  The hydrogen Lyman lines provide important diagnostic information about the
dynamics of the chromosphere, but there have been few systematic studies of
their variability during flares. We investigate Doppler shifts in these lines
in several flares, and use these to calculate plasma speeds. We use spectral
data from the Multiple EUV Grating Spectrograph B (MEGS-B) detector of the
Extreme-Ultraviolet Variability Experiment (EVE) instrument on the Solar
Dynamics Observatory. MEGS-B obtains full-disk spectra of the Sun at a
resolution of 0.1nm in the range 37-105 nm, which we analyse using three
independent methods. The first method performs Gaussian fits to the lines, and
compares the quiet-Sun centroids with the flaring ones to obtain the Doppler
shifts. The second method uses cross-correlation to detect wavelength shifts
between the quiet-Sun and flaring line profiles. The final method calculates
the "center-of-mass" of the line profile, and compares the quiet-Sun and
flaring centroids to obtain the shift. In a study of 6 flares we find strong
signatures of both upflow and downflow in the Lyman lines, with speeds measured
in Sun-as-a-Star data of around 10 km/s, and speeds in the flare excess signal
of around 30 km/s All events showing upflows in Lyman lines are associated with
some kind of eruption or coronal flow in imaging data, which may be responsible
for the net blueshifts. Events showing downflows in the Lyman lines may be
associated with loop contraction or faint downflows, but it is likely that
chromospheric condensation flows are also contributing.
