If the pressure inside and outside a balloon balance, then why does air leave when it pops? Sorry for the primitive question but when we inflate a rubber balloon and tie the end, its volume increases until its inner pressure equals atmospheric pressure.
But after that equality is obtained why does the air goes out when we pop the balloon? If there is pressure equality what causes the air flow?
 A: 
until its inner pressure equals to the atmospheric pressure

The inference that the balloon is not growing (or shrinking) because the pressure is the same is not correct.
The balloon is not growing because the effective force pushing the balloon out from inside is the same as the effective force pushing the balloon in from outside.
The force pushing outwards is indeed due to the pressure of the air inside the balloon.
But the force trying to collapse the balloon is the pressure of the air on the outside (atmospheric pressure) plus the elastics potential of the balloon trying to return to its original size and shape.
So, to counteract this additional force the pressure inside the balloon has to be higher than the air pressure outside the balloon.
A: For an inflated and tied balloon, the inner and outer pressures aren't equal. The inner pressure is higher by an amount $2 \gamma |H|$, where $\gamma$ is the inflated balloon's surface tension and $H$ is its mean curvature (which is $-1/R$ for a sphere). This is called the Young-Laplace equation.
After the balloon is untied and deflates, the pressures equalize and the surface tension becomes negligible.
A: Blowing into a balloon is harder than just blowing into the air, because it takes higher air pressure to stretch the rubber. once the balloon is tied the stretched rubber continues to squeeze the air inside, so inner air pressure stays higher than outer air pressure. Untie the balloon and the stretched rubber will squeeze the air out until it shrinks to its normal un-stretched size. Sticking the inflated balloon with a needle will create a flaw in the stretched rubber causing it to split open and release the inner air pressure very fast, pop.
A: But after that equality is obtained why does the air goes out when we penetrate the balloon? If there is pressure equality what causes the air flow?
You need to take into account that the elastic tension of the balloon skin pulls inwards. This makes the pressure in the balloon greater than its surroundings. Since there is a pressure difference the air blows out when you penetrate the skin defeating the elastic tension of the balloon skin.
Think about what happens when you blow up a balloon. At the end when the balloon gets taut it gets harder it to blow it up until it bursts. Clearly the outside pressure has not changed. The elastic tension of the balloon material has increased, like what happens when you stretch a rubber band just before it snaps.
Hope this helps.
A: I had the same doubt.
But what  i think as an answer is the pressure inside balloon is higher because not the atmosphere pressure is same as pressurein balloon, but because effective force is same.
Let me explain
Suppose a normal balloon, now you blow it  what actuallyyou are doing is creating high pressure in balloon so maintain an equilibrium balloon expands , Now pressure is decreasing but ...It will not decrease upto atmospheric pressure but a little higher ,Why??!!
Because I am neglecting something, as balloon is expanding it is gaining an elastic potential or tension  along with a little bit decrease in inner pressure ( as area increase pressure decrease ) so elastic potential is like a ...just an example u r squeezing balloon with your hand, I know it is very rough example still helpful! And yah remember the tension of balloon skin is on balloon itself not on the air inside ( this was my misconception that tension of balloon wall is applied on air inside)  .
So there are kinda more net OUTSIDE force i.e atmosphere pressure plus tension of balloon on itself , so to balance this  net force the INNER  pressure has to be high comparative to "Alone" atmospheric pressure.
Hope it helps.
Any expert here please check if I am correct or not but this is my understanding  , correct if I am wrong
A: The pressure inside is greater until it balances with external pressure. The rubber is the only thing maintaining the balance. If it were any greater inside, it would continue to expand.
It takes very little pressure to lift large weight when applied to large surface areas. Since this minor pressure it applied to the entire inner surface it takes very little pressure to maintain.
Inflation takes pressure, pressure has to balance or inflation continues. It's not a steel belted tire. How much pressure does a thin rubber membrane take? How small a flaw destroys it?
I actually untied a helium balloon and let it go many years ago and it did not deflate. AS IT floated up we all could see into the balloon through the opening as it lifted, but did not deflate at all. It continued til out of sight.
