When to use continuity equation vs. V=IR

[laczlacylaci]

The correct answer is C.

The key used V=IR. Length is directly proportional to R and Area is inversely proportional. As area increases, R decreases, causing a higher flow rate.

My thought process was A1v2=constant. A larger area, causes slower flow rate.

When should I not use the continuity equation?

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[ThujaOccidentalis]

Flow rate = Volume / time = Area * speed = A *v, increasing either area or speed will increase flow rate. The continuity equation holds. We eliminate A or B for having smaller diameters. The longer the pipe, the more resistance, therefore we eliminate D.

Also I believe flow rate is the "fluid system equivalent" of electrical current.

 

[laczlacylaci]

Flow rate = Volume / time = Area * speed = A *v, increasing either area or speed will increase flow rate. The continuity equation holds. We eliminate A or B for having smaller diameters. The longer the pipe, the more resistance, therefore we eliminate D.

Also I believe flow rate is the "fluid system equivalent" of electrical current.

Doesn't the continuity equation say: as you increase A, velocity decreases?

 

[ThujaOccidentalis]

Doesn't the continuity equation say: as you increase A, velocity decreases?

That's true if you're talking about a continuous pipe (i.e. Pipe X with a smaller area is connected to Pipe Y with a greater area) then yeah, increasing A will decrease v, so you will see liquid flowing faster in Pipe X than Pipe Y. But the VOLUME PER TIME = flow rate will be the same at Pipe X and Pipe Y

But in the question's case, we're talking about separate "situations" (i.e. separate needles). Which needle will deliver most liquid in a given time, which will deliver the most volume in time? The needle with 1.) the largest volume and 2.) the least resistance. The continuity equation applies in a sense that A*V=constant, but the question is asking which of the needles will yield the greatest constant. The constant is the same value for within a given pipe system (within the length of a needle), but can vary between pipe systems (between different needles).

 

[el_duderino]

View attachment 207987
The correct answer is C.

The key used V=IR. Length is directly proportional to R and Area is inversely proportional. As area increases, R decreases, causing a higher flow rate.

My thought process was A1v2=constant. A larger area, causes slower flow rate.

When should I not use the continuity equation?

Larger area means less velocity, yes. But besides the other answers, think about it for a second. A needle that's both shorter and wider will have a higher flow rate intuitively. Don't overthink things.