in this example, we are required to calculate
the grawce lift force on an airplane wing,
of length 10 meter and width 2 meter. we are
also given that air speed above the wing is
1 20 meter per second, and below the wing
is 90 meter per second. and air density is
also given. in this problem, the situation
would be like this, if this is an airplane,
there is a point at the top and there is a
point at the bottom of the wing. and here
we can see, the air speed above the wing is,
here if the air speed is v t, and here if
air speed is v b, we can see here at the top
speed is more than the bottom that means if
we talk about the pressure at top and pressure
at bottom, we can say pressure at bottom will
be more than pressure at top. so due to the
difference in pressure, it’ll experience
an upward lift force. we are required to find
the lift force, so here it can be directly
given as, lift force, is equal to the pressure
difference which is, p b minus p t, multiplied
by the surface area of the wing. and for area,
we are already given with its length and width.
so we need to 1st calculate the pressure difference
at top and bottom point of the wing. for this,
we use, bernawlli’s theorem, at points t
and b respectively. and almost we can neglect
the width of the wing or thickness of wing
can be ignored, so we can consider that, these
2 points are almost at the same horizontal
level or having same height above the ground.
so in this situation we can use pressure at
top plus, half ro v t square, is equal to
pressure at bottom plus, half ro v b square.
using this we can find out p b minus p t as,
half ro, v t square minus v b square, if we
substitute the values it is half, density
of air is given as, 1 point 3 multiplied by,
we put the velocity values, at top velocity
is 1 20 meter per second and at bottom it
is, 90 meters per second. we just simplify
this numerical calculation finally we’ll
get it, 4 point 1 into, 10 to power 3 newton
per meter square. so we find out the grawce
lift force. as we have just now calculated
force can be given as, p b minus p t multiplied
by, area of wing. so this can be written as
4 point 1 into, 10 to power 3, multiplied
by, the area of wing in this situation is,
10 into 2 it is 20 meter square. so result
can be given as, 8 point 2 into, 10 to power
4 newton. that’ll be the answer to this
problem.
