Pressure and depth in a static fluid

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The discussion focuses on calculating the absolute pressure in a meat baster bulb based on the height of the basting sauce. The formula used is Pbaster = Pair - dgH, where Pair is the atmospheric pressure, d is the density of the sauce, g is the acceleration due to gravity, and H is the height of the sauce column. For a height of 0.17 m, the calculated pressure is approximately 98917.62 Pa, while for 0.10 m, it is around 99898.6 Pa. These calculations demonstrate how pressure changes with varying fluid heights in a static fluid system. Understanding these principles is essential for applications involving fluid dynamics in everyday tools.
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A meat baster consists of a squeeze bulb attached to a plastic tube. When the bulb is squeezed and released, with the open end of the tube under the surface of the basting sauce, the sauce rises in the tube to a distance h, as the drawing shows. Using 1.013 × 1055Pa for the atmospheric pressure and 1430 kg/m3 for the density of the sauce, find the absolute pressure PB in the bulb when the distance h is (a) 0.17 m and (b) 0.10 m.

Pbaster = Pair - dgH
Pbaster = 1.013 x 105 - 1430(9.8)(0.17) = 98917.62 Pa?

and second Pa is Pa = 99898.6 Pa?
 
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That looks good to me.
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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