In the figure shown density of lower liquid is three times of density of upper liquid. The cross- sectional areas of openings shown are same. The ratio of mass flow rate from upper opening to lower opening at initial moment is:

In the figure shown cross-section area of holes are same and very small in comparison to area of cross-section of water tank : (tanks are the open from the top) Choose the correct option(s) :

A Pitot tube (figure) is mounted along the axis of a gas pipeline whose cross-sectional area is equal to S. Assuming the viscosity to be negligible, find the volume of gas flowing across the section of the pipe per unit time, if the difference in the liquid columns is equal to Deltah , and the densities of the liquid and the gas are rho_0 and rho respectively.

Two smooth prisms of similar right-triangular sections are arranged on a smooth horizontal plane as shown in figure. The lower prism has a mass eta times the upper prism. The prisms are held in an initial position as shown and are then released. As the upper prism touches the horizontal plane, the distance moved b y the lower prism is

A container of a large uniform cross-sectional area A resting on a horizontal surface holds two immiscible, non viscous and incompressible liquids of densities d and 2d , each of height H//2 as shown in figure. The lower density liquid is open to atmosphere. A homogeneous solid cylinder of length L(L lt (H)/(2)) , cross-sectional area A//5 is immersed such that it floats with its axis vertical of the liquid-liquid interface with length L//4 denser liquid. Determine (a) density D of the solid and (b) the total pressure at the bottom of the container. (Atmospheric pressure = P_0 ). .

A container of large uniform cross-sectional area A resting on a horizontal surface, holes two immiscible, non-viscon and incompressible liquids of densities d and 2d each of height H//2 as shown in the figure. The lower density liquid is open to the atmosphere having pressure P_(0) . A homogeneous solid cylinder of length L(LltH//2) and cross-sectional area A//5 is immeresed such that it floats with its axis vertical at the liquid-liquid interface with length L//4 in the denser liquid, The cylinder is then removed and the original arrangement is restroed. a tiny hole of area s(sltltA) is punched on the vertical side of the container at a height h(hltH//2) . As a result of this, liquid starts flowing out of the hole with a range x on the horizontal surface. The density D of the material of the floation cylinder is

A container of large uniform cross-sectional area A resting on a horizontal surface, holes two immiscible, non-viscon and incompressible liquids of densities d and 2d each of height H//2 as shown in the figure. The lower density liquid is open to the atmosphere having pressure P_(0) . A homogeneous solid cylinder of length L(LltH//2) and cross-sectional area A//5 is immeresed such that it floats with its axis vertical at the liquid-liquid interface with length L//4 in the denser liquid, The cylinder is then removed and the original arrangement is restroed. a tiny hole of area s(sltltA) is punched on the vertical side of the container at a height h(hltH//2) . As a result of this, liquid starts flowing out of the hole with a range x on the horizontal surface. The initial speed of efflux without cylinder is

A container of large uniform cross-sectional area A resting on a horizontal surface, holes two immiscible, non-viscon and incompressible liquids of densities d and 2d each of height H//2 as shown in the figure. The lower density liquid is open to the atmosphere having pressure P_(0) . A homogeneous solid cylinder of length L(LltH//2) and cross-sectional area A//5 is immeresed such that it floats with its axis vertical at the liquid-liquid interface with length L//4 in the denser liquid, The cylinder is then removed and the original arrangement is restroed. a tiny hole of area s(sltltA) is punched on the vertical side of the container at a height h(hltH//2) . As a result of this, liquid starts flowing out of the hole with a range x on the horizontal surface. The initial value of x is

A container of large uniform cross-sectional area A resting on a horizontal surface, holes two immiscible, non-viscon and incompressible liquids of densities d and 2d each of height H//2 as shown in the figure. The lower density liquid is open to the atmosphere having pressure P_(0) . A homogeneous solid cylinder of length L(LltH//2) and cross-sectional area A//5 is immeresed such that it floats with its axis vertical at the liquid-liquid interface with length L//4 in the denser liquid, The cylinder is then removed and the original arrangement is restroed. a tiny hole of area s(sltltA) is punched on the vertical side of the container at a height h(hltH//2) . As a result of this, liquid starts flowing out of the hole with a range x on the horizontal surface. The total pressure with cylinder, at the bottom of the container is

A liquid of density rho is flowing with a speed v through a pipe of cross sectional area A. The pipe is bent in the shape of a right angles as shown. What force should be exerted on the pipe at the corner to keep it fixed?

A piot tube figure is mounted along the axis of a gas pipeline whose cross -sectional area is equal to S. Assuming the viscosity to be negligible, find the volume of the gas flowing across the section of the pipe per unit time, if the difference in the liquid columns is equal to Deltah , and the densities of the liquids and the gas are rho_(0) and rho respectively.