Fluid Dynamics: Using Bernoulli's equation and Volume Flow Rate

Beginner@Phys

1. The problem statement, all variables and given/known data
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?


2. Relevant 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)

3. 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.

Redbelly98

It looks good to me. I didn't check your calculations precisely, but the procedure is correct and I get approximately the same numbers at each step doing the calculations roughly in my head.