Water flows in a horizontal pipe whose one end is closed with a valve. The reading of the pressure gauge attached to the pipe is $P_1$. The reading of the pressure gauge falls to $P_2$ when the valve is opened. The speed of water flowing in the pipe is proportional to

$A$ bottle has a thin nozzle on top. It is filled with water,held horizontally at a height of $1 \,m$ and squeezed slowly by hands,so that the water jet coming out of the nozzle hits the ground at a distance of $2 \,m$. If the area over which the hands squeeze it is $10 \,cm^{2}$,the force applied by hand is close to .......... $N$ (take $g=10 \,m/s^{2}$ and density of water $=1000 \,kg/m^{3}$).

$A$ horizontal pipe of non-uniform cross-section allows water to flow through it with a velocity $1 \ m/s$ when the pressure is $50 \ kPa$ at a point. If the velocity of flow has to be $2 \ m/s$ at some other point,the pressure at that point should be: (in $kPa$)

Water is flowing in streamline motion through a horizontal tube. The pressure at a point in the tube is $p$ where the velocity of flow is $v$. At another point, where the pressure is $p/2$, the velocity of flow is (density of water $= \rho$)

Air streams horizontally past an airplane. The speed over the top surface is $60 \, m/s$ and that under the bottom surface is $45 \, m/s$. The density of air is $1.293 \, kg/m^3$. The difference in pressure is ....... $N/m^2$.

Explain the upward force (dynamic lift) acting on an airplane wing.