A piston of a syringe pushes a liquid with a speed of 1 cm/sec. The radii of the syringe tube and the needle…

Q: 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 = 1cm and r = 0.5 mm respectively. The velocity of the liquid coming out of the needle is

(A) 2 cm/sec

(B) 400 cm/sec

(C) 10 cm/sec

(D) None of these

Solution: According to the equation of continuity,

Av = av’

$ \displaystyle v’ = \frac{A}{a} \times v $

where A = πR² and a = πr²

$ \displaystyle v’ = (\frac{R}{r})^2 \times v $

$ \displaystyle v’ = (\frac{1 cm}{0.05 cm})^2 \times 1 cm/s $

v’ = 400 cm/sec.