Question

Water is flowing through a pipe of constant cross-section. At some point the pipe becomes narrow and the cross-section is halved. The speed of water is

Answer 1

Answer:

Given, That area of cross section at initial point is more than the final point,

From the equation of continuity, we can say that velocity at the final point is more than initial point.

Bernoulli theorem states that P+dgh+

2

1

dv

2

=constant

At final point, the velocity is more, so the pressure will be less.

Therefore the pressure decreases,

So, the correct answer is decreases.

Answer 2

Given:

The cross section of the pipe is halved

To find:

The new speed.

Solution:

We have been given that water is flowing through pipe of cross section $A_{1}$ (say) with some initial velocity $V_{1}$. After one point, the area of the pipe becomes narrow lets say the new area is $A_{2}$ and the water here, moves with a speed of $V_{2}$.

According to the question, $A_{2}=\frac{A_{1} }{2}$

We know, the volume of water entering the pipe is equal to the volume of water leaving the pipe.

According to the law of continuity,

$A_{1} V_{1} =A_{2} V_{2}$

Substituting the known values in the equation, we get

$A_{1} V_{1} =\frac{A_{1} }{2} V_{2}$

$V_{2} =2V_{1}$

Final answer:

Hence, the speed of water in the pipe increases by a factor of 2.