Water flows through a frictionless duct with a cross-section varying as shown in the figure. The pressure $p$ at points along the axis is represented by:

$A$ liquid enters at point $A_{1}$ with a speed of $3.5 \ m/s$ and leaves at point $A_{2}$. Find the height attained by the liquid above point $A_{2}$ (in $cm$). (in $.25$)

Two light balls are suspended as shown in the figure. When a stream of air passes through the space between them,the distance between the balls will

State Bernoulli's equation in words and write its mathematical formula.

As shown in the figure, a pump is designed as a horizontal cylinder with a piston having area $A$ and an outlet orifice having an area $a$. The piston moves with a constant velocity under the action of force $F$. If the density of the liquid is $\rho$, then the speed of the liquid emerging from the orifice is (assume $A \gg a$):

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 $\,m$)