Question

Water emerges straight down from a faucet with a 1.55-cm diameter at a speed of 0.515 m/s. (Because of the construction of the faucet, there is no variation in speed across the stream.)

a.  What is the flow rate through this faucet, in cubic centimeters per second? answer Q=97.12

b. What is the diameter, in centimeters, of the stream 0.200 m below the faucet? Neglect any effects due to surface tension.

need help with part b only

Answer 1

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A.

flow rate = Q = V*A

Q = 0.515*pi*(0.0155/2)^2 = 8.96*10^-5 m^3/sec

Q = 97.1763 cm^3/sec

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B.

Using bernoulli's theoram:

P1 + 0.5*rho*v1^2 + rho*g*h = P2 + 0.5*rho*v2^2 + rho*g*h2

P1 = P2 = atmospheric pressure, So

v2^2 = v1^2 + 2*g*(h1 - h2)

v2 = sqrt (0.515^2 + 2*9.81*0.2) = 2.0468 m/sec

Using continuity equation:

A1v1 = A2v2

A2 = A1*(v1/v2)

d2^2 = d1^2*(v1/v2)

d2 = d1*sqrt (v1/v2)

d2 = 1.55*sqrt (0.515/2.0468)

d2 = 0.7775 cm

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