|Jan17-09, 12:40 PM||#1|
Fluid Dynamics: Using Bernoulli's equation and Volume Flow Rate
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:
v_2=Q/A_2= 0.0003/7.85*10^-5 m^2 =3.81971...
Finding the height:
h=(1/2*p*v_1^2)-(1/2*p*v_2^2)/pg---> (p cancels out)
But, I feel that I must have done something wrong in my calculations. I don't know if my answer makes sense.
|bernoulli's equation, continuity equation, volume flow rate|
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