Question

Ques. The liquid is flowing separately through each of two pipes whose diameters are in the ratio of 2:1, if the ratio of the velocities of flow in the two pipes by 1:2, then the ratio of the amounts of the liquid flowing per sec through the pipe will be A. 2:1 B. 1:1 C. 4:1 D. 1:8

Answer 1

Due to high velocity in the water and density flowing through a pipe determines small amount of radius.

In fact, the surface tension of the water density should be measured by evaluating diameters 2 cm and 4 cm are connecting each other and filled at a height 4h.

Then ration of the velocities at entry and exit of liquid is 2:1.

Answer 2

The ratio of the amounts of liquid flowing per second through the pipes​ is 2 : 1

Explanation:

Given diameters of two pipes are in the ratio 2:1

If the radius of the pipes are $r_1$ and $r_2$ then

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

The area of the cross sections of pipes 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

Given that

$\frac{v_1}{v_2}=\frac{1}{2}$

We know that amount of liquid flowing per second at any point whose cross sectional area is $A$ and velocity of flow is $v$ is given by

$Q=vA$

$\implies Q_1=v_1A_1$

And

$\implies Q_2=v_2A_2$

$\frac{Q_1}{Q_2}=\frac{v_1A_1}{v_2A_2}$

$\implies \frac{Q_1}{Q_2}=\frac{v_1A_1}{v_2A_2}$

$\implies \frac{Q_1}{Q_2}=\frac{v_1}{v_2}\times\frac{\pi r_1^2}{\pi r_2^2}$

$\implies \frac{Q_1}{Q_2}=\frac{1}{2}\times(\frac{r_1}{r_2})^2$

$\implies \frac{Q_1}{Q_2}=\frac{1}{2}\times(\frac{2}{1})^2$

$\implies \frac{Q_1}{Q_2}=\frac{1}{2}\times\frac{4}{1}$

$\implies \frac{Q_1}{Q_2}=\frac{2}{1}$

$\implies Q_1:Q_2=2:1$

Hope this answer is helpful.

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