Elasticity Pressure

1. May 3, 2008

fredrick08

Elasticity!! Pressure!!

1. The problem statement, all variables and given/known data
A cylindrical steel pressure vessel with volume 1.3m^3 is to be tested. The vessel is filled with water, then a piston at one end pushes until the pressure inside increases by 2000kPa, then suddenly a safety plug on the top bursts.
how many litres of water come out???
B=.02x10^10Pa

2. Relevant equations

P1=P0+$$\rho$$gh
P1=-B($$\Delta$$V/V)
3. The attempt at a solution

P1=P0+2000kPa
$$\Delta$$V=-V(P1/B)=-1.3(P0+2000/.2x10^10)m^3
please i need help.... i got no idea where to go from now.... i dont have density, or a height, or youngs modulus of steel?? plz can someone help?

Last edited: May 3, 2008
2. May 3, 2008

fredrick08

am i missing any formulas???? coz im really stuck with this one

3. May 3, 2008

alphysicist

Hi fredrick08,

The container originally held 1.3 m^3 of water; once the pressure has increased (by the piston being pushed inwards) how much has that volume decreased? (This would be related to how far were they able to push in the piston, but you find it using the equation you have with $\Delta V$.) What number do you get?

Once the safety plug burst, the water goes back to its original volume (since it's open to the atmosphere), but the container is still at its new volume. So how much water escapes?

4. May 3, 2008

fredrick08

ok yes, but how can i find the distance?? coz i dont know the initial pressure??

5. May 3, 2008

fredrick08

i mean how can i find the distance the piston goes in.... coz dont i need the initial pressure, coz the pressure increases by 2000kPa??

6. May 3, 2008

alphysicist

I just mentioned the distance to show what was happening in the experiment; you cannot find the distance here.

What you want to find first is the change in the volume, using the equation you had in your first post. What number do you get for the change in volume $\Delta V$?

7. May 3, 2008

fredrick08

i dont know, coz the $$\Delta$$V=-1.3(P0+2000kPa/.2x10^10) i dont understand how i can find this because i dont know P0????

8. May 3, 2008

alphysicist

P0 is the pressure before the piston began pushing, when the water was just poured into the container. So it would be atmospheric pressure.

9. May 3, 2008

fredrick08

oh ya ok ty lol ok well $$\Delta$$V=-1.3x10^-3m^3

10. May 3, 2008

fredrick08

which is 1.3L??? is this right??

11. May 3, 2008

alphysicist

It looks like your formula is a bit off. You just need the change in pressure, which is the 2000kPa. The formula is

$$\Delta P = -B \frac{\Delta V}{V}$$

so

$$\Delta V = -V (\Delta P)/B$$

12. May 4, 2008

fredrick08

ok thankyou, this book im using is hopeless..... btw that other tank question i got rite, ty for all help = )

13. May 4, 2008