The tubular system in an aquarium
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The tubular system in an aquarium
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[post_content] => Practice Passage (Question 1-5)
*This passage is the property of Khan Academy and has been reformatted into an AAMC-style interface in their entirety by MedLife Mastery. MedLife Mastery does not endorse and is not an affiliate of Khan Academy.
Administration at an aquarium are interested in improving the water filtration process for a series of tanks. In order to accomplish this, engineers arrange for unclean water to be collected in a large reservoir with a high-efficiency filter, as opposed to the multiple smaller filters that the aquarium currently uses. To accomplish this, a number of tubes are installed to collect water from individual tanks and transport it to the main reservoir.
One of these tubes is shown below (Figure 1). As depicted, water, an incompressible fluid, is flowing without turbulence through a tube that has different diameter sections seen in the diagram. The absolute pressure at point 1 is 220,000 Pascals and the speed of the fluid at point 1 is 8.0m/s. The radius of the tube at point 1 is 0.50m. The radius of the tube at point 3 is 0.25m. The radius of the tube at point 4 is 1.0m.
Figure 1. A singular tube that leads to the new filtration reservoir.
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[question] => What would be the correct ranking of the speeds of the fluids at points 1,2,3,4?
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[description] => Reason for the Correct Answer:
Since the fluid is incompressible, the volume flow rate must be constant.
Since the volume flow rate is constant, Area x speed must be constant along the pipe.
The fluid will move fastest where the area is smallest, and therefore the radius is smallest.
Since the ranking of radii is 3<2<1<4 the ranking of speeds are the opposite 3>2>1>4 .
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[each_answer] => A. v2 > v3 > v1 > v4
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[each_answer] => B. v3 > v2 > v1 > v4
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[each_answer] => C. v1 > v2 > v3 > v4
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[each_answer] => D. v4 > v1 > v2 > v3
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[question] => How does the pressure at point 2 compare to the pressure at point 4?
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[answer] => 1
[description] => Reason for the Correct Answer:
The fluid is moving faster at point 2 compared to point 4.
Point 2 is at the same height as point 4, so height does not factor into this.
Bernoulli’s principle says that if height is not a factor the pressure decreases if speed increases.
Since the speed is greater at point 2 compared to pint 4, the pressure will be smaller at point 2 compared to point 4.
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[each_answer] => A. the pressure at point 2 is smaller since the water is moving faster there
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[each_answer] => B. the pressure at point 2 is greater since the water is moving faster there
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[each_answer] => C. the pressure at point 2 is the same as the pressure at point 4 since the fluid is incompressible
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[each_answer] => D. the pressure at point 2 is greater since the water is more compressed together
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[question] => What will be the speed of the fluid at point 3 and point 4?
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[answer] => 1
[description] => Reason for the Correct Answer:
Since the fluid is incompressible, the volume flow rate must be constant.
Since the volume flow rate is constant, Area x speed must be constant along the pipe. The area of the tube is given by πr2.
The volume flow rate is given by (speed) x (πr2).
Since the area at point 3 is four times smaller than the area at point 1, the speed must be four times larger, and since the area at point 4 is four times larger than the area at point 1, the speed must be four times smaller.
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[each_answer] => A. v3= 32m/s, v4=2m/s
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[each_answer] => B. v3= 16m/s, v4=4m/s
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[each_answer] => C. v3= 4m/s, v4=16m/s
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[each_answer] => D. v3= 2m/s, v4=32m/s
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[question] => What would be a possible pressure of the fluid at point 3 based on the information given?
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[answer] => 4
[description] => Reason for the Correct Answer:
The speed of the fluid is larger at point 3 compared to point 1.
Bernoulli’s principle say that if height is not a factor, as speed increases the pressure decreases.
The only option that is less than the pressure at point 1 is 160,000Pa.
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[each_answer] => A. 280,000 Pa
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[each_answer] => B. 250,000 Pa
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[each_answer] => C. 220,000 Pa
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[each_answer] => D. 160,000 Pa
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[question] => What is the gauge pressure at point 1?
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[description] => Reason for the Correct Answer:
Atmospheric pressure is 101,000 Pa.
The absolute pressure is Pabs = Pgauge + Patm.
Solving for Pgauge = Pabs – Patm = 220,000 Pa – 101,000 Pa = 119,000 Pa
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[each_answer] => A. 119,000 Pa
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[each_answer] => B. 219,000 Pa
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[each_answer] => C. 220,000 Pa
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[each_answer] => D. 101,000 Pa
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