Fluid Mechanics

Q: The vessel shown in Fig. has two sections of area of cross-section A₁ and A₂ . A liquid of density ρ fills both the sections, upto height h in each. Neglecting atmospheric pressure,

(a) The pressure at the base of the vessel is 2 h ρ g

(b) The weight of the liquid in vessel is equal to 2 h ρ g

(c) The force exerted by the liquid on the base of vessel is 2 h ρ g A₂

(d) The walls of the vessel at the level X exert a force h ρ g(A₂ – A₁ )downwards on the liquid

Q: A cylindrical vessel is filled with equal amounts by weights of mercury and water. The total height of the two layers is 29.2 cm. The pressure of the liquid at the bottom of the vessel is: (specific gravity of mercury is 13.6)

(a) 8 cm of Hg

(b) 6 cm of Hg

(c) 4 cm of Hg

(d) 2 cm of Hg

Q: A U-tube is partially filled with water. oil which does not mix with water is next poured into one side until water rises by 25 cm on the other side, if the density of oil be 0.8, the oil level will stand higher than the water level by:

(a) 6.25 cm

(b) 12.50 cm

(c) 31.25 cm

(d) 62.50 cm

Q: A given shaped glass tube having uniform cross section is filled with water and is mounted on a rotatable shaft as shown in figure. If the tube is rotated with a constant angular velocity ω then

(a) Water levels in both sections A and B go up

(b) Water level in Section A goes up and that in B comes down

(c) Water level in Section A comes down and that in B it goes up

(d) Water levels remains same in both sections

Q: An open glass tube is immersed in mercury in such a way that a length of 8 cm extends above the mercury level. The open end of the tube is then closed and sealed and the tube is raised vertically up by additional 46 cm. what will be length of the air column above mercury in the tube now (Atmospheric pressure = 76 cm of Hg)

(a) 16 cm

(b) 22 cm

(c) 38 cm

(d) 6 cm