### Fluid Mechanics

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The arrow with a pointed tip can move faster in air than that of with a blunt tip.
Figure shows a large closed cylindrical tank containing water. Initially, the air trapped above the water surface has a height $h_0$ and pressure $2p_0$ wherre $p_0$ is the atmospheric pressure. There is a hole in the wall of the tank at a depth $h_1$ below the top from which water comes out. A long vertical tube is connected as shown.
Liquid reaches equilibrium as shown, in a capacity tube of internal radius r. If the surface tension of the liquid is T, the angle of contact $\theta$ are difference between P and Q is
A container of a large uniform cross-sectional area $A$ resting on horizontal surface holds two immiscible,non-viscous and incompressible liquids of densities $d$ and $2d,$ each of height $\dfrac{H}{2}$ as shown in the figure. The lower density liquid is open to atmosphere. A homogeneous solid cylinder of length $L (L < H/2),$ cross-sectional area $\dfrac{A}{5}$ is immersed such that it floats with its axis vertical of the liquid-liquid interface with length $\dfrac{L}{4}$ in the denser liquid. Determine
A container of large uniform cross-sectional area $A,$ resting on horizontal surface, holds two immiscible non-viscous and incompressible liquids of density $d$ and $2d,$ each of height $\dfrac{H}{2}$ as shown in the figure. The lower density liquid is open to the atmosphere having pressure $P_0$. A tiny hole of area $s (s << A)$ is punched on the vertical side of the container at a height $h (h < H/2).$