Question

An ideal fluid flows through a pipe made of two sectionswith diameters of 1.0 and 3.0cm, respectively. By what factor wouldyou have to multiply the velocity of the liquid flowing through the1.0 cm section to obtain the velocity of liquid flowing through the3.0cm section?

A) 6.0
B) 9.0
C) 1/3
D) 1/9

Answer 1

The factor is
`(1)/(9)` to obtain velocity pf liquid flowing through second pipe.

Option (D) is correct

Step-by-step explanation:

Given:

Diameter of first pipe
`d _(1) = 1` cm

Diameter of second pipe
`d _(2) = 3` cm

From the equation of continuity

`Av = constant`

Where
`A =` area of tube,
`v =` velocity of fluid

`A_(1) v_(1) = A_(2) v_(2)`

Where
`A = \pi r^(2) = \pi (d^(2) )/(4)`

By putting above value,

`\pi (d_(1) ^(2) )/(4) v_(1) = \pi (d_(2) ^(2) )/(4) v_(2)`

`d_(1) ^(2) v_(1) = d_(2) ^(2) v_(2)`

So velocity at the second pipe end is,

`v_(2) = (d_(1) ^(2) v_(1) )/(d_(2) ^(2) )`

By putting values of diameter,

`v_(2) = (1)/(9) v_(1)`

`(v_(2) )/(v_(1) ) = (1)/(9)`

Therefore, the factor is
`(1)/(9)` to obtain velocity pf liquid flowing through second pipe.