Two water pipes of diameters $ 2 cm $ and $4 cm $ are connected with the main supply line. The velocity of flow of water in the pipe of $ 2 cm$ diameter is
Medium
Download our app for free and get started
(a)${d_A} = 2\,cm$and${d_B} = 4\;cm$ $\therefore \;\;{r_A} = 1\;cm$ and ${r_B} = 2\;cm$
From equation of continuity, av = constant
$\frac{{{v_A}}}{{{v_B}}} = \frac{{{a_B}}}{{{a_A}}} = \frac{{\pi {{({r_B})}^2}}}{{\pi {{({r_A})}^2}}} = {\left( {\frac{2}{1}} \right)^2} \Rightarrow {v_A} = 4{v_B}$
From equation of continuity, av = constant
$\frac{{{v_A}}}{{{v_B}}} = \frac{{{a_B}}}{{{a_A}}} = \frac{{\pi {{({r_B})}^2}}}{{\pi {{({r_A})}^2}}} = {\left( {\frac{2}{1}} \right)^2} \Rightarrow {v_A} = 4{v_B}$
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1Two cyllinders of same cross-section and length $L$ but made of two material of densities $d_1$ and $d_2$ are cemented together to form a cylinder of length $2L$. The combination floats in a liquid of density $d$ with $a$ length $L/2$ above the surface of the liquid. If $d_1 > d_2$ then:View Solution
- 2The velocity of a small ball of mass ' $m$ ' and density $d _{1}$, when dropped in a container filled with glycerine, becomes constant after some time. If the density of glycerine is $d _{2}$, then the viscous force acting on the ball, will beView Solution
- 3The reading of a spring balance when a block is suspended from it in air is $60 \,N$. This reading is changed to $40 \,N$ when the block is submerged in water. The specific gravity of the block must be therefore ............View Solution
- 4A cylindrical tank of height $1$ $m$ and cross section area $A$ $=$ $4000$ $cm^2$ is initially empty when it is kept under a tap of cross sectional area $1$ $cm^2$. Water starts flowing from the tap at $t$ $=$ $0$, with a speed $= $ $2$ $m/s$. There is a small hole in the base of the tank of cross-sectional area $0.5$ $cm^2$. The variation of height of water in tank (in meters) with time $t$ is best depicted byView Solution
- 5A plane is in level flight at constant speed and each of its two wings has an area of $40 \mathrm{~m}^2$. If the speed of the air is $180 \mathrm{~km} / \mathrm{h}$ over the lower wing surface and $252 \mathrm{~km} / \mathrm{h}$ over the upper wing surface, the mass of the plane is______ $\mathrm{kg}$. (Take air density to be $1 \mathrm{~kg} \mathrm{~m}^{-3}$ and $\mathrm{g}=10 \mathrm{~ms}^{-2}$ )View Solution
- 6Air streams horizontally past an air plane. The speed over the top surface is $60 \,m / s$ and that under the bottom surface is $45 \,m / s$. The density of air is $1.293 \,kg / m ^3$, then the difference in pressure is ....... $N / m ^2$View Solution
- 7Water from a pipe is coming at a rate of $100\, litres$ per minute. If the radius of the pipe is $5\, cm$, the Reynolds number for the flow is of the order of : (density of water $= 1000\, kg/m^3$, coefficient of viscosity of water $= 1\, mPa\, s$)View Solution
- 8A metallic block of density $5\,gm \,cm^{-3}$ and having dimensions $5 cm × 5 cm × 5 cm$ is weighed in water. Its apparent weight will beView Solution
- 9A tiny spherical oil drop carrying a net charge $q$ is balanced in still air with a vertical uniform electric field of strength $\frac{81 \pi}{7} \times 10^5 \mathrm{Vm}^{-1}$. When the field is switched off, the drop is observed to fall with terminal velocity $2 \times 10^{-3} \mathrm{~ms}^{-1}$. Given $\mathrm{g}=9.8 \mathrm{~ms}^{-2}$, viscosity of the air $=1.8 \times 10^{-5} \mathrm{Ns} \mathrm{m}^{-2}$ and the density of oil $=$ $900 \mathrm{~kg} \mathrm{~m}^{-3}$, the magnitude of $\mathrm{q}$ isView Solution
- 10Consider a water jar of radius $R$ that has water filled up to height $H$ and is kept on a stand of height $h$ (see figure) . Through a hole of radius $r$ $(r << R)$ at its bottom, the water leaks out and the stream of water coming down towards the ground has a shape like a funnel as shown in the figure. If the radius of the cross-section of water stream when it hits the ground is $x.$ ThenView Solution
