Water is filled in a cylindrical container to a height of $3 \ m$. The ratio of the cross-sectional area of the orifice and the beaker is $0.1$. The square of the speed of the liquid coming out from the orifice is ....... $m^2/s^2$ $(g = 10 \ m/s^2)$.

The weight of an aeroplane flying in the air is balanced by:

Why does a flag (or ensign) flutter when there is strong wind? Explain.

$Assertion :$ The pressure of water increases when it flows from a narrow pipe to a wider pipe.
$Reason :$ According to the equation of continuity,$A_1v_1 = A_2v_2$,and by Bernoulli's principle,where velocity is high,pressure is low.

Water from a tap emerges vertically downwards with an initial velocity of $4 \,m/s$. The cross-sectional area of the tap is $A$. The flow is steady and the pressure is constant throughout the stream of water. The distance $h$ vertically below the tap,where the cross-sectional area of the stream becomes $\frac{2}{3} A$,is (take $g = 10 \,m/s^2$): (in $\,m$)

Obtain Bernoulli's equation for a fluid at rest.