Embibe Experts Solutions for Chapter: Fluid Mechanics, Exercise 1: Exercise-1

A crown made of gold and copper weights $210\mathit{ }\mathrm{g}$ in air and $198 \mathrm{g}$ in water. The weight of gold in crown is:[Given : Density of gold $=19.3\mathit{ }\mathrm{g} {\mathrm{cm}}^{-3}$ and Density of copper $\left.=8.5\mathit{ }\mathrm{g}\mathit{ }{\mathrm{cm}}^{-3}\right]$

Two vessels $A$ and $B$ have the same base area and contain water to the same height, but the mass of water in $A$ is four times that in $B\mathit{.}$ The ratio of the liquid thrust at the base of $A$ to that at the base of $B$ is :-

One end of a horizontal pipe is closed with the help of a valve and the reading of a barometer attached to the pipe is $3\times {10}^5$ Pascal. When the value in the pipe is opened then the reading of barometer falls to ${10}^5$ Pascal. The velocity of water flowing through the pipe will be in $\mathrm{m} {\mathrm{s}}^{-1}$ :-

Water is flowing through a rectangular cross-sectional channel that is $12 \mathrm{m}$ wide with a speed of $0.75 \mathrm{m} {\mathrm{s}}^{-1}.$ The water then flows into four identical channels that have a width of $4.0 \mathrm{m}.$ The depth of the water does not change as it flows into the four channels. What is the speed of the water in one of the smaller channels?

A U-tube of small and uniform cross section contains water of total length $4H$. The height difference between the water columns on the left and on the right is $H$ when the valve $K$ is closed. The valve is suddenly open, and water is flowing from left to right. Ignore friction. Find the speed of water when the heights of the left and the right water columns are the same,

A tank of height $5 \mathrm{m}$ is full of water. There is a hole of cross sectional area $1{ \mathrm{cm}}^2$ in its bottom. The initial volume of water that will come out from this hole per second is :-

The diagram (figure) shows a venturimeter, through which water is flowing. The speed of water at $X$ is $2 \mathrm{cm} {\mathrm{s}}^{-1}.$ The speed of water at $Y$ (taking $\left.g=1000 \mathrm{cm} {\mathrm{s}}^{-2}\right)$ is :-

Water contained in a tank flows through an orifice of a diameter $2 \mathrm{cm},$ under a constant pressure difference, of $10 \mathrm{cm}$ of water column. The rate of flow of water through the orifice is:-