How long will it take to fill a tank?

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In summary, the question is asking how long it will take to fill a tank with a volume of 180 m3 using the equation Q=vA, where Q is the volumetric flow rate, v is the velocity, and A is the area. Both ends of the pipe have the same volumetric flow rate, so it doesn't matter which end is used. The equation for volumetric flow rate is Q=V/t, where V is the volume and t is the time. Using this equation, the time required to fill the tank is 45.2 seconds.
  • #1
ScienceGeek24
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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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  • #2
How does v1a1 compare to v2a2?
 
  • #3
Hmmm can you be more specific?
 
  • #4
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?
 
  • #5
ah! so it really doesn't matter which end i use because they are both going to have the same volumetric flow?
 
  • #6
however, is volumteric flow correct to approach this problem?
 
  • #7
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?
 
  • #8
Q=vA= (12 m/s)(0.3318 m2)= 3.98 m3 s-1

and the equation is Q=V/t?
 
  • #9
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.
 

1. How do you calculate the time it takes to fill a tank?

The time it takes to fill a tank can be calculated by dividing the volume of the tank by the flow rate of the filling source. This will give you the total time in hours or minutes.

2. Does the size of the tank affect the filling time?

Yes, the size of the tank does affect the filling time. The larger the tank, the longer it will take to fill it. This is because a larger volume of liquid needs to be filled, and the flow rate remains constant.

3. What factors can affect the filling time of a tank?

The filling time of a tank can be affected by several factors, such as the size of the tank, the flow rate of the filling source, the viscosity of the liquid being filled, and any obstructions or restrictions in the filling process.

4. Can the filling time of a tank be decreased?

Yes, the filling time of a tank can be decreased by increasing the flow rate of the filling source or by using a larger filling source. Additionally, minimizing obstructions or restrictions in the filling process can also decrease the filling time.

5. Is there a way to accurately predict the filling time of a tank?

While the filling time of a tank can be estimated using calculations, there are various factors that can impact the actual filling time. Therefore, it is difficult to accurately predict the exact filling time of a tank. Regular monitoring and adjustments may be necessary to achieve the desired filling time.

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