In this illustration, we'll be analyzing,
a given l shaped accelerating tube. here the
figure shows a tube filled with a liquid which
is l shaped and accelerating horizontally
at acceleration ay, we are required to find
ay for which no liquid will fall out of the
tube from any ends of the tube which are opened.
so in this solution. we can analyze the tube,
as an accelerating reference frame in which
liquid is filled, and, we already discussed
that in an accelerating reference frame the
effective gravity changes to root of g square
plus ay square. so in this case, if we talk
about the liquid in the tube when, g is acting
in downward direction and with respect to
tube pseudo acceleration will be acting in
this direction. so this is the effective.
acceleration, on liquid, due to, pseudo force.
in frame of. tube, this we already discussed.
when both ay and g are acting the free surfaces
of, the liquid get inclined. and when it'll
get inclined in such a way that free surface
is along the line joining of the 2 ends ay
and b of the tube. and liquid will not spill
over from any end. so in the situation as
we are given this height is h this is l. we
can consider this angle to be theta, so here
we can write. if liquid. is not coming out.
from, any end. of tube. here, we can directly
write this implies the value of tan theta
should be equal to, ay by g which we already
discussed in concept, and the same can be
written as h by, l. and this implies the value
of acceleration we are getting is h g by l
that is the result of this problem. and we
can also solve it in an alternative way. for
this problem like, from end ay, to b. here
pressure is p atmospheric here also pressure
is p atmospheric. so liquid should be at rest,
in the tube, in the reference frame of tube
so we can write, as liquid is at rest, in
the frame of tube. we can use, pascal's equation,
from. ay to b. as, here we can write pressure,
is atmospheric at end ay, if we calculate
pressure at this band it'll be plus, h ro
g as in vertical direction, this ay will not
affect the pressure, then again from this
point to this point pressure will be, minus,
l ro ay because opposite to the direction
of ay here pressure will decrease. and this
should also be p atmospheric. so, this gets
canceled out and simplifying this relation
we are again getting the value of ay is equal
to h g by l. which is the result of this problem,
and we have calculated it in an alternative
way by using pascal's pressure equation. here
we have calculated it by using the angle theta.
which the free surfaces of liquid make in
accelerated reference frame.
