An ideal fluid is flowing in two pipes of the same cross-sectional pipe area. Both the pipes are connected with two vertical tubes, of length h₁ and h₂ as shown in the figure. The flow is streamline in both pipes. If the velocity of the fluid at A, B, and C are $2 \mathrm{m}/\mathrm{s}$, $4 \mathrm{m}/\mathrm{s}$, and $4 \mathrm{m}/\mathrm{s}$ respectively, the velocity of the fluid at $D$ (in m/s) is $\sqrt{x}$. Find the value of $x$

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_________

Figure below shows a liquid being pushed out of the tube by a piston having area of cross section $2.0 {\mathrm{cm}}^2$. The area of cross section at the outlet is $10 {\mathrm{mm}}^2$. If the piston is pushed at a speed of $4 \mathrm{cm} {\mathrm{s}}^{-1}$, the speed of outgoing fluid is _____ $\mathrm{cm} {\mathrm{s}}^{-1}$