The tuba and euphonium both require a high volume of air to function. For the lower keyed tubas, this can approach the exhalation of nearly 5 liters of air per second, (a figure which is put into stark relief when considering the average adult lung capacity of around 6 liters). As a result, the young tubist and euphonist learns first and foremost how to control and regulate their breathing, in order to maximize their ability to perform for long periods of time.
For composers, this means that any work written for the tuba family must necessarily consider the demands that their music places on the performer’s breathing, as the musical and physical elements of performance are necessarily intertwined for tubists and euphonists. In the author’s experience, this can often be accomplished by simply allowing for the performer to place breathing spots where necessary throughout the work; from a very early age, all serious performers of the tuba family learn how to place musically-sensible breathing spots, and this is true even of the contemporary repertoire. If the composer is aware of the immense breathing demands placed by the tuba and euphonium, and is amenable to small, nearly inaudible breaks in certain musical phrases, then the performer will take care of the rest.
If the composer wishes to manually adjust
their music for the breathing demands of the tuba and euphonium, a few
guidelines are necessary. First, all members of the tuba family require a
larger volume of exhalations in the low range than in the high range. There may
be only a small differential between air usage in the low vs. the high range,
but it is noticeable to the performer. Second, although it may seem
counterintuitive, playing at a soft dynamic does not necessarily mean that the
performer will need to use less air than at louder dynamics. This is due to the
nature of the embouchure buzz; at high dynamics, a large quantity is required
to sustain the energy of the buzz, while at low dynamics a large quantity is still
needed to sustain the shape of the lips while buzzing less vigorously. Finally,
the tuba-euphonium community encompasses a wide variety of lung capacities, as a
large vital capacity is not required to perform to a high standard on the tuba
and euphonium. Everyone has a different physiology, and this is dealt with
fully in the course of a traditional training as a tubist and/or euphonist. If
you are composing a work for a professional tubist and/or euphonist, rest
assured that the performer will know how to use and control their personal
physiology to the best of their ability. If writing for an intermediate or
beginning performer, then some caution might be taken to not write music that
taxes the physical abilities of the performer (for instance, by eschewing
overly long legato lines, being careful about extended sections of loud
playing, and similar drains on the lung capacity of the performer).
 “Lung Capacity and Aging | American Lung Association,” American Lung Association, accessed January 3, 2019, http://www.lung.org/lung-health-and-diseases/how-lungs-work/lung-capacity-and-aging.html.