a group of students are developing a plan to deliver water from a lake to a down

Question

a group of students are developing a plan to deliver water from a lake to a downhill village. The students plan to use siphon for this purpose so a pump is not needed. It is known that the height that highest point of the siphon tube is 11m above the surface of the lake.
Is this plan feasible? What is the maximum height that the siphon can overcome? Assume the village is located in Puerto Rico and the water inside the tube can reach as high as 50 °C in the summer. The velocity of water flowing in the siphon tube can be neglected.

Part 2). A 0.4 m3 rigid vessel initially contains a saturated liquid-vapor mixture of water at 100 C. The water is heated until it reaches its critical point.
(a) Indicate the process on a P-v diagram, (b) What is the mass of liquid water (kg) at the initial state? (c) Determine the volume occupied by vapor (m3) at the initial state. (d) Calculate the change in internal energy (MJ) during the process. (e) Calculate the amount of heat transfer (MJ) associated with this process.

Explanation / Answer

Part 1) siphons work because of atmospheric pressure and vaccuums. At 1 atm, air pressure can support 760 mm of Hg. Hg has a density of 13.546 g/cc, which is 13.546 times the density of water at 5C. .760m(13.546) = 10.29 m, so 11m is too high. At 50C the density of water is lower, which would increase the maximum height possible, but the vapor pressure is also higher, which would decrease the maximum height. The vapor pressure of water at 50C is about 110 mm Hg (hopefully you have a better chart to find exactly what it is) So, max height times two factors, the first for the vapor pressure of the hot water, and the second for the decreased density. 10.29m [(760-110)/760][1.0/.988] = 8.9 m is the new maximum height. Part 2) We need the starting pressure. I assume it is one. I am out of time. Sorry.

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