In this illustration we'll, discuss about
water flowing out from a tube. we are given
that the figure shows a big water tank having
connected with a narrow tube of length l and
internal radius r. here we are given that
water flows out from tube at a rate of q meter
cube per second.
and we are required to find the torque on
tube due to reaction forces because of ejection
of water about the point o, where tube is
connected to the tank. here in solution first
we can calculate if, water flows out.
at speed v, then, volume flow rate, is given
as, we can write the value of q is equal to
v multiplied by cross sectional area that
is pie r square, of the opening through which
the liquid is coming out. and this gives us
the flow velocity v as q by, pie r square.
and if we got the flow velocity v area we
are already having so we can write.
due to, ejection of.
liquid.
the reaction force.
on vessel.
in opposite direction is.
this force of reaction we know it is given
as ro ay v square this we already studied
in concept videos. and we have calculated
it by using, the rate at which momentum is
coming out and the same, force will be exerted
on, the tube in opposite direction.
so as we have got the value of force we can
now calculate, the torque of, this force.
about point, o is, as the reaction force is
opposite to the direction of ejection it'll
act in upward direction.
so the torque we can write as f multiplied
by l. and if we substitute the value fore
is ro, area of cross section, is pie r square.
multiplied by v square we can substitute as
q by pie r square whole square multiplied
by l. so this torque finally we are getting
is q square.
ro l divided by, pie r square that is a result
of this problem.
