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

A wind with speed $40 \mathrm{m} {\mathrm{s}}^{-1}$ blows parallel to the roof of a house. The area of the roof is $250 {\mathrm{m}}^2$. Assuming that the pressure inside the house is atmospheric pressure, the force exerted by the wind on the roof and the direction of the force will be $\left({\rho }_{\mathrm{air} }=1.2 \mathrm{kg} {\mathrm{m}}^{-3}\right)$

The cylindrical tube of a spray pump has radius $R$, one end of which has $n$ fine holes, each of radius $r$. If the speed of the liquid in the tube is $V$, the speed of ejection of the liquid through the holes is,

Two non-mixing liquids of densities $\rho$ and $n\rho$ $(n>1)$are put in a container. The height of each liquid is $h$. A solid cylinder of length $L$ and density $d$ is put in this container. The cylinder floats with its axis vertical and length $\mathrm{pL}(\mathrm{p}<1)$ in the denser liquid. The density $d$ is equal to:

A $U$ tube with both ends open to the atmosphere is partially filled with water. Oil; which is immiscible with water, is poured into one side until it stands at a distance of $10 \mathrm{mm}$ above the water level on the other side. Meanwhile, the water rises by $65 \mathrm{mm}$ from its original level (see diagram). The density of the oil is:

A small hole of area cross-section $2\mathrm{ }\mathrm{m}{\mathrm{m}}^2$ is present near the bottom of a fully filled open tank of height $2\mathrm{ }\mathrm{m}.$ Taking $g=10\mathrm{ }\mathrm{m} {\mathrm{s}}^{-2}$, the rate of flow of water through the open hole would be nearly

Water is flowing continuously from a tap having an internal diameter of $8\times {10}^{-3 }\mathrm{m}$. The water velocity as it leaves the tap is $0.4 \mathrm{m} {\mathrm{s}}^{-1}$. The diameter of the water stream at a distance $2\times {10}^{-1} \mathrm{m}$ below the tap, is close to

There is a circular tube in a vertical plane. Two liquids that do not mix and of densities $d_1$ and $d_2$ are filled in the tube. Each liquid subtends $90°$ angle at the centre. Radius joining their interface makes an angle $\alpha$ with vertical. Ratio $\frac{d_1}{d_2}$ is:

A load of mass $M \mathrm{kg}$ is suspended from a steel wire of length $2 \mathrm{m}$ and radius $1.0 \mathrm{mm}$ in Searle's apparatus experiment. The increase in length produced in the wire is $4.0 \mathrm{mm}.$ Now the load is fully immersed in a liquid of relative density $2.$ The relative density of the material of load is $8.$ The new value of the increase in length of the steel wire is -