- #1

northmop

- 11

- 3

I'm trying to do the math for a backyard thermodynamic pump experiment, and getting stuck. Suppose an empty 3.79 liter container was airlocked by a vertical 25 cm long empty tube whose end sits at the top of an unlimited supply of water in a basin. The tube protrudes through the container such that there is a length of tube above the base of the container so that any water entering the container cannot escape back down the tube and into the basin. If the temperature of the external environment, water, and gas are all constant (295°K), what volume of water (density of 1000 kg/m3) would enter the container if the pressure differential between of the external environment (100 kPa) and the inside the container (96 kPa) is 4 kPa?

I know that some of the vacuum pressure will be consumed to maintain the 25 cm height of the water column in the tube. This means that 4 kPa - (9.80665 m/s2 * 1000 kg/m3 * 0.25 m) = 1.54834 kPa is "available" to vacuum up the water from the basin into the container. What I'm getting stuck with is how to calculate the hypothetical volume of water that will get sucked up and stored in the container: my head is mush after thinking about this too long. Would you please be so kind as to share the formulas used to figure this out?

I know that some of the vacuum pressure will be consumed to maintain the 25 cm height of the water column in the tube. This means that 4 kPa - (9.80665 m/s2 * 1000 kg/m3 * 0.25 m) = 1.54834 kPa is "available" to vacuum up the water from the basin into the container. What I'm getting stuck with is how to calculate the hypothetical volume of water that will get sucked up and stored in the container: my head is mush after thinking about this too long. Would you please be so kind as to share the formulas used to figure this out?

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