EK Bernoulli Equation and Equation of Continuity

[ImDiene0412]

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The question states:

A container is filled with an ideal fluid. Spigot a and b are at the same height. Spigot b has a larger cross-sectional area than spigot a. According to the Bernoulli Equation and the Equation of Continuity, how will the velocity and volume flow rate compare at the spigots a and b?

A. The velocity and flow rate will be greatest at a.
B. The velocity will be greatest at a, but the flow rate will be the same.
C. The velocity and flow rate will be the same.
D. The velocity will be the same, but the flow rate will be greatest at b.

The answer is D and their explanation is:

According to Bernoulli's Equation, the velocities must be v=sqrt(2gh). But if the velocities are the same, the flow rate must be greater at the larger spigot. Doesn't this violate the rule that volume flow rate is the same at all points in a conduit of ideal fluid? No. The volume flow rate rule says that volume of fluid flowing in must be equal to volume flowing out. For instance, imagine putting a vertical divider along the length of spigot b. You would not expect to change the velocity just because you divided the flow.

Could someone please elaborate on why we assume the two velocities are equal? Because both spigots are on the same container, pressure cancels out in the equation and velocity is only dependent upon height?

 

[5words]

Have you checked their erreta? I am getting B for some reason, and there is no reason why the flow rate ought to be different unless some thing else isbsuplying the system.. BTW is there a graph or something?

 

[aldol16]

I also believe it should be B. Volume flow rate shouldn't change when it's an incompressible liquid flowing through a rigid tube. In other words, what goes in must come out - you can't just create mass.

 

[ImDiene0412]

Have you checked their erreta? I am getting B for some reason, and there is no reason why the flow rate ought to be different unless some thing else isbsuplying the system.. BTW is there a graph or something?

I've had a hard time finding their erreta unfortunately. I got B too and thought the same thing you and aldol16 thought...wouldn't you think of it the same way you would think of an artery branching? BR says A1V1= A2V2 + A3V3 + A4V4 ... etc.

No graph, just a diagram of a tank with two spigots at the same height, one with a larger cross sectional area.

 

[ImDiene0412]

I also believe it should be B. Volume flow rate shouldn't change when it's an incompressible liquid flowing through a rigid tube. In other words, what goes in must come out - you can't just create mass.

I thought the same thing, but wasn't sure if I was overlooking something

 

[desperadoflakes]

Sorry to revive an old thread - I want to understand too. The word 'spigot' makes me think that the flow of water is directed downward. If this were true would the area of the spigot affect the velocity? Wouldn't gravity make it so that water in both spigots falls at the same speed, but because there is more water coming out of spigot B than the flow rate would be larger?