B M Sharma Solutions for Chapter: Fluid Mechanics, Exercise 6: Exercises

When at rest, a liquid stands at the same level in the tube shown in figure. But as indicated a height difference $h$ occurs when the system is given an acceleration a towards the right. Then $h$ is equal to

Equal volume of two immiscible liquids of densities $\rho$ and $2\rho$ are filled in a vessel as shown in figure. Two small holes are punched at depth $\frac{h}{2}$ and $\frac{3h}{2}$ from the surface of lighter liquid. If $v_1$ and $v_2$ are the velocities of efflux at these two holes, then $\frac{v_1}{v_2}$ is

The cubical container $\mathrm{ABCDEFGH}$ which is completely filled with an ideal (nonviscous and incompressible) fluid, moves in a gravity free space with $a$ acceleration of $a=a_0\left(\hat{\mathrm{i}}-\hat{\mathrm{j}}+\hat{\mathrm{k}}\right)$, where $a_0$ is a positive constant. Then the pressure will be minimum at point 

In this figure, an ideal liquid flows through the tube, which is of uniform cross-section. The liquid has velocities $V_A$ and $V_B$, and pressure $P_A$ and $P_B$ at points $A$ and $B$ respectively.Choose correct option.

A liquid flows through a horizontal tube. The velocities of the liquid in the two sections, which have areas of cross-section $A_1$ and $A_2$, are $v_1$ and $v_2$ respectively. The difference in the levels of the liquid in the two vertical tubes is $h$.

A siphon has a uniform circular base of diameter $\frac{8}{\sqrt{\pi }}\mathrm{c}\mathrm{m}$ with its crests $1.8\mathrm{m}$ above water level as shown in figure. Find absolute pressure at the crest level $A$ (in $kPa$). [Use $P_0={10}^5\mathrm{N}/{\mathrm{m}}^2$ and $g=10\mathrm{m}/{\mathrm{s}}^2$]

A uniform rod of length $b=90\mathrm{c}\mathrm{m}$ capable of turning about its end which is out of water, rests inclined to the vertical. If its specific gravity is $5/9$, find the length immersed in water (in $\mathrm{c}\mathrm{m}$).

A solid block of volume $V={10}^{-3}{\mathrm{m}}^3$ and density $d=800\mathrm{k}\mathrm{g}/{\mathrm{m}}^3$ is tied to one end of a string, the other end of which is tied to the bottom of the vessel. The vessel contains two immiscible liquids of densities ${\rho }_1=1000\mathrm{k}\mathrm{g}/{\mathrm{m}}^3$ and ${\rho }_2=1500\mathrm{k}\mathrm{g}/{\mathrm{m}}^3$ The solid block is immersed with $2/5\mathrm{t}\mathrm{h}$ of its volume in the liquid of higher density and $3/5\mathrm{t}\mathrm{h}$ in the liquid of lower density. The vessel is placed in an elevator which is moving up with an acceleration of $a=g/2$. Find the tension in the string (in $\mathrm{N}$).
$[g=10\mathrm{m}/{\mathrm{s}}^2]$