$A$ 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 $kPa$)

The area of cross-section of a large tank is $0.5 \; m^{2}$. It has a narrow opening near the bottom having an area of cross-section $1 \; cm^{2}$. $A$ load of $25 \; kg$ is applied on the water at the top in the tank. Neglecting the speed of water in the tank,the velocity of the water coming out of the opening at the time when the height of water level in the tank is $40 \; cm$ above the bottom will be $\dots \; cm \; s^{-1}$. [Take $g = 10 \; m \; s^{-2}$]

$A$ plane is in level flight at constant speed and each of its two wings has an area of $40 \,m^2$. If the speed of the air is $180 \,km/h$ over the lower wing surface and $252 \,km/h$ over the upper wing surface,the mass of the plane is . . . . . . $kg$. (Take air density to be $1 \,kg \,m^{-3}$ and $g=10 \,ms^{-2}$)

$A$ streamline flow of a liquid of density $\rho$ is passing through a horizontal pipe of cross-sectional area $A_1$ and $A_2$ at two ends. If the pressure of the liquid is $P$ at a point where the flow speed is $v$,then the pressure at another point where the flow speed becomes $3v$ is:

Obtain Bernoulli's equation for a fluid at rest.

The figure shows a liquid of given density flowing steadily in a horizontal tube of varying cross-section. The cross-sectional areas at $A$ is $1.5 \, cm^2$,and at $B$ is $25 \, mm^2$. If the speed of the liquid at $B$ is $60 \, cm/s$,then find $(P_A - P_B)$ in $Pa$. (Given: $P_A$ and $P_B$ are liquid pressures at points $A$ and $B$ respectively. Density $\rho = 1000 \, kg/m^3$. $A$ and $B$ are on the axis of the tube.)