(C) According to the equation of continuity for an incompressible fluid,the product of the cross-sectional area and the velocity of flow remains const

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(C) According to the equation of continuity for an incompressible fluid,the product of the cross-sectional area and the velocity of flow remains constant: $A_1 V_1 = A_2 V_2$.Here,$d_1 = 3\, cm$ (radius $r_1 = 1.5\, cm$) and $d_2 = 6\, cm$ (radius $r_2 = 3.0\, cm$).The velocity in the narrower pipe is $V_1 = 4\, m/s$.Substituting the values into the equation: $\pi (r_1)^2 V_1 = \pi (r_2)^2 V_2$.$\pi (1.5)^2 \times 4 = \pi (3.0)^2 \times V_2$.$2.25 \times 4 = 9 \times V_2$.$9 = 9 \times V_2$.Therefore,$V_2 = 1\, m/s$.

Class 11 Physics Fluid Mechanics and Surface Tension Types of Flow, Equation of Continuity and Flow Rate

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Water is flowing through two horizontal pipes of different diameters which are connected together. The diameters of the two pipes are $3\, cm$ and $6\, cm$ respectively. If the speed of water in the narrower pipe is $4\, m/s$ and the pressure is $2.0 \times 10^4\, Pa$,then the speed of water in the wider pipe is ........ $m/s$.

A
$4$
B
$2$
C
$1$
D
$16$

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Fluid Mechanics and Surface Tension

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Types of Flow, Equation of Continuity and Flow Rate

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$A$ pipe having an internal diameter $D$ is connected to another pipe of the same size. Water flows into the second pipe through $n$ holes, each of diameter $d$. If the water in the first pipe has speed $v$, what is the speed of water leaving the second pipe?

DifficultTS EAMCET 2012

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Water is flowing through a tube of non-uniform cross-section. The ratio of the radius at the entry and exit end of the pipe is $3:2$. Then the ratio of velocities at the entry and exit of the liquid is:

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$A$ liquid flows steadily through a cylindrical pipe having a radius $2R$ at point $A$ and radius $R$ at point $B$ farther along the flow direction. If the velocity at point $B$ is $4v$, what will be the velocity at point $A$?

EasyTS EAMCET 2022

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