Question

Water flowing out of a 14.0 mm -diameter faucet fills a 2.00 L bottle in 14.0 s .

At what distance below the faucet has the water stream narrowed to 10 mm diameter?

Answer 1

d1 = 14mm => r1 = 7mm; V = 2L = 2 x 10^-3 ; t = 14 s ; d2 = 10 mm => r2 = 5 mm

We know that, volume flow rate is

Q = V/t = 2 x 10^-3/10 = 2 x 10-4 m^3/s

Also, Q = vA

v = Q/A = 2 x 10^-4/3.14 (0.007)^2 = 1.3 m/s

from eqn of continuity

A1v1 = A2v2

v2 = v1 (A1/A2)

v2 = 1.3 (D1/D2)^2 = 1.3 (14/100) = 2.55 m/s

Now from Bernaulli's eqn

P1 + 1/2 rho v1^2 + h1 rho g = P2 + 1/2 rho v2^2 + h2 rho g

since P1 = P2 and rho is same same both sides and h1 - h2 = d

d = (v2^2 - v1^2)/2g

d = (2.55^2 - 1.3^2)/2 x 9.8 = 0.246 m = 24.6 cm

Hence, d = 0.246 m = 24.6 cm = 246 mm