**Pressure in a Fluid:**A cubical box, 8.00 cm on each side, is immersed in a fluid. The gauge pressure at the top surface of the box is 544 Pa and the gauge pressure on the bottom surface is 1,166 Pa. What is the density of the fluid?**Explanation for Diagrams (if any):**There are no graphs or diagrams associated with the provided text.**Solution:**To determine the density of the fluid, let's use the difference in pressure between the top and bottom of the box. We can use the hydrostatic pressure formula:\[ P = \rho g h \]where:- \( P \) is the pressure difference,- \( \rho \) is the density of the fluid,- \( g \) is the acceleration due to gravity (approximately \( 9.81 \, \text{m/s}^2 \)),- \( h \) is the height of the box.First, find the pressure difference (\( \Delta P \)):\[ \Delta P = 1166 \, \text{Pa} - 544 \, \text{Pa} = 622 \, \text{Pa} \]Convert the height of the box from cm to meters:\[ h = 8.00 \, \text{cm} = 0.0800 \, \text{m} \]Next, rearrange the hydrostatic pressure formula to solve for the density (\( \rho \)) of the fluid:\[ \rho = \frac{\Delta P}{g h} \]Substitute the known values:\[ \rho = \frac{622 \, \text{Pa}}{9.81 \, \text{m/s}^2 \times 0.0800 \, \text{m}} \]\[ \rho = \frac{622}{0.7848} \]\[ \rho \approx 792.6 \, \text{kg/m}^3 \]Therefore, the density of the fluid is approximately \( 792.6 \, \text{kg/m}^3 \).

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Description: **Pressure in a Fluid:**A cubical box, 8.00 cm on each side, is immersed in a fluid. The gauge pressure at the top surface of the box is 544 Pa and the gauge pressure on the bottom surface is 1,166 Pa. What is the density of the fluid?**Explanation

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Pressure in a fluid: A cubical box, 8.00 cm on each side, is immersed in a fluid. The gauge pressure at the top surface of the box is 544 Pa and the gauge pressure on the bottom surface is 1,166 Pa. What is the density of the fluid?

Pressure in a fluid: A cubical box, 8.00 cm on each side, is immersed in a fluid. The gauge pressure at the top surface of the box is 544 Pa and the gauge pressure on the bottom surface is 1,166 Pa. What is the density of the fluid?

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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