- #1

evelynhott

- 16

- 4

- Homework Statement
- I need to do this experiment, but I'm not sure if I did the calculation part correctly

- Relevant Equations
- Punch a hole in the cap of a one and a 1.5l cylindrical glass bottle. Fill the bottles half with water, then screw the cap back on. Turn it upside down and measure how much water comes out. Also, measure the height of the water in the bottle when the leakage stops. Using the measurement results, we determined what the air pressure was when the experiment was taken.

V

_{c}-volume of the water that came out

V

_{all}-volume of the water before leakage

S-area of the glass bottle

h-bottles high

h

_{1}-height of air column before leakage

h

_{2}-height of the air column after leakage

h

_{v,1}-height of the water column before leakage

h

_{v,2}-height of the water column after leakage

(1)p

_{a}V

_{1}=pV

_{2}

p

_{a}Sh

_{1}=pSh

_{2}

p=p

_{a}h

_{1}/h

_{2}

(2)p+ρgh

_{v,2}=p

_{a}

p

_{a}h

_{1}/h

_{2}+ρgh

_{v,2}=p

_{a}

p

_{a}(h

_{1}/h

_{2}-1)=-ρgh

_{v,2}

p

_{a}=(ρgh

_{v,2})/(1-(h

_{1}/h

_{2}))

(3)V

_{c}=(h

_{1}-h

_{2})S ->h

_{2}=(V

_{c}+Sh

_{1})/S

(4)V

_{all}=h

_{v,2}S

(5)h

_{2}=(V

_{c}-V

_{all})/(S)+h

(6)h

_{1}=h-h

_{v,1}=h-(V

_{all}/S)

I substitute:

p

_{a}=(h

_{v,2}gV

_{c}ρ-h

_{v,2}V

_{all}gρ+h

_{v,2}gSh)/V

_{c}

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