An engine pumps water through a hose pipe. Water passes through the pipe and leaves it with a velocity of $2\, m/s$. The mass per unit length of water in the pipe is $100\, kg/m$. ......... $W$ is the power of the engine .

A spherical solid ball of volume $V$ is made of a material of density ${\rho _1}$ . It is falling through a liquid of density ${\rho _2}\left( {{\rho _2} < {\rho _1}} \right)$. Assume that the liquid  applies a viscous force on the ball that is propoertional to the square of its speed $v$ , i.e., ${F_{{\rm{viscous}}}} =  - k{v^2}\left( {k > 0} \right)$. Then terminal speed of the bal is

Application of Bernoulli's theorem can be seen in

A solid sphere of radius $r$ made of a soft material of bulk modulus $K$ is surrounded by a liquid in a cylindrical container. A massless piston of area a floats on the surface of the liquid, covering entire cross-section of cylindrical container. When a mass m is placed on the surface of the piston to compress the liquid, the fractional decrement in the radius of the sphere$\left( {\frac{{dr}}{r}} \right)$ is

The work done in splitting a drop of water of $1\, mm$ radius into $10^6$ droplets is (surface tension of water $72\times10^{-3}\, N/m$) :

What is the pressure on a swimmer $20 \,m$ below the surface of water is ..... $atm$