Water flows steadily through a horizontal pipe of variable cross-section. If the pressure of water is $P$ at a point where flow speed is $v$,the pressure at another point where the flow speed is $2v$,is (Take density of water as $\rho$)

Obtain Bernoulli's equation for a fluid at rest.

$A$ horizontal pipe line carries water in a streamline flow. At a point along the tube where the cross-sectional area is $10^{-2} \ m^2$,the water velocity is $2 \ m/s$ and the pressure is $8000 \ Pa$. The pressure of water at another point where the cross-sectional area is $0.5 \times 10^{-2} \ m^2$ is ........ $Pa$.

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 $g = 10 \; m \; s^{-2}$]

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

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