An incompressible fluid flows steadily through a cylindrical pipe which has radius $2r$ at point $A $ and radius $r $ at $B $ further along the flow direction. If the velocity at point $A$ is $v, $ its velocity at point $B$ is
A$2v$
B$v$
C$v/2$
D$4v$
Medium
Download our app for free and get started
D$4v$
d (d) From equation of continuity volume of water entering per second at $\mathrm{A}=$ volume of water exiting per second from $B$
Let $v$ be the velocity at point $B$, then
$\pi(2 R)^{2} v=\pi\left(R^{2}\right) v^{\prime}$
$v^{\prime}=4 v$
Download our app
and 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.*
Two large, identical water tanks, $1$ and $2$ , kept on the top of a building of height $H$, are filled with water up to height $h$ in each tank. Both the tanks contain an identical hole of small radius on their sides, close to their bottom. A pipe of the same internal radius as that of the hole is connected to tank $2$ , and the pipe ends at the ground level. When the water flows the tanks $1$ and $2$ through the holes, the times taken to empty the tanks are $t_1$ and $t_2$, respectively. If $H=\left(\frac{16}{9}\right) h$, then the ratio $t_1 / t_2$ is. . . . .
A tall tank filled with water has an irregular shape as shown. The wall $C D$ makes an angle of $45^{\circ}$ with the horizontal, the wall $A B$ is normal to the base $B C$. The lengths $A B$ and $C D$ 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 $A B$, base $B C$ and the wall $C D$ respectively. Density of water is $\rho$ and $g$ is acceleration due to gravity. Then, approximately
Consider two solid spheres $\mathrm{P}$ and $\mathrm{Q}$ each of density $8 \mathrm{gm} \mathrm{cm}^{-3}$ and diameters $1 \mathrm{~cm}$ and $0.5 \mathrm{~cm}$, respectively. Sphere $\mathrm{P}$ is dropped into a liquid of density $0.8 \mathrm{gm} \mathrm{cm}^{-3}$ and viscosity $\eta=3$ poiseulles. Sphere $Q$ is dropped into a liquid of density $1.6 \mathrm{gm} \mathrm{cm}^{-3}$ and viscosity $\eta=2$ poiseulles. The ratio of the terminal velocities of $\mathrm{P}$ and $\mathrm{Q}$ is
A wide vessel with a small hole at the bottom is filled with two liquids. The density and heightof one liquid are $\rho_1$ and $h_1$ and that of the otherare $\rho_2$ and $h_2 \ (\rho_1 >\rho_2)$. The velocity of liquid coming out of the hole is :
Consider the configuration of a stationary water tank of cross-section area $A_{0}$ and a small bucket as shown in figure below; the speed $v$ is .......... $m/s$ of the bucket, so that the water leaking out of a hole of cross-section area $A$ (as shown) from the water tank does not fall outside the bucket? (Take, $h=5 \,m , H=5 \,m , g=10 \,m / s ^{2}, A=5 \,cm ^{2}$ and $\left.A_{0}=500 \,cm ^{2}\right)$.
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 the ejection of the liquid through the holes is
The rate of steady volume flow of water through a capillary tube of length $ 'l' $ and radius $ 'r' $ under a pressure difference of $P$ is $V$. This tube is connected with another tube of the same length but half the radius in series. Then the rate of steady volume flow through them is (The pressure difference across the combination is $ P$)
An object is fitted in a hole at base of a container as shown in figure, the force due to liquid on object is (Assume no leakage of water, volume of object inside container is $V$ and density of liquid is $\rho $ )