A square hole of side length $l$ is made at a depth of $h$ and a circular hole of radius $r$ is made at a depth of $4\,h$ from the surface of water in a water tank kept on a horizontal surface. If $l << h,\,r << h$ and the rate of water flow from the holes is the same, then $r$ is equal to

The velocity of small ball of mass $m$ and density $\rho $ when dropped in a container filled with glycerine of density $\sigma $ becomes constant after sometime. The viscous force acting on the ball in the final stage is

Horizontal tube of non-uniform cross-section has radius of  $0.2\,m$ and  $0.1\,m$  respectively at $P$  and  $Q$ . For streamline flow of liquid, the rate of liquid flow

Water is flowing through two horizontal pipes of different diameters which are connected together. The diameters of the two pipes are $3\, cm$ and $6\, cm$ respectively. If the speed of water in narrower pipe is $4\, m/sec$ and the pressure is $2.0\times10^4$ pascal, then the speed of water in the wider pipe is …….. $m/sec$

For a constant hydraulic stress on an object, the fractional change in the object’s volume $(\Delta V/V)$ and its bulk modulus $(B)$ are related as