$A$ manometer connected to a closed tap reads $4.5 \times 10^5 \text{ Pa}$. When the tap is opened,the reading of the manometer falls to $4 \times 10^5 \text{ Pa}$. The velocity of the flow of water is ........ $m/s$.

$A$ closed water tank has a cross-sectional area $A$. It has a small hole at a depth of $h$ from the free surface of the water. The radius of the hole is $r$ such that $r \ll \sqrt{\frac{A}{\pi}}$. If $p_o$ is the pressure inside the tank above the water level and $p_a$ is the atmospheric pressure,the rate of flow of the water coming out of the hole is ($\rho$ is the density of water).

Water containing air bubbles flows without turbulence through a horizontal pipe which has a region of narrow cross-section. In this region,the bubbles

Bernoulli’s theorem is a consequence of

The reading of a pressure gauge connected to a closed tap is $3.5 \times 10^5 \, N/m^2$. When the tap is opened,the reading of the pressure gauge falls to $3.0 \times 10^5 \, N/m^2$. The velocity of water is ........ $m/s$.

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 ....... $m^2/s^2$ $(g = 10 \ m/s^2)$.