Question

Water is flowing through a tube of radius r with a speed v. If this tube is joined to another tube of radius r/2, what is the speed of water in the second tube?

Answer 1

Answer:

It's in the teacher's notes I Guess?

Answer 2

The speed of water in the second tube is 4v.

Explanation:

To calculate the speed of the water in the second tube use equation of continuity as

$A_1v_1=A_2v_2$

Here, A_1 and A_2 are  the cross-sectional areas of the first and second tube and v_1 and v_2 are the velocities through first and second tube respectively.

Equation of continuity can be written in radius form as,

$\pi (r_{1})^2 v_1=\pi( r_{2})^2v_2$

Substitute the given values, we get

$r^2v=(\frac{r}{2})^2v_2$

$v_2=4v$

Thus, the speed of water in the second tube is 4v.

#Learn More: equation of continuity.

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