- #1
ZanyCat
- 21
- 0
The problem statement:
You and a friend are in a boat in a river, the combined mass of this system is 200kg.
The boat hits a rock and a hole of 1-cm diameter forms in the bottom of the boat, which is 20cm below the water line.
1) What is the gauge pressure of the water at the depth of the hole?
2) What is the velocity of the water entering the hole?
[/B]
The attempt at a solution:
I got 1) fine, by using P=ρgh, and got 1960Pa.
For 2) I'm trying to use Bernoulli's principle (P + 1/2*ρv2 + ρgy = constant), but I don't know if this is valid seeing as we're talking about vertical (and not horizontal) velocity.
So I made the LHS of Bernoulli apply to the water surface, where P= 0 (gauge pressure is relative to atmospheric pressure), v= 0 and y= 0, so the entire LHS= 0.
Then for the RHS at the hole, P= 1960Pa, y= -0.2m, and v is unknown,
Solving this got me v=0, however. Even making y positive did nothing, it gave imaginary values.
I've even tried using P=F/A to work out the force pushing upwards at the hole, but that gets me nowhere also.
Help would be much appreciated, thanks!
You and a friend are in a boat in a river, the combined mass of this system is 200kg.
The boat hits a rock and a hole of 1-cm diameter forms in the bottom of the boat, which is 20cm below the water line.
1) What is the gauge pressure of the water at the depth of the hole?
2) What is the velocity of the water entering the hole?
[/B]
The attempt at a solution:
I got 1) fine, by using P=ρgh, and got 1960Pa.
For 2) I'm trying to use Bernoulli's principle (P + 1/2*ρv2 + ρgy = constant), but I don't know if this is valid seeing as we're talking about vertical (and not horizontal) velocity.
So I made the LHS of Bernoulli apply to the water surface, where P= 0 (gauge pressure is relative to atmospheric pressure), v= 0 and y= 0, so the entire LHS= 0.
Then for the RHS at the hole, P= 1960Pa, y= -0.2m, and v is unknown,
Solving this got me v=0, however. Even making y positive did nothing, it gave imaginary values.
I've even tried using P=F/A to work out the force pushing upwards at the hole, but that gets me nowhere also.
Help would be much appreciated, thanks!