Bernoulli Equation VS. V1A1 = V2A2

[grandprix]

Hi!

I came across a problem involving a spigot. In order to find the velocity in the spigot which is located h meters in the tank, one uses the reduced V= sqrt (2gh) equation... how is this different from using V1A1 = V2A2? When would you use this equation?

For instance, say you have a tank filled with a fluid with 2 spigots located at the same depth on each side of the container but spigot A has a larger cross sectional area than spigot B. According to my notes, the velocity will be the same in each but the flow rate will be greatest at A.

why wouldn't you use V1A1=V2A2 and say that spigot B would have a larger velocity given that it has a smaller cross sectional area?? I get that they used bernoullis for this one.. but i don't understand why the other equation wouldn't work either..

 

[cjl]

Because V1A1 = V2A2 only applies when the flow rate is forced to be the same (such as two different locations with different diameters along the same pipe). Since mass is conserved, you have to have the same mass flow rate in one place in a pipe as in any other place (assuming that it's just a single pipe, with no junctions). However, if you remove the pipe completely and replace it with a different pipe, you have changed the system. There is no particular reason why the flow rate of your new system has to be the same as for your old system, which is why that equation does not apply.