State properties of an ideal fluid. 

Consider the configuration of a stationary water tank of cross-section area $A_0$ and a small bucket as shown in figure below;

What should be the speed $v$ of the bucket, so that the water leaking out of a hole of cross-section area $A$ (as shown) from the water tank does not fall outside the bucket?

(Take, $h=5 \mathrm{m}, H=5 \mathrm{m}, \mathrm{g}=10 \mathrm{m} {\mathrm{s}}^{-2}, A=5 {\mathrm{cm}}^2$ and $A_0=500 {\mathrm{cm}}^2$).

What will be the nature of flow of water from a circular tap, when its flow rate increased from $0.18 \mathrm{L} {\left(\min \right)}^{-1}$ to $0.48 \mathrm{L} {\left(\min \right)}^{-1}?$ The radius of the tap and viscosity of water are $0.5 \mathrm{cm}$ and ${10}^{-3} \mathrm{Pa} \mathrm{s}$, respectively. (Density of water : ${10}^3 \mathrm{kg} {\mathrm{m}}^{-3}$)

Water stands at a depth of $15 \mathrm{m}$ behind a reservoir dam. A horizontal pipe $4 \mathrm{cm}$ in diameter passes through the dam $6 \mathrm{m}$ below the surface $01$ water as shown. There is a plug which secures the pipe opening. Then find the friction between the plug and pipe wall.