Water flows through a frictionless duct with a cross-section varying as shown in the figure. Pressure $P$ at points along the axis is represented by

  

A cylindrical tank has a hole of $1\mathrm{ }{\mathrm{cm}}^2$ in its bottom. If the water is allowed to flow into the tank from a tube above it at the rate of $70\mathrm{ }{\mathrm{cm}}^3 {\mathrm{s}}^{-1}$ then the maximum height up to which water can rise in the tank is :

A cylindrical container of radius$R$ and height $h$ is completely filled with a liquid. Two horizontal $L$ shaped pipes of a small cross-section area $a$ are connected to the cylinder as shown in the figure. Now the two pipes are opened and fluid starts coming out of the pipes horizontally in opposite directions. Then the torque due to ejected liquid on the system is:

The velocity of the liquid coming out of a small hole of a large vessel containing two different liquids of densities $2\rho$ and $\rho$as shown in the figure is

A long capillary tube of mass $\text{'}\pi \text{'}$ $\mathrm{g},$ radius $2 \mathrm{mm}$ and negligible thickness, is partially immersed in a liquid of surface tension $0.1 \mathrm{N}/\mathrm{m}.$ Take angle of contact zero and neglect the buoyant force of liquid. The force required to hold the tube vertically is $\frac{3\pi }{2500}x$ newton. Find $x.\left(g=10 \mathrm{m}/{\mathrm{s}}^2\right)$

If $\mathrm{NaCl}$ is dissolved into water, then its surface tension

A large number of liquid drops each of radius $a$ are merged to form a single spherical drop of radius $b$. The energy released in the process is converted into kinetic energy of the big drop formed. The speed of the big drop is $[\rho$ is density of liquid, $T$ is surface tension of liquid]