A liquid flows steadily through a cylindrical | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

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

Vedclass · Accepted Answer

$v$

Vedclass · Answer

(B) According to the equation of continuity for an incompressible fluid,the product of the cross-sectional area and the velocity of the fluid remains constant at all points along the flow: $A_A v_A = A_B v_B$ Given that the pipe is cylindrical,the cross-sectional area $A = \pi r^2$. At point $A$,the radius is $2R$,so $A_A = \pi (2R)^2 = 4\pi R^2$. At point $B$,the radius is $R$,so $A_B = \pi R^2$. The velocity at point $B$ is given as $v_B = 4v$. Substituting these values into the continuity equation: $4\pi R^2 	imes v_A = \pi R^2 	imes 4v$ Dividing both sides by $4\pi R^2$: $v_A = v$

$A$ 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 $A$?

Similar Questions

Select the correct statement regarding streamline flow.

Water falls from a tap,down the streamline.

The blades of a windmill sweep out a circle of area $A$. If the wind flows at a velocity $v$ perpendicular to the circle,then the mass of the air of density $\rho$ passing through it in time $t$ is

Water coming out of the mouth of a tap and falling vertically in streamline flow forms a tapering column,i.e.,the area of cross-section of the liquid column decreases as it moves down. Which of the following is the most accurate explanation for this?

$A$ liquid flows in the tube from left to right as shown in the figure. $A_1$ and $A_2$ are the cross-sections of the portions of the tube as shown. The ratio of speed $\frac{v_1}{v_2}$ will be ..........

Vedclass Test Series

Exam Paper Generator

Online Exam Module