Water is flowing continuously from a tap having an internal diameter $8 \times 10^{-3}\, m$. The water velocity as it leaves the tap is $0.04\, ms^{-1}$. The diameter of the water stream at a distance $8 \times 10^{-1}\, m$ below the tap is close to

$A$ horizontal tube of non-uniform cross-section has radii of $0.2\,m$ and $0.1\,m$ at points $P$ and $Q$ respectively. For the streamline flow of an incompressible liquid,the rate of liquid flow is:

Fountains usually seen in gardens are generated by a wide pipe with an enclosure at one end having many small holes. Consider one such fountain which is produced by a pipe of internal diameter $2 \ cm$ in which water flows at a rate $3 \ ms^{-1}$. The enclosure has $100$ holes each of diameter $0.05 \ cm$. The velocity of water coming out of the holes is (in $ms^{-1}$):

The cylindrical tube of a spray pump has radius $R,$ one end of which has $n$ fine holes,each of radius $r.$ If the speed of the liquid in the tube is $v,$ the speed of the ejection of the liquid through the holes is

Water flows through a hose pipe whose internal diameter is $4 \,cm$ at a speed of $1 \,ms^{-1}$. If water has to emerge at a speed of $4 \,ms^{-1}$, then the diameter of the nozzle should be (in $\,cm$)

The surface of water in a water tank of cross-section area $750 \text{ cm}^2$ on the top of a house is $h \text{ m}$ above the tap level. The speed of water coming out through the tap of cross-section area $500 \text{ mm}^2$ is $30 \text{ cm/s}$. At that instant, $dh/dt$ is $y \times 10^{-3} \text{ m/s}$. The value of $y$ will be