A large water tank is open to the air, and has a small hole...

A large water tank is open to the air, and has a small hole in the side, 6.35 m below water level. At what speed does water leave the hole? [ ? ] m/s Hint: The water at the top and the water leaving the tank are both exposed to the atmosphere.

Transcript

00:01 This is a bernoulli's equation problem.

00:04 So i have a big tank, right? let me draw.

00:07 Big giant water tank, right? and there's a little tiny hole right here and water spues out.

00:13 We're trying to figure out what's the velocity of that water coming out, right? so there's some level of water in here.

00:22 And bernoulli's equation is basically p1 plus, what did i say equals, p1 plus row gh1, plus one half row v1 squared equals pressure two plus row gh plus one half row v2 squared right and um let's see so okay it says the hint the water at the top and the water leaving the tank are both exposed to the atmosphere so we know that p1 equals p2 equals atmospheric pressure.

01:04 So it's just going to cancel out, right? because if i subtract from one side, it goes away.

01:08 So let me get rid of that.

01:10 All right.

01:11 Next, we know that the water up here.

01:18 So think about this giant thing of water.

01:19 If i take a swimming pool and i poke a teeny tiny hole in the side, how fast is this water level going to be moving down, right? it's going to be basically zero meters per second.

01:31 So this whole, this amount of water is tiny compared to this whole thing.

01:35 So this water level is hardly going to drop it all.

01:38 So that means i'm going to call the water here one and the water coming out too.

01:44 So my v1 is going to be zero.

01:48 So let me go cancel v1.

01:49 V1 is zero.

01:50 That means this whole thing is zero.

01:53 Okay.

01:54 And then because height is a relative.

01:58 Measurement, right? i can call this height, right? it says six point, it has a whole 6 .35 meters below the water level.

02:07 So this is 6 .35 meters from the water level down to the hole.

02:13 So i can call the height of the hole zero.

02:17 So h2 is going to be zero.

02:19 So again, let me go back into my equation, h2, that's zero...

Question

A large water tank is open to the air, and has a small hole in the side, 6.35 m below water level. At what speed does water leave the hole? [ ? ] m/s Hint: The water at the top and the water leaving the tank are both exposed to the atmosphere.

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