How long will it take to fill a tank?

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To determine how long it takes to fill a tank with a volume of 180 m3 using water from a pipe, the volumetric flow rate can be calculated using the equation Q = vA. The flow velocity at position one is 12 m/s, and the cross-sectional area is 0.3318 m2, resulting in a flow rate of approximately 3.98 m3/s. Since the volumetric flow rate remains constant throughout the pipe, either position can be used for calculations. By applying the formula Q = V/t, it is determined that the tank will be filled in about 45.2 seconds. This approach effectively utilizes principles of fluid dynamics to solve the problem.
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Homework Statement



The water from a pipe flows into a tank of volume 180 m3. If the tank is initially empty, how long will it take to fill the tank?

Homework Equations



Q=vA

v1=12m/s
v2=22m/s
A2=0.180982 m2
A1=0.3318 m2

The Attempt at a Solution



This question is the third question from a 3 part problem. In the first two part they were asking me to find the velocity of position 2 of the pipe which is 22m/s, in the second part they were asking me for the diameter of position 2 in the pipe which is 48 cm and in this third part they are asking me how long does it take to fill in the tank with 180 m3.

My attempt was using volumetric flow, but which end should I use? v1a1 or v2a2 since they don't mention where is the tank located at.

any hints to where to start from?
 
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How does v1a1 compare to v2a2?
 
Hmmm can you be more specific?
 
You mentioned using the volume flow rate to find the answer, but is the volume flow rate at position one different than volume flow rate at position two?
 
ah! so it really doesn't matter which end i use because they are both going to have the same volumetric flow?
 
however, is volumteric flow correct to approach this problem?
 
Exactly! All points along a point have the same volumetric flow, therefore you can choose any point you desire.And what is the equation and units for volumetric flow?
 
Q=vA= (12 m/s)(0.3318 m2)= 3.98 m3 s-1

and the equation is Q=V/t?
 
ScienceGeek24 said:
Q=vA= (12 m/s)(0.3318 m2)= 3.98 m3 s-1

and the equation is Q=V/t?

Right! Can Q=V/t be used to answer the question?
 
  • #10
yep just got it! 45.2 secs thanks!
 
  • #11
No problem, good luck with the rest of your physics.
 
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