Question

A faucet is turned on with a flow rate that allows the fluid to flow smoothly (i.e. laminar flow). As the fluid falls the fluid accelerates due to gravity and the diameter of the fluid stream decreases.
The initial speed, at the faucet, is 9 cm/s, and the inital diameter of the fluid stream is 0.7 cm.
What is the diameter of the fluid stream 4.3 cm below the faucet.
    (Reminder: v_f² = v_i² + 2g(Δy) (using positive direction, as direction of acceleration). So,

v_f²(at 4.3 cm below the faucet) = (9 cm/s)² + 2(980 cm/s²)(4.3 cm) = 8509 cm²/s² giving v_f = 92.244 cm/s)
  At 4.3 cm below the faucet, the diameter of the fluid stream is  .

Answer 1

For a laminar flow,

as calculated, the velocity of fow at 4.3cm from the faucet = 92.244 cm/s.

We now apply the equation of continuity, i.e. A x v = constant.

i.e.   

Therefore, at a distance of 4.3 cm below the faucet, the diameter of the fluid stream is 0.22 cm.