Water enters through end $A$ with speed $v_1$ and leaves through end $B$ with speed $v_2$ of a cylindrical tube $AB$. The tube is always completely filled with water. In case $\mathrm{I}$ tube is horizontal and in case $\mathrm{II}$ it is vertical with end $A$ upwards and in case $\mathrm{III}$ it is vertical with end $B$ upwards. We have $v_1=v_2$ for

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 : ${10}^3 \mathrm{kg} {\mathrm{m}}^{-3}$)

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