You partially fill an Erlenmeyer flask (wider at the bottom than the top) with cold water. You measure the pressure at the bottom with a sensitive barometer. You heat the water until it is nearly boiling and measure the pressure at the bottom again. What happens to the reading of the barometer?
A) It increases a lot. B) It increases a bit. C) It remains the same. D) It decreases a bit. E) It decreases a lot.
Solution: The water expands which decreases the density and increases the depth. But unlike the case with a cylinder, the depth increases by a greater percentage than the density goes down. So the pressure goes up a bit. Think of an extreme case where the only space for the water to expand into is a very narrow opening at the top. The depth would increase a lot with a small decrease in density. You can also analyze this with Newton's laws. The weight force remains the same, but there is additional downward force from the tapered sides of the flask as the water expands. So the force on the bottom increases and the pressure increases. The reverse would hold true with a v-shaped container. The pressure at the bottom would go down as the depth increased less than the density went down.