Fluid Mechanics

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 $$h (h < H/2).$$