Speed of escaping gas from a cylinder

[Jahnavi]

Homework Statement

Homework Equations

The Attempt at a Solution

I don't understand which concept to apply in this question . The hint says to apply Bernoulli's equation and uses ∆P (excess pressure ) = (1/2) ρ v² . This does give right answer .

But I think this is wrong . We cannot apply Bernoulli's equation as it will not be a steady flow .

What is the relevant principle to be applied in this problem ?

 

[Orodruin]

Bernoulli’s principle. The flow is approximately steady.

 

[Jahnavi]

The flow is approximately steady.

I think the gas would come out quite rapidly . No ?

Why does the question say " small opening " and " large cylinder " ? How do these assumptions help in applying Bernoulli's principle ?

 

[Chestermiller]

I think the gas would come out quite rapidly . No ?

Why does the question say " small opening " and " large cylinder " ? How do these assumptions help in applying Bernoulli's principle ?

If the opening is small, then the gas would not come out quite rapidly. Suppose point 1 is only a few oriface diameters upstream of the oriface, and point 2 is only a few oriface diameters downstream from the oriface. That would mean that, for fluid parcels to get from point 1 to point 2 would require only a fraction of a second. This would be small compared to the time scale required for the pressure in the large tank to change significantly. Therefore, for all intents and purposes, the flow would be considered steady.

 

[Jahnavi]

Thank you very much .