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 ........ $m/s$.

Derive Bernoulli's equation for a steady,incompressible,and non-viscous (ideal) fluid flow.

At a hydroelectric power plant,the water pressure head is at a height of $300\; m$ and the water flow available is $100\; m^{3} s^{-1}.$ If the turbine generator efficiency is $60\%,$ estimate the electric power available from the plant (in $MW$) $\left(g=9.8\; m s^{-2}\right).$

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:

Water is flowing through a horizontal tube having cross-sectional areas of its two ends as $A$ and $A'$ such that the ratio $A/A'$ is $5$. If the pressure difference of water between the two ends is $3 \times 10^5 \, N \, m^{-2}$,the velocity of water with which it enters the tube will be ......... $m \, s^{-1}$ (neglect gravity effects).

Rank in order, from highest to lowest, the liquid heights $h_a$ to $h_d$. The air flow is from left to right. The liquid columns are not drawn to scale.