite smooth. This is usually the

case when we are considering calculations. In use, however, they are liable to corrode. Corrosion is practically the same in all pipes irrespective of diameter, and is usually considered as making the diameter 1 in. less, that is, we assume in. of corrosion all round. To prevent the rapid corrosion of pipes (to altogether avoid it is as yet an impossibility), they should always be coated with Dr Angus Smith's patent solution, or they may undergo a treatment called the Barff process, which consists of heating the pipes to a cherry-red and exposing them to the effects of highly superheated steam. The superheat must, however, not be too great, because it has been found in steam superheaters for power purposes that at very high temperatures disassociation of the steam will take place, and the iron will rapidly corrode to red oxide by the action of the free oxygen. In the actual process the oxygen of the steam will combine with the iron and form a protective coating of magnetic oxide of iron. In our chapter on Weirs we mentioned certain formulæ which would receive consideration in reference to 6-1 Concrete

the same.

FIGS. 524 and 525.

When a weir is placed across a river to raise the water-level it will effect that level some distance back by raising it above the actual weir crest. Now if we know the discharge over the weir Q, and the breadth of the b, then the height on the sill to which the water will rise will be

weir

=

This assumes the weir not to be drowned. The calculations referring to the amount of backwater so produced are rather too complex for a work of this class. For further information see Rankine's Civil Engineering, p. 690.

=

A peculiar form of measuring weir used extensively on irrigation works is illustrated in figs. 524 and 525. The opening B the orifice of discharge constant in width, but its height may vary. The total rise of the floor space is 16 in. There is a stone lintel at A and flooring CD. The bottom of A is set level with the underside of B and 4 in. below the surface-level and 2 in. above the sill of the sluice. The tail chamber starts by being 4 in. wider than the orifice and tapers outwards. It has a 2-in. drip and a 2-in. fall to its ends. To work the gauge we must have 8 in. difference of level on the two sides of the

sluice. They are of Italian origin, and not more than 6 ounces of water are allowed to pass through any one opening. The formulæ for discharge are

c=4'96, H= head to centre of orifice from top level. Of course the primary object of these gauges is to do away with measurements, their construction being such that the head will not vary, and consequently the flow remains constant once for all.

We shall now explain what is commonly known as the venturi law, as applied to a very efficient form of water meter which is described under

P

Pi

FIG. 526.

Waterworks Distribution. Referring to fig. 526, which is a line diagram only, we see a narrow throat and 2 expanding cones, the downstream one being considerably longer than the upstream. Now when water flows along this pipe,

we should find that the pressure due to its head at P was not the same as that at P1, in fact it will be somewhat greater. Call the pressure at P=P and at P1 = P1.

1

Then P-P, gives us what we call the venturi head.

The principle of the meter in its practical form is that the diminution of

area of the pipe causes a corresponding increase of velocity and at the same time a loss of head. Then if H1 = the venturi head, the theoretical velocity in the throat

V

for which a coefficient of say 77 would be used, but it is usual to determine a coefficient for each meter by experiment. Then the discharge in gallons per minute

d being throat diameter in inches and c the constant.

(337)

Now take the following hydraulic problem as illustrating some of our previous reasoning. Say we have a diving-bell in fig. 527. The bell is assumed to be 10 ft. long and the top water-level in the bell is known to be 50 ft. below the surface. We want to know, when the air is entrapped by the water, how high the water will rise in the bell. Now if the depth 50 ft

= H, and the length of the bell = L, and h = the height of the water barometer = 34 ft., the distance

In some hydraulic problems, especially those of centrifugal pumps and turbines, we have to deal with what is called the vortex. A vortex may be either free or forced. In the free vortex the energy of the fluid is the same at all points, but in the latter it is different at different places. Fig. 528 shows a diagram of the free vortex. At any point which is a distance h below the surface, the velocity due to the head is obviously

V=8√h

But in addition to this we have a horizontal force equal to

(339)

r being the radius at the point in question, m being the mass of a particle of

Hence, for this reason, we have the vortex chamber or volute in a centrifugal pump, to convert the kinetic energy into pressure energy. A simple example of a free vortex is the whirl which water usually takes when flowing down the waste pipe of a lavatory basin, noticeable by everyone. Now the forced vortex is really the free vortex turned upside down, and is parabolic in form. It is shown in fig. 529, and the same reasoning applies to it. It was before stated that the pressure due to any head of water was = This is called the statical pressure. The reaction pressure =2wah

and is the force which acts upon a turbine vane or similar appliance.

P

wah

(342) But say,

by means of a suitable guide, we have a double reaction so

we have a

pressure at P1 = 4wah. In a moving vane, however, such as a Pelton wheel, we shall have certain modifications (vide Use of Water Power). Another thing to notice also is that when water flows down a pipe as in fig. 530, which would take place in the discharge pipe of a large flushing tank, the actual area of the stream will only be about half that of the actual pipe. The manner in which all water flows in fact depends above a certain limit upon the velocity, but below that limit upon its viscosity. The point of change is called the critical point. The former is called eddy flow, the latter steady flow. The critical velocity will vary as—

1. The ratio of viscosity to density.

2. Inversely as the diameter of the pipe.

Take now the case of water flowing through an orifice shown by fig. 531, when its length in feet, h, and h2 measured in feet as shown,

=

and for holes 6", 9", and 3" square, c = 60, h is the mean of h1 and h2. When both sides of the orifice are flooded, and the orifice is submerged, the above Equation 343 still holds good if c='67 and h = difference of surface levels. It is, of course, quite necessary to have records of the heads on each side of the orifice in question. We will now conclude the chapter with two problems which will no doubt affect the engineer sometime or other during his career. For instance

Problem. The discharge from an 8-in. pipe whose length is 6 miles (11,440 yds.), heads 190 ft. and 180 ft. respectively. Before one can ascertain the exact quantity of discharge it is necessary to make deductions from the head-i.e. (1) for velocity at entry; (2) for friction against the sides, or perimeter of the pipe. The formula undermentioned is the one in general use by engineers, and is known as "Box's formula," which makes allowance for friction, and its results are quite accurate enough for practical purposes. The loss of head due to velocity at entry may be neglected, as on a long length of pipe it would not make a great deal of difference.