Embibe Experts Solutions for Chapter: Fluid Mechanics, Exercise 2: Exercise 2

There is a steady water flow in a horizontal tube in which one part has cross-sectional area $A_1$ and the other part has cross-sectional area $A_2$. Assume that water is incompressible. If $\frac{A_1}{A_2}=16\text{,}$ the ratio of the speed $u_1$ in part $1$ and the speed $u_2$ in part $2$, i.e., $\frac{u_1}{u_2}$ is 

A block of wood is floating on oil with half of its volume submerged. If the density of oil $840 \mathrm{kg} {\mathrm{m}}^{-3}$, the relative density of wood (relative to water) is

A rubber pipe with a diameter of $10 \mathrm{cm}$ is connected to a nozzle $2 \mathrm{cm}$ in diameter. Water flowing through the pipe at a speed of $0.6 {\mathrm{ms}}^{-1}$, comes out like a jet through the nozzle. The backward force of the nozzle is about:

Two immiscible liquids, $A$ and $B$ are kept in a $U$-tube. If the density of liquid $A$ is smaller than the density of liquid $B$, then the equilibrium situation is.

An object with uniform density $\rho$ is attached to a spring that is known to stretch linearly with applied force as shown below.

When the spring object system is immersed in a liquid of density ${\rho }_1$ as shown in the figure, the spring stretches by an amount $x_1\left(\rho >{\rho }_1\right).$ When the experiment is repeated in a liquid of density ${\rho }_2<{\rho }_1$, the spring stretches by an amount, $x_2$. Neglecting any buoyant force on the spring, the density of the object is 

A solid cube and a solid sphere both made of same material are completely submerged in water but to different depths. The sphere and the cube have same surface area. The buoyant force is

A tall tank filled with water has an irregular shape as shown. The wall $CD$ makes an angle of $45°$ with the horizontal; the wall $AB$ is normal to the base $BC$. The lengths $AB$ and $CD$ are much smaller than the height $h$ of water (figure not to scale).

Let $P_1,P_2$ and $P_3$ be the pressures exerted by the water on the wall $AB,$ base $BC$ and the wall $CD$ respectively. Density of water is $\rho$ and $g$ is acceleration due to gravity. Then, approximately