Embibe Experts Solutions for Chapter: Fluid Mechanics, Exercise 3: Exercise-3

For the system shown in the figure, the cylinder on the left at $L$ has a mass of $600 \mathrm{kg}$ and a cross-sectional area of $800{ \mathrm{cm}}^2.$ The piston on the right, at $S$ has cross-sectional area $25{ \mathrm{cm}}^2$ and negligible weight. If the apparatus is filled with oil $\left(\mathrm{\rho }=0.75 \frac{\mathrm{gm}}{{\mathrm{cm}}^3}\right)$ Find the force $F$ (in $\left.\mathrm{N}\right)$ required to hold the system in equilibrium. Take $g=10 \mathrm{m} {\mathrm{s}}^{-2}$.

A light metal stick of square cross-section $\left(5 \mathrm{cm}\times 5 \mathrm{cm}\right)$ and length$\text{'}4 \mathrm{m}\text{'}$ mass $2.5 \mathrm{kg}$ is shown in the figure below. Determine its angle (in degrees) of inclination when the water surface is $1 \mathrm{m}$ above the hinge.

A block weight $15 \mathrm{N}$ in air and $12 \mathrm{N}$ when immersed in water. Find the specific gravity of block.

A wooden plank of length $1 \mathrm{m}$ and uniform cross-section is hinged at one end to the bottom of a tank as shown in figure. The tank is filled with water upto a height $0.5 \mathrm{m}.$ The specific gravity of the plank is $0.5.$ Find the angle $\theta$ (in degrees) that the plank makes with the vertical in the equilibrium position. (exclude the $\cos \theta =0°).$

A glass beaker is placed partially filled with water in a sink. It has a mass of $390 \mathrm{gm}$ and an interior volume of $500{ \mathrm{cm}}^3.$ When water starts filling the sink, it is found that if beaker is less than half full it will float. But if it is more than half full, it remains on the bottom of the sink, as the water rises to its rim. What is the density of the material (in $\frac{\mathrm{gm}}{{\mathrm{cm}}^3}$ of which the beaker is made?

A large open top container of negligible mass and uniform cross-sectional area A has a small holes of cross-sectional area $\frac{A}{100}$ in its side wall near the bottom. The container contains a liquid of density $\rho$ and mass $m_0.$ Assuming that the liquid starts flowing out horizontally through the hole at $t=0.$ Calculate the acceleration ( in ${\text{m s}}^{-2}$) of the container.

In a movable container shown in figure a liquid of density $\rho$ is filled up to a height $h$ $(1.8 \mathrm{m}).$ The upper $\&$ lower tube cross sectional areas are $A_2 \&{ A}_1$ respectively $\left(A_2>>A_1\right).$ If the liquid leaves out the container through the tube of cross-sectional area $A_1$ then find the velocity of liquid $\left(\mathrm{in} \mathrm{m} {\sec }^{-1}\right)$ coming out. $\left(\mathrm{Take} \mathrm{g}=10 \mathrm{m} {\sec }^{-2}\right)$

A large tank is filled with two liquids of specific gravities $2\mathrm{\sigma }$ and $\mathrm{\sigma }.$ Two holes are made on the wall of the tank as shown. Find the ratio of the distance from $O$ of the points on the ground where the jets from holes $A \text{\&} B$ strike. If the ratio is $\sqrt{\frac{a}{b}},$ find the value of $(a+b).$