QQuestionPhysics
QuestionPhysics
If the density of water is 0.0361 lb/in^3, and the column of water is 27.7”.
a) what is the pressure in psi?
b) If the fluid is mercury would the pressure increase or decrease? Explain your answer.
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Answer
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Step 1: Calculate the pressure in psi (pounds per square inch) using the formula for pressure, where pressure (P) is equal to the density (\rho) times the acceleration due to gravity (g) times the height (h) of the fluid column.
h = 27.7 \, in \times 0.083333 \, \frac{ft}{in} = 2.305 \, ft
Convert the given density from pounds per cubic inch to slugs per cubic inch for consistency with the acceleration due to gravity in slugs per square inch second (sis). Use the conversion factor of 1 lb/in³ = 0.01601846 slugs/in³. Use the standard acceleration due to gravity, which is 32.174 sis². Convert the height from inches to feet to use the standard value for acceleration due to gravity in feet per second squared (ft/s²). Use the conversion factor of 1 in = 0.083333 ft.
Step 2: Substitute the known values into the formula and calculate the pressure.
P = \left(5.789 \times 10^{-4} \, \frac{slugs}{in^3}\right) \times \left(32.174 \, \frac{sis^2}{in}\right) \times \left(2.305 \, ft \times \frac{12 \, in}{ft}\right)
Final Answer
Step 4: Explain the effect of mercury on the pressure. If the fluid is mercury, the pressure would increase. Mercury has a much higher density than water, approximately 13.53 times greater. Therefore, with a higher density and the same height, the pressure exerted by mercury would be significantly higher than that of water.
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