Question

the ratio of diameters at two points of a pipe are 2:1,then what will be ratio of velocity of liquid flow through there points​

Answer 1

Answer:

1:4 is the ratio

Explanation:

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Answer 2

The ratio of velocity of liquid flow through the given two points​ is 1 : 4

Explanation:

Given diameters of two points of a pipe are in the ratio 2:1

If the radius of two points of the pipe are $r_1$ and $r_2$ then

$\frac{r_1}{r_2}=\frac{2}{1}$

The area of the cross sections of these two points will be $A_1=\pi r_1^2$ and $A_2=\pi r_2^2$ respectively

If the velocities of these two points are $v_1$ and $v_2$ respectively

Then

From continuity equation we know that

$v_1A_1=v_2A_2$

$\implies \frac{v_1}{v_2}=\frac{A_2}{A_1}$

$\implies \frac{v_1}{v_2}=\frac{\pi r_2^2}{\pi r_1^2}$

$\implies \frac{v_1}{v_2}=\frac{r_2^2}{r_1^2}$

$\implies \frac{v_1}{v_2}=(\frac{r_2}{r_1})^2$

$\implies \frac{v_1}{v_2}=(\frac{1}{2})^2$

$\implies \frac{v_1}{v_2}=\frac{1}{4}$

$\implies v_1:v_2=1:4$

Hope this answer is helpful.

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