Water is flowing through a tube of non-uniform cross-section. If the radii of the tube at the entrance and exit are in the ratio 3:2 , then the ratio of the velocity of liquid entering and leaving the tube is

Question

Water is flowing through a tube of non-uniform cross-section. If the radii of the tube at the entrance and exit are in the ratio 3:2 , then the ratio of the velocity of liquid entering and leaving the tube is (A) 1:1 (B) 4:9 (C) 9:4 (D) 8:27

Tardigrade Admin · Accepted Answer

Using equation of continuity A1v1=A2v2 ⇒ π r12v1=π r22v2 ⇒ (v1/v2)=(r22/r12)=((2/3))2=(4/9)

Q. Water is flowing through a tube of non-uniform cross-section. If the radii of the tube at the entrance and exit are in the ratio $3 : 2$ , then the ratio of the velocity of liquid entering and leaving the tube is

$1 : 1$

$4 : 9$

$9 : 4$

$8 : 27$

Using equation of continuity
$A_{1} v_{1} = A_{2} v_{2} \Rightarrow π r_{1}^{2} v_{1} = π r_{2}^{2} v_{2}$
$\Rightarrow \frac{v _{1}}{v _{2}} = \frac{r _{2}^{2}}{r _{1}^{2}} = (\frac{2}{3})^{2} = \frac{4}{9}$

Q. Water is flowing through a tube of non-uniform cross-section. If the radii of the tube at the entrance and exit are in the ratio 3:2 , then the ratio of the velocity of liquid entering and leaving the tube is

1:1

4:9

9:4

8:27