Question

A piston of a syringe pushes a liquid with a speed of 1

cm/sec. The radii of the syringe tube and the needle

are R = 1 cm and r = 0.5 mm respectively. The velocity

of the liquid coming out of the needle is

Answer 1

According to equation of continuity,  

Av = av'

So,

v' = [ A / a ] v

As,  

A = π R2

v' = [ π R2 / π r2 ] v

According to given data,

R = 1 cm

r = 0.5 cm

v = 1 cm per sec

v' = 400 cm per sec

Answer 2

"From the given,

Radii of the syringe R = 1 cm

Radii of the needle = .5 cm

Let’s draw a diagram for the given data as follows.

 

By equation continuity

Av=av^1

v^1= (A/a)……………..(1)

A is considered as Radii of the syringe  

a is Radii of the needle  

Let’s substitute the give values in equation (1)

((πA^2)/(πa^2 ))= ((3.14(1)^2)/(3.14(0.5)^2 ))

=3.14/0.775=4.05 ≅ 400 cm/sec

v^1= 400 cm/sec

Therefore, the velocity of the liquid coming out of the needle is 400 cm/sec.

"