The Locomotive - Lighthouse Survival Blog

1901.] THE LOCOMOTIVE, 51
case, in which the cock is closed instantaneously; and this will give us some idea, at
least, of the forces that are in operation in the actual case.
For simplicity we will consider a straight, horizontal blow-off pipe that is attached
directly to the back head of the boiler, as shown in Fig. 2. To conform to the actual
conditions shown in Fig. 1, we will assume that this pipe is 3 inches in diameter inter-
nally, and o£ feet long; and we will take the boiler pressure to be GO pounds per square
inch, as it was in the actual case.
The first thing to do, is to find how many foot-pounds of energy the moving column
of water in the blow-off pipe possesses, on account of its velocity. The rule for doing
this is as follows: Find the height, in feet, of a column of water which would produce
a static pressure equal to the actual pressure at the entrance of the blow-off pipe. Then
multiply this height by the total weight of water (in pounds) in the blow-oft' pipe, be-
tween the boiler and the cock; and the product is the number of foot-pounds of energy
that the moving column possesses, on account of its velocity when the blow-cock is
wide open.
In applying this rule to the case in hand, we will assume that it takes a column of
water 2.4 feet high (at the temperature corresponding to 60 pounds pressure) to give a
static pressure of 1 pound per square inch. The height of a column that would give a
static pressure of 60 pounds would therefore be 60x2.4 = 144 feet.
To find the weight of water in the pipe, we multiply the sectional area of the pipe
by the distance from the boiler to the blow-cock (expressing everything in inches), and
then divide the product by the number of cubic inches of water that it takes to weigh
Fig. 2.
—
Illustrating the ""Water Ram" in Blow-off Pipes.
one pound. The area of a 3-inch circle is 7.07 square inches, and the distance from the
boiler to the blow-cock, in the present case, is 66 inches. Hence the volume of the pipe
is 66x7.07=467 cubic inches (in round numbers). Taking the density of the water to
be such that 29 cubic inches of it weigh one pound, we have 467-^-29 = 16.1 pounds (or,
say, 16 pounds), as the weight of the water in the blow-pipe.
Following out the rule given above, we find that the energy that the water in the
blow-pipe has, on account of its motion, is 144x16 = 2,304 foot-pounds.
Now if the blow-off pipe is closed instantly, what becomes of this energy? It has
got to appear somewhere, by compressing things, or stretching things, or breaking
things, or doing some other definite kind of work. If we assume the water to be in-
compressible, and the blow-pipe to be securely fixed where it enters the boiler, the
kinetic energy of the water in the pipe (that is, the energy due to its velocity) must be
expended principally in stretching the pipe itself. This fact enables us to calculate the
maximum stress that can be produced in the pipe by the sudden closing of the valves.
The rule for this part of the calculation is as follows: Multiply the area of metal in the
cross-section of the pipe (expressed in square inches) by twice the "kinetic energy" of
the moving column of water (expressed in foot-pounds, and calculated as described