A container, closed on the right side but open to the atmosphere on the left, is

Question

A container, closed on the right side but open to the

atmosphere on the left, is almost completely filled with

water as shown at right.

[2 points] (a) Rank the pressure at points A, B and C.

[ ] C > B > A [ ] B > A > C [ ] B > A = C

[ ] A = B > C [ ] C > A = B

[ ] Some other order

[2 points] (b) What is the pressure at point D? Choose ALL

the correct statements.

[ ] Cannot be determined [ ] PA

A container, closed on the right side but open to the atmosphere on the left, is almost completely filled with water as shown at right. Rank the pressure at points A, B and C. [ ] C > B > A [ ] B > A > C [ ] B > A = C [ ] A = B > C [ ] C > A = B [ ] Some other order What is the pressure at point D? Choose ALL the correct statements. [ ] Cannot be determined [ ] PA - (?)(g)(0.2m) [ ] PA + (?)(g)(0.2m) [ ] Atmospheric pressure [ ] None of the above In the above, PA is the pressure at point A and ? is the density of the fluid. What is the pressure at point E? Choose ALL the correct statements. [ ] Cannot be determined [ ] PC - (?)(g)(0.2m) [ ] PC + (?)(g)(0.2m) [ ] Atmospheric pressure [ ] None of the above In the above, PC is the pressure at point C and ? is the density of the fluid. If an opening is made in the container at point X, calculate the speed of the fluid coming out of the opening. The density of the fluid is 1000 kg/m3 and gravitational acceleration is 10 m/s2 If, instead, an opening is made in the container at point Y, what is the speed of the fluid coming out of the opening?

Explanation / Answer

a) Pressure at same elevation is the same. Pressure at higher elevation is lower, so [ ] A = B > C

b) point D is at same height as surface of water exposed to room pressure, so [ ] Atmospheric pressure

c) Two answers [ ] cannot be determined numerically and [ ] Pressure at C - density(g)(0.2m)

pressure here is usually zero. We don't know if there is any air above the water, or if it is a vacuum. Some water would vaporize creating some small pressure, that would gradually increase (you can get water to boil if there is a vacuum above it)

d) speed of fluid is only being pushed by pressure of 0.2 m of water on top

potential energy is converted to kinetic energy

SQRT(2gh) = SQRT(2*9.8 m/s^2*0.2m) = 2 m/s Torricelli introduced a factor of 0.6 since stream has smaller cross section than opening. This would give 1.2 m/s

e) we would have to say zero, since it is at the level of the surface connected to the atmosphere, once some bubbles started coming in, and there was turbulence, water would run out.

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