An incompressible fluid flows steadily throug | vedclass

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

Question

(D) According to the equation of continuity for an incompressible fluid,the volume flow rate remains constant at all points in the pipe.Therefore,the

Vedclass · Accepted Answer

$4v$

Vedclass · Answer

(D) According to the equation of continuity for an incompressible fluid,the volume flow rate remains constant at all points in the pipe.Therefore,the volume of fluid entering per second at point $A$ must equal the volume of fluid exiting per second at point $B$.Let $v_A$ be the velocity at point $A$ and $v_B$ be the velocity at point $B$.The area of cross-section at $A$ is $A_A = \pi(2r)^2 = 4\pi r^2$.The area of cross-section at $B$ is $A_B = \pi(r)^2 = \pi r^2$.Using the equation of continuity: $A_A v_A = A_B v_B$.Substituting the given values: $(4\pi r^2) v = (\pi r^2) v_B$.Solving for $v_B$: $v_B = \frac{4\pi r^2 v}{\pi r^2} = 4v$.

An incompressible fluid flows steadily through a cylindrical pipe which has radius $2r$ at point $A$ and radius $r$ at point $B$ further along the flow direction. If the velocity at point $A$ is $v$,what is its velocity at point $B$?

Similar Questions

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:

Select the $WRONG$ statement from the following. In a streamline flow,

In a streamline flow,

When water falls from a tap,what happens to the cross-sectional area of the water stream as it moves downwards?

Vedclass Test Series

Exam Paper Generator

Online Exam Module