- #1

Beginner@Phys

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## Homework Statement

Water flowing out of a 15.0mm -diameter faucet fills a 1.50 L bottle in 5.00s. At what distance below the faucet has the water stream narrowed to 10 mm in diameter?

## Homework Equations

Bernoulli's equation: P_1+pgh+1/2pv^2=constant

Q(volume flow rate)=vA

Continuity Equation: A_1(V_1)=A_2(V_2)

## The Attempt at a Solution

Finding the intial velocity of the fluid:

A_1=pi(0.0075m^2)= 1.77*10^-4 m^2

Q=1.5L/5.00s=0.3L/s --->Q=vA (Rearrange the equation)--> v_1=Q/A_1= 0.0003m^3/s / 1.77*10^-4m^2 = 1.69765..m/s

Finding the final velocity of the fluid:

A_2=pi(0.005m^2)=7.85*10^-5 m^2

v_2=Q/A_2= 0.0003/7.85*10^-5 m^2 =3.81971...

Finding the height:

1/2pv_1^2=pgh+1/2pv_2^2

h=(1/2*p*v_1^2)-(1/2*p*v_2^2)/pg---> (p cancels out)

=(1/2*v_1^2)-(1/2*v_2^2)/g=0.597m

But, I feel that I must have done something wrong in my calculations. I don't know if my answer makes sense.